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Digital image processing

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</style><div role="note" class="hatnote navigation-not-searchable">This article is about mathematical processing of digital images. For artistic processing of images, see <a href="Image_editing" title="Image editing">Image editing</a>. For compression algorithms, see <a href="Image_compression" title="Image compression">Image compression</a>.</div>

<div role="note" class="hatnote navigation-not-searchable">"Image processing" redirects here; not to be confused with <a href="Analog_image_processing" title="Analog image processing">Analog image processing</a>.</div>

Digital image processing is the use of a <a href="Digital_computer" class="mw-redirect" title="Digital computer">digital computer</a> to process <a href="Digital_image" title="Digital image">digital images</a> through an <a href="Algorithm" title="Algorithm">algorithm</a>.<a href="#cite_note-1">[1]</a><a href="#cite_note-Gonzalez_2018_p.-2">[2]</a> As a subcategory or field of <a href="Digital_signal_processing" title="Digital signal processing">digital signal processing</a>, digital image processing has many advantages over <a href="Analog_image_processing" title="Analog image processing">analog image processing</a>. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of <a href="Noise_(signal_processing)" title="Noise (signal processing)">noise</a> and <a href="Distortion" title="Distortion">distortion</a> during processing. Since images are defined over two dimensions (perhaps more), digital image processing may be modeled in the form of <a href="Multidimensional_system" title="Multidimensional system">multidimensional systems</a>. The generation and development of digital image processing are mainly affected by three factors: first, the development of computers;<a href="#cite_note-3">[3]</a> second, the development of mathematics (especially the creation and improvement of <a href="Discrete_mathematics" title="Discrete mathematics">discrete mathematics theory</a>);<a href="#cite_note-4">[4]</a> and third, the demand for a wide range of applications in environment, agriculture, military, industry and medical science has increased.<a href="#cite_note-5">[5]</a>

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<div role="note" class="hatnote navigation-not-searchable">Further information: <a href="Digital_image#History" title="Digital image">Digital image § History</a>, and <a href="Digital_imaging#History" title="Digital imaging">Digital imaging § History</a></div>

Many of the techniques of <a href="Digital_image" title="Digital image">digital image</a> processing, or digital picture processing as it often was called, were developed in the 1960s, at <a href="Bell_Laboratories" class="mw-redirect" title="Bell Laboratories">Bell Laboratories</a>, the <a href="Jet_Propulsion_Laboratory" title="Jet Propulsion Laboratory">Jet Propulsion Laboratory</a>, <a href="Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a>, <a href="University_of_Maryland%2C_College_Park" title="University of Maryland, College Park">University of Maryland</a>, and a few other research facilities, with application to <a href="Satellite_imagery" title="Satellite imagery">satellite imagery</a>, <a href="Wirephoto" title="Wirephoto">wire-photo</a> standards conversion, <a href="Medical_physics" title="Medical physics">medical imaging</a>, <a href="Videophone" class="mw-redirect" title="Videophone">videophone</a>, <a href="Character_recognition" class="mw-redirect" title="Character recognition">character recognition</a>, and photograph enhancement.<a href="#cite_note-6">[6]</a> The purpose of early image processing was to improve the quality of the image. It was aimed for human beings to improve the visual effect of people. In image processing, the input is a low-quality image, and the output is an image with improved quality. Common image processing include image enhancement, restoration, encoding, and compression. The first successful application was the American Jet Propulsion Laboratory (JPL). They used image processing techniques such as geometric correction, gradation transformation, noise removal, etc. on the thousands of lunar photos sent back by the Space Detector Ranger 7 in 1964, taking into account the position of the Sun and the environment of the Moon. The impact of the successful mapping of the Moon's surface map by the computer has been a success. Later, more complex image processing was performed on the nearly 100,000 photos sent back by the spacecraft, so that the topographic map, color map and panoramic mosaic of the Moon were obtained, which achieved extraordinary results and laid a solid foundation for human landing on the Moon.<a href="#cite_note-:1-7">[7]</a>

The cost of processing was fairly high, however, with the computing equipment of that era. That changed in the 1970s, when digital image processing proliferated as cheaper computers and dedicated hardware became available. This led to images being processed in real-time, for some dedicated problems such as <a href="Television_standards_conversion" title="Television standards conversion">television standards conversion</a>. As <a href="General-purpose_computer" class="mw-redirect" title="General-purpose computer">general-purpose computers</a> became faster, they started to take over the role of dedicated hardware for all but the most specialized and computer-intensive operations. With the fast computers and signal processors available in the 2000s, digital image processing has become the most common form of image processing, and is generally used because it is not only the most versatile method, but also the cheapest.

<div class="mw-heading mw-heading3"><h3 id="Image_sensors">Image sensors</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Image_sensor" title="Image sensor">Image sensor</a></div>

The basis for modern <a href="Image_sensors" class="mw-redirect" title="Image sensors">image sensors</a> is <a href="Metal%E2%80%93oxide%E2%80%93semiconductor" class="mw-redirect" title="Metal–oxide–semiconductor">metal–oxide–semiconductor</a> (MOS) technology,<a href="#cite_note-Williams-8">[8]</a> invented at Bell Labs between 1955 and 1960,<a href="#cite_note-9">[9]</a><a href="#cite_note-10">[10]</a><a href="#cite_note-11">[11]</a><a href="#cite_note-12">[12]</a><a href="#cite_note-13">[13]</a><a href="#cite_note-Lojek1202-14">[14]</a> This led to the development of digital <a href="Semiconductor" title="Semiconductor">semiconductor</a> image sensors, including the <a href="Charge-coupled_device" title="Charge-coupled device">charge-coupled device</a> (CCD) and later the <a href="CMOS_sensor" class="mw-redirect" title="CMOS sensor">CMOS sensor</a>.<a href="#cite_note-Williams-8">[8]</a>

The charge-coupled device was invented by <a href="Willard_S._Boyle" class="mw-redirect" title="Willard S. Boyle">Willard S. Boyle</a> and <a href="George_E._Smith" title="George E. Smith">George E. Smith</a> at Bell Labs in 1969.<a href="#cite_note-15">[15]</a> While researching MOS technology, they realized that an electric charge was the analogy of the magnetic bubble and that it could be stored on a tiny <a href="MOS_capacitor" class="mw-redirect" title="MOS capacitor">MOS capacitor</a>. As it was fairly straightforward to <a href="Semiconductor_device_fabrication" title="Semiconductor device fabrication">fabricate</a> a series of MOS capacitors in a row, they connected a suitable voltage to them so that the charge could be stepped along from one to the next.<a href="#cite_note-Williams-8">[8]</a> The CCD is a semiconductor circuit that was later used in the first <a href="Digital_video_camera" class="mw-redirect" title="Digital video camera">digital video cameras</a> for <a href="Television_broadcasting" class="mw-redirect" title="Television broadcasting">television broadcasting</a>.<a href="#cite_note-16">[16]</a>

The <a href="NMOS_logic" title="NMOS logic">NMOS</a> <a href="Active-pixel_sensor" title="Active-pixel sensor">active-pixel sensor</a> (APS) was invented by <a href="Olympus_Corporation" title="Olympus Corporation">Olympus</a> in Japan during the mid-1980s. This was enabled by advances in MOS <a href="Semiconductor_device_fabrication" title="Semiconductor device fabrication">semiconductor device fabrication</a>, with <a href="MOSFET_scaling" class="mw-redirect" title="MOSFET scaling">MOSFET scaling</a> reaching smaller <a href="List_of_semiconductor_scale_examples" title="List of semiconductor scale examples">micron and then sub-micron</a> levels.<a href="#cite_note-fossum93-17">[17]</a><a href="#cite_note-18">[18]</a> The NMOS APS was fabricated by Tsutomu Nakamura's team at Olympus in 1985.<a href="#cite_note-19">[19]</a> The <a href="CMOS" title="CMOS">CMOS</a> active-pixel sensor (CMOS sensor) was later developed by <a href="Eric_Fossum" title="Eric Fossum">Eric Fossum</a>'s team at the <a href="NASA" title="NASA">NASA</a> <a href="Jet_Propulsion_Laboratory" title="Jet Propulsion Laboratory">Jet Propulsion Laboratory</a> in 1993.<a href="#cite_note-Fossum2014-20">[20]</a> By 2007, sales of CMOS sensors had surpassed CCD sensors.<a href="#cite_note-21">[21]</a>

MOS image sensors are widely used in <a href="Optical_mouse" title="Optical mouse">optical mouse</a> technology. The first optical mouse, invented by <a href="Richard_F._Lyon" title="Richard F. Lyon">Richard F. Lyon</a> at <a href="Xerox" title="Xerox">Xerox</a> in 1980, used a <a href="6_%CE%BCm_process" title="6 μm process">5 μm</a> <a href="NMOS_logic" title="NMOS logic">NMOS</a> <a href="Integrated_circuit" title="Integrated circuit">integrated circuit</a> sensor chip.<a href="#cite_note-22">[22]</a><a href="#cite_note-23">[23]</a> Since the first commercial optical mouse, the <a href="IntelliMouse" title="IntelliMouse">IntelliMouse</a> introduced in 1999, most optical mouse devices use CMOS sensors.<a href="#cite_note-24">[24]</a><a href="#cite_note-hackaday-25">[25]</a>

<div class="mw-heading mw-heading3"><h3 id="Image_compression">Image compression</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Image_compression" title="Image compression">Image compression</a></div>

An important development in digital <a href="Image_compression" title="Image compression">image compression</a> technology was the <a href="Discrete_cosine_transform" title="Discrete cosine transform">discrete cosine transform</a> (DCT), a <a href="Lossy_compression" title="Lossy compression">lossy compression</a> technique first proposed by <a href="N._Ahmed" class="mw-redirect" title="N. Ahmed">Nasir Ahmed</a> in 1972.<a href="#cite_note-Ahmed-26">[26]</a> DCT compression became the basis for <a href="JPEG" title="JPEG">JPEG</a>, which was introduced by the <a href="Joint_Photographic_Experts_Group" title="Joint Photographic Experts Group">Joint Photographic Experts Group</a> in 1992.<a href="#cite_note-t81-27">[27]</a> JPEG compresses images down to much smaller file sizes, and has become the most widely used <a href="Image_file_format" title="Image file format">image file format</a> on the <a href="Internet" title="Internet">Internet</a>.<a href="#cite_note-28">[28]</a> Its highly efficient DCT compression algorithm was largely responsible for the wide proliferation of <a href="Digital_images" class="mw-redirect" title="Digital images">digital images</a> and <a href="Digital_photo" class="mw-redirect" title="Digital photo">digital photos</a>,<a href="#cite_note-Atlantic-29">[29]</a> with several billion JPEG images produced every day as of 2015.<a href="#cite_note-30">[30]</a>

Medical imaging techniques produce very large amounts of data, especially from CT, MRI and PET modalities. As a result, storage and communications of electronic image data are prohibitive without the use of compression.<a href="#cite_note-31">[31]</a><a href="#cite_note-32">[32]</a> <a href="JPEG_2000" title="JPEG 2000">JPEG 2000</a> image compression is used by the <a href="DICOM" title="DICOM">DICOM</a> standard for storage and transmission of medical images. The cost and feasibility of accessing large image data sets over low or various bandwidths are further addressed by use of another DICOM standard, called <a href="JPIP" title="JPIP">JPIP</a>, to enable efficient streaming of the <a href="JPEG_2000" title="JPEG 2000">JPEG 2000</a> compressed image data.<a href="#cite_note-33">[33]</a>

<div class="mw-heading mw-heading3"><h3 id="Digital_signal_processor_(DSP)">Digital signal processor (DSP)</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Digital_signal_processor" title="Digital signal processor">Digital signal processor</a></div>

Electronic <a href="Signal_processing" title="Signal processing">signal processing</a> was revolutionized by the wide adoption of <a href="MOS_technology" class="mw-redirect" title="MOS technology">MOS technology</a> in the 1970s.<a href="#cite_note-Grant-34">[34]</a> <a href="MOS_integrated_circuit" class="mw-redirect" title="MOS integrated circuit">MOS integrated circuit</a> technology was the basis for the first single-chip <a href="Microprocessors" class="mw-redirect" title="Microprocessors">microprocessors</a> and <a href="Microcontrollers" class="mw-redirect" title="Microcontrollers">microcontrollers</a> in the early 1970s,<a href="#cite_note-ieee-35">[35]</a> and then the first single-chip <a href="Digital_signal_processor" title="Digital signal processor">digital signal processor</a> (DSP) chips in the late 1970s.<a href="#cite_note-computerhistory1979-36">[36]</a><a href="#cite_note-Taranovich-37">[37]</a> DSP chips have since been widely used in digital image processing.<a href="#cite_note-computerhistory1979-36">[36]</a>

The <a href="Discrete_cosine_transform" title="Discrete cosine transform">discrete cosine transform</a> (DCT) <a href="Image_compression" title="Image compression">image compression</a> algorithm has been widely implemented in DSP chips, with many companies developing DSP chips based on DCT technology. DCTs are widely used for <a href="Encoding" class="mw-redirect" title="Encoding">encoding</a>, decoding, <a href="Video_coding" class="mw-redirect" title="Video coding">video coding</a>, <a href="Audio_coding" class="mw-redirect" title="Audio coding">audio coding</a>, <a href="Multiplexing" title="Multiplexing">multiplexing</a>, control signals, <a href="Signaling" class="mw-redirect" title="Signaling">signaling</a>, <a href="Analog-to-digital_conversion" class="mw-redirect" title="Analog-to-digital conversion">analog-to-digital conversion</a>, formatting <a href="Luminance" title="Luminance">luminance</a> and color differences, and color formats such as <a href="YUV444" class="mw-redirect" title="YUV444">YUV444</a> and <a href="YUV411" class="mw-redirect" title="YUV411">YUV411</a>. DCTs are also used for encoding operations such as <a href="Motion_estimation" title="Motion estimation">motion estimation</a>, <a href="Motion_compensation" title="Motion compensation">motion compensation</a>, <a href="Inter-frame" class="mw-redirect" title="Inter-frame">inter-frame</a> prediction, <a href="Quantization_(signal_processing)" title="Quantization (signal processing)">quantization</a>, perceptual weighting, <a href="Entropy_encoding" class="mw-redirect" title="Entropy encoding">entropy encoding</a>, variable encoding, and <a href="Motion_vector" class="mw-redirect" title="Motion vector">motion vectors</a>, and decoding operations such as the inverse operation between different color formats (<a href="YIQ" title="YIQ">YIQ</a>, <a href="YUV" class="mw-redirect" title="YUV">YUV</a> and <a href="RGB" class="mw-redirect" title="RGB">RGB</a>) for display purposes. DCTs are also commonly used for <a href="High-definition_television" title="High-definition television">high-definition television</a> (HDTV) encoder/decoder chips.<a href="#cite_note-Stankovic-38">[38]</a>

<div class="mw-heading mw-heading2"><h2 id="Tasks">Tasks</h2></div>

Digital image processing allows the use of much more complex algorithms, and hence, can offer both more sophisticated performance at simple tasks, and the implementation of methods which would be impossible by analogue means.

In particular, digital image processing is a concrete application of, and a practical technology based on:

<ul><li><a href="Statistical_classification" title="Statistical classification">Classification</a></li>

<li><a href="Feature_extraction" class="mw-redirect" title="Feature extraction">Feature extraction</a></li>

<li><a href="Multi-scale_signal_analysis" class="mw-redirect" title="Multi-scale signal analysis">Multi-scale signal analysis</a></li>

<li><a href="Pattern_recognition" title="Pattern recognition">Pattern recognition</a></li>

<li><a href="Graphical_projection" class="mw-redirect" title="Graphical projection">Projection</a></li></ul>

Some techniques which are used in digital image processing include:

<ul><li><a href="Anisotropic_diffusion" title="Anisotropic diffusion">Anisotropic diffusion</a></li>

<li><a href="Hidden_Markov_model" title="Hidden Markov model">Hidden Markov models</a></li>

<li><a href="Image_editing" title="Image editing">Image editing</a></li>

<li><a href="Digital_photograph_restoration" title="Digital photograph restoration">Image restoration</a></li>

<li><a href="Independent_component_analysis" title="Independent component analysis">Independent component analysis</a></li>

<li><a href="Linear_filter" title="Linear filter">Linear filtering</a></li>

<li><a href="Artificial_neural_networks" class="mw-redirect" title="Artificial neural networks">Neural networks</a></li>

<li><a href="Partial_differential_equations" class="mw-redirect" title="Partial differential equations">Partial differential equations</a></li>

<li><a href="Pixelation" title="Pixelation">Pixelation</a></li>

<li><a href="Point_feature_matching" class="mw-redirect" title="Point feature matching">Point feature matching</a></li>

<li><a href="Principal_components_analysis" class="mw-redirect" title="Principal components analysis">Principal components analysis</a></li>

<li><a href="Self-organizing_map" title="Self-organizing map">Self-organizing maps</a></li>

<li><a href="Wavelet" title="Wavelet">Wavelets</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Digital_image_transformations">Digital image transformations</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Filtering">Filtering</h3></div>

Digital filters are used to blur and sharpen digital images. Filtering can be performed by:

<ul><li><a href="Kernel_(image_processing)#Convolution" title="Kernel (image processing)">convolution</a> with specifically designed <a href="Kernel_(image_processing)" title="Kernel (image processing)">kernels</a> (filter array) in the spatial domain<a href="#cite_note-:0-39">[39]</a></li>

<li>masking specific frequency regions in the frequency (Fourier) domain</li></ul>

The following examples show both methods:<a href="#cite_note-Gonzalez_2008-40">[40]</a>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}0&0&0\\0&1&0\\0&0&0\end{bmatrix}}}</annotation>

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</math><img src="./5bf6623ca763ba780b471a565eb1b06cd14b445c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:11.985ex; height:9.176ex;" alt="{\displaystyle {\begin{bmatrix}0&0&0\\0&1&0\\0&0&0\end{bmatrix}}}" loading="lazy">

</td>

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<td><a href="Lowpass" class="mw-redirect" title="Lowpass">Spatial Lowpass</a>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {1}{9}}\times {\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}}</annotation>

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</math><img src="./fd0334e2eba0c8ade0a603b8fcadb1ecad64042b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:16.824ex; height:9.176ex;" alt="{\displaystyle {\frac {1}{9}}\times {\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}}" loading="lazy">

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<td><a href="Edge_detection" title="Edge detection">Spatial Highpass</a>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}0&-1&0\\-1&4&-1\\0&-1&0\end{bmatrix}}}</annotation>

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</math><img src="./9b629b1894659e926464af9782a0566c993bef9a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:17.409ex; height:9.176ex;" alt="{\displaystyle {\begin{bmatrix}0&-1&0\\-1&4&-1\\0&-1&0\end{bmatrix}}}" loading="lazy">

</td>

<td>

</td></tr>

<tr>

<td><a href="Fast_Fourier_transform" title="Fast Fourier transform">Fourier Representation</a>

</td>

<td>Pseudo-code:

image = checkerboard

F = Fourier Transform of image

Show Image: log(1+Absolute Value(F))

</td>

</td></tr>

<tr>

<td>Fourier Lowpass

</td>

</td>

</td></tr>

<tr>

<td>Fourier Highpass

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</tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Image_padding_in_Fourier_domain_filtering">Image padding in Fourier domain filtering</h4></div>

Images are typically padded before being transformed to the Fourier space, the <a href="Highpass_filter" class="mw-redirect" title="Highpass filter">highpass filtered</a> images below illustrate the consequences of different padding techniques:

<th>Zero padded

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<td>

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</tbody></table>

Notice that the highpass filter shows extra edges when zero padded compared to the repeated edge padding.

<div class="mw-heading mw-heading4"><h4 id="Filtering_code_examples">Filtering code examples</h4></div>

MATLAB example for spatial domain highpass filtering.

<div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>img=checkerboard(20); % generate checkerboard

% ************************** SPATIAL DOMAIN ***************************

klaplace=[0 -1 0; -1 5 -1; 0 -1 0]; % Laplacian filter kernel

X=conv2(img,klaplace); % convolve test img with

% 3x3 Laplacian kernel

figure()

imshow(X,[]) % show Laplacian filtered

title('Laplacian Edge Detection')

</pre></div>

<div class="mw-heading mw-heading3"><h3 id="Affine_transformations">Affine transformations</h3></div>

<a href="Affine_transformations" class="mw-redirect" title="Affine transformations">Affine transformations</a> enable basic image transformations including scale, rotate, translate, mirror and shear as is shown in the following examples:<a href="#cite_note-Gonzalez_2008-40">[40]</a>

<th>Transformation Name

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<th>Affine Matrix

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}-1&0&0\\0&1&0\\0&0&1\end{bmatrix}}}</annotation>

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</math><img src="./b6f3c4219a22cd7963c3bed901717c1b34edda32.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:13.793ex; height:9.176ex;" alt="{\displaystyle {\begin{bmatrix}-1&0&0\\0&1&0\\0&0&1\end{bmatrix}}}" loading="lazy">

</td>

<td>

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<tr>

<td><a href="Scale_(ratio)" title="Scale (ratio)">Scale</a>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}c_{x}=2&0&0\\0&c_{y}=1&0\\0&0&1\end{bmatrix}}}</annotation>

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</math><img src="./75c9c1d42880a29086ffc303cd6aecd0d83c3bb9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:22.417ex; height:9.509ex;" alt="{\displaystyle {\begin{bmatrix}c_{x}=2&0&0\\0&c_{y}=1&0\\0&0&1\end{bmatrix}}}" loading="lazy">

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<td><a href="Rotate" class="mw-redirect" title="Rotate">Rotate</a>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}\cos(\theta )&\sin(\theta )&0\\-\sin(\theta )&\cos(\theta )&0\\0&0&1\end{bmatrix}}}</annotation>

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</math><img src="./1e7686d473b2f40fbb3e867b4b3409bf63bcd823.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:23.621ex; height:9.509ex;" alt="{\displaystyle {\begin{bmatrix}\cos(\theta )&\sin(\theta )&0\\-\sin(\theta )&\cos(\theta )&0\\0&0&1\end{bmatrix}}}" loading="lazy">

</td>

<td> where θ = <style data-mw-deduplicate="TemplateStyles:r1214402035">

/* start https://en.wikipedia.org/ */

.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}

/* end https://en.wikipedia.org/ */

</style>⁠π/6⁠ =30°

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<td><a href="Shear_matrix" class="mw-redirect" title="Shear matrix">Shear</a>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}1&c_{x}=0.5&0\\c_{y}=0&1&0\\0&0&1\end{bmatrix}}}</annotation>

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</math><img src="./0063f16565cecf78a3732068701f46390ad2f4a7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:24.226ex; height:9.509ex;" alt="{\displaystyle {\begin{bmatrix}1&c_{x}=0.5&0\\c_{y}=0&1&0\\0&0&1\end{bmatrix}}}" loading="lazy">

</td>

<td>

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To apply the affine matrix to an image, the image is converted to matrix in which each entry corresponds to the pixel intensity at that location. Then each pixel's location can be represented as a vector indicating the coordinates of that pixel in the image, [x, y], where x and y are the row and column of a pixel in the image matrix. This allows the coordinate to be multiplied by an affine-transformation matrix, which gives the position that the pixel value will be copied to in the output image.

However, to allow transformations that require translation transformations, 3-dimensional <a href="Homogeneous_coordinates" title="Homogeneous coordinates">homogeneous coordinates</a> are needed. The third dimension is usually set to a non-zero constant, usually 1, so that the new coordinate is [x, y, 1]. This allows the coordinate vector to be multiplied by a 3×3 matrix, enabling translation shifts. Thus, the third dimension, i.e. the constant 1, allows translation.

Because matrix multiplication is <a href="Associative_property" title="Associative property">associative</a>, multiple affine transformations can be combined into a single affine transformation by multiplying the matrix of each individual transformation in the order that the transformations are done. This results in a single matrix that, when applied to a point vector, gives the same result as all the individual transformations performed on the vector [x, y, 1] in sequence. Thus a sequence of affine transformation matrices can be reduced to a single affine transformation matrix.

For example, 2-dimensional coordinates only permit rotation about the origin (0, 0). But 3-dimensional homogeneous coordinates can be used to first translate any point to (0, 0), then perform the rotation, and lastly translate the origin (0, 0) back to the original point (the opposite of the first translation). These three affine transformations can be combined into a single matrix—thus allowing rotation around any point in the image.<a href="#cite_note-41">[41]</a>

<div class="mw-heading mw-heading3"><h3 id="Image_denoising_with_mathematical_morphology">Image denoising with mathematical morphology</h3></div>

<a href="Mathematical_morphology" title="Mathematical morphology">Mathematical morphology</a> (MM) is a nonlinear image processing framework that analyzes shapes within images by probing local pixel neighborhoods using a small, predefined function called a <a href="Structuring_element" title="Structuring element">structuring element</a>. In the context of <a href="Grayscale_image" class="mw-redirect" title="Grayscale image">grayscale images</a>, MM is especially useful for denoising through <a href="Dilation_(morphology)" title="Dilation (morphology)">dilation</a> and <a href="Erosion_(morphology)" title="Erosion (morphology)">erosion</a>—primitive operators that can be combined to build more complex filters.

Suppose we have:

<ul><li>A discrete grayscale image: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f={\begin{bmatrix}45&50&65\\40&60&55\\25&15&5\end{bmatrix}},\quad f:\Omega \rightarrow \mathbb {R} ,\quad \Omega =\{0,1,2\}^{2},}">

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<annotation encoding="application/x-tex">{\displaystyle f={\begin{bmatrix}45&50&65\\40&60&55\\25&15&5\end{bmatrix}},\quad f:\Omega \rightarrow \mathbb {R} ,\quad \Omega =\{0,1,2\}^{2},}</annotation>

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</math><img src="./a204a261a319d147c8dfc0c982c243606df9d52d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:51.106ex; height:9.176ex;" alt="{\displaystyle f={\begin{bmatrix}45&50&65\\40&60&55\\25&15&5\end{bmatrix}},\quad f:\Omega \rightarrow \mathbb {R} ,\quad \Omega =\{0,1,2\}^{2},}" loading="lazy"></li></ul>

<ul><li>A structuring element: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B={\begin{bmatrix}1&2&1\\2&1&1\\1&0&3\end{bmatrix}},\quad B:{\mathcal {S}}\rightarrow \mathbb {R} ,\quad {\mathcal {S}}=\{-1,0,1\}^{2}.}">

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<annotation encoding="application/x-tex">{\displaystyle B={\begin{bmatrix}1&2&1\\2&1&1\\1&0&3\end{bmatrix}},\quad B:{\mathcal {S}}\rightarrow \mathbb {R} ,\quad {\mathcal {S}}=\{-1,0,1\}^{2}.}</annotation>

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</math><img src="./fda8004a9622f89d8dac474a9a57037b4284969b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:50.026ex; height:9.176ex;" alt="{\displaystyle B={\begin{bmatrix}1&2&1\\2&1&1\\1&0&3\end{bmatrix}},\quad B:{\mathcal {S}}\rightarrow \mathbb {R} ,\quad {\mathcal {S}}=\{-1,0,1\}^{2}.}" loading="lazy"></li></ul>

Here, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {S}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {S}}}</annotation>

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</math><img src="./2302a18e269dbecc43c57c0c2aced3bfae15278d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.492ex; height:2.176ex;" alt="{\displaystyle {\mathcal {S}}}" loading="lazy"> defines the neighborhood of relative coordinates <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (m,n)}">

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<annotation encoding="application/x-tex">{\displaystyle (m,n)}</annotation>

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</math><img src="./274d4857135a7d28a94ba9ee8135779615084d43.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.278ex; height:2.843ex;" alt="{\displaystyle (m,n)}" loading="lazy"> over which local operations are computed. The values of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B(m,n)}">

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<annotation encoding="application/x-tex">{\displaystyle B(m,n)}</annotation>

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</math><img src="./7f1a73c7fa714079c1d7d34ac057cc268407d334.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.042ex; height:2.843ex;" alt="{\displaystyle B(m,n)}" loading="lazy"> bias the image during dilation and erosion.

<dl><dt>Dilation</dt>

<dd>Grayscale dilation is defined as:</dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle (f\oplus B)(i,j)=\max _{(m,n)\in {\mathcal {S}}}{\Bigl \{}f(i+m,j+n)+B(m,n){\Bigr \}}.}</annotation>

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<dl><dd>For example, the dilation at position (1, 1) is calculated as:</dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}(f\oplus B)(1,1)=\max \!{\Bigl (}&f(0,0)+B(-1,-1),&\;45+1;&\\&f(1,0)+B(0,-1),&\;50+2;&\\&f(2,0)+B(1,-1),&\;65+1;&\\&f(0,1)+B(-1,0),&\;40+2;&\\&f(1,1)+B(0,0),&\;60+1;&\\&f(2,1)+B(1,0),&\;55+1;&\\&f(0,2)+B(-1,1),&\;25+1;&\\&f(1,2)+B(0,1),&\;15+0;&\\&f(2,2)+B(1,1)&\;5+3{\Bigr )}=66.\end{aligned}}}</annotation>

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</math><img src="./0631728a2ffadc5df7daa75d19f73b120edc8ad6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -15.171ex; width:60.82ex; height:31.509ex;" alt="{\displaystyle {\begin{aligned}(f\oplus B)(1,1)=\max \!{\Bigl (}&f(0,0)+B(-1,-1),&\;45+1;&\\&f(1,0)+B(0,-1),&\;50+2;&\\&f(2,0)+B(1,-1),&\;65+1;&\\&f(0,1)+B(-1,0),&\;40+2;&\\&f(1,1)+B(0,0),&\;60+1;&\\&f(2,1)+B(1,0),&\;55+1;&\\&f(0,2)+B(-1,1),&\;25+1;&\\&f(1,2)+B(0,1),&\;15+0;&\\&f(2,2)+B(1,1)&\;5+3{\Bigr )}=66.\end{aligned}}}" loading="lazy">

<dl><dt>Erosion</dt>

<dd>Grayscale erosion is defined as:</dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle (f\ominus B)(i,j)=\min _{(m,n)\in {\mathcal {S}}}{\Bigl \{}f(i+m,j+n)-B(m,n){\Bigr \}}.}</annotation>

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<dl><dd>For example, the erosion at position (1, 1) is calculated as:</dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}(f\ominus B)(1,1)=\min \!{\Bigl (}&f(0,0)-B(-1,-1),&\;45-1;&\\&f(1,0)-B(0,-1),&\;50-2;&\\&f(2,0)-B(1,-1),&\;65-1;&\\&f(0,1)-B(-1,0),&\;40-2;&\\&f(1,1)-B(0,0),&\;60-1;&\\&f(2,1)-B(1,0),&\;55-1;&\\&f(0,2)-B(-1,1),&\;25-1;&\\&f(1,2)-B(0,1),&\;15-0;&\\&f(2,2)-B(1,1)&\;5-3{\Bigr )}=2.\end{aligned}}}</annotation>

</semantics>

</math><img src="./f01a0f563d9856869b98e80f7322f38d9503c69a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -15.171ex; width:59.207ex; height:31.509ex;" alt="{\displaystyle {\begin{aligned}(f\ominus B)(1,1)=\min \!{\Bigl (}&f(0,0)-B(-1,-1),&\;45-1;&\\&f(1,0)-B(0,-1),&\;50-2;&\\&f(2,0)-B(1,-1),&\;65-1;&\\&f(0,1)-B(-1,0),&\;40-2;&\\&f(1,1)-B(0,0),&\;60-1;&\\&f(2,1)-B(1,0),&\;55-1;&\\&f(0,2)-B(-1,1),&\;25-1;&\\&f(1,2)-B(0,1),&\;15-0;&\\&f(2,2)-B(1,1)&\;5-3{\Bigr )}=2.\end{aligned}}}" loading="lazy">

<div class="mw-heading mw-heading4"><h4 id="Results">Results</h4></div>

After applying dilation to <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}45&50&65\\40&66&55\\25&15&5\end{bmatrix}}}</annotation>

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After applying erosion to <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">

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<annotation encoding="application/x-tex">{\displaystyle f}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}45&50&65\\40&2&55\\25&15&5\end{bmatrix}}}</annotation>

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<div class="mw-heading mw-heading4"><h4 id="Opening_and_Closing">Opening and Closing</h4></div>

MM operations, such as <a href="Opening_(morphology)" title="Opening (morphology)">opening</a> and <a href="Closing_(morphology)" title="Closing (morphology)">closing</a>, are composite processes that utilize both dilation and erosion to modify the structure of an image. These operations are particularly useful for tasks such as noise removal, shape smoothing, and object separation.

<ul><li>Opening: This operation is performed by applying erosion to an image first, followed by dilation. The purpose of opening is to remove small objects or noise from the foreground while preserving the overall structure of larger objects. It is especially effective in situations where noise appears as isolated bright pixels or small, disconnected features.</li></ul>

For example, applying opening to an image <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">

</mstyle>

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</math><img src="./132e57acb643253e7810ee9702d9581f159a1c61.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" loading="lazy"> with a structuring element <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

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</math><img src="./47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> would first reduce small details (through erosion) and then restore the main shapes (through dilation). This ensures that unwanted noise is removed without significantly altering the size or shape of larger objects.

<ul><li>Closing: This operation is performed by applying dilation first, followed by erosion. Closing is typically used to fill small holes or gaps within objects and to connect broken parts of the foreground. It works by initially expanding the boundaries of objects (through dilation) and then refining the boundaries (through erosion).</li></ul>

For instance, applying closing to the same image <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle f}</annotation>

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</math><img src="./132e57acb643253e7810ee9702d9581f159a1c61.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" loading="lazy"> would fill in small gaps within objects, such as connecting breaks in thin lines or closing small holes, while ensuring that the surrounding areas are not significantly affected.

Both opening and closing can be visualized as ways of refining the structure of an image: opening simplifies and removes small, unnecessary details, while closing consolidates and connects objects to form more cohesive structures.

<th>Structuring element

</th>

<th>Mask

</th>

<th>Code

</th>

<th>Example

</th></tr>

<tr>

<td>Original Image

</td>

<td>None

</td>

<td>Use Matlab to read Original image

<div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>original = imread('scene.jpg');

image = rgb2gray(original);

[r, c, channel] = size(image);

se = logical([1 1 1 ; 1 1 1 ; 1 1 1]);

[p, q] = size(se);

halfH = floor(p/2);

halfW = floor(q/2);

time = 3; % denoising 3 times with all method

</pre></div>

</td>

<td>

</td></tr>

<tr>

<td><a href="Dilation_(morphology)" title="Dilation (morphology)">Dilation</a>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}}</annotation>

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</td>

<td>Use Matlab to dilation

<div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>imwrite(image, "scene_dil.jpg")

extractmax = zeros(size(image), class(image));

for i = 1 : time

dil_image = imread('scene_dil.jpg');

for col = (halfW + 1): (c - halfW)

for row = (halfH + 1) : (r - halfH)

dpointD = row - halfH;

dpointU = row + halfH;

dpointL = col - halfW;

dpointR = col + halfW;

dneighbor = dil_image(dpointD:dpointU, dpointL:dpointR);

filter = dneighbor(se);

extractmax(row, col) = max(filter);

end

imwrite(extractmax, "scene_dil.jpg");

end

</pre></div>

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<td>

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<td><a href="Erosion_(morphology)" title="Erosion (morphology)">Erosion</a>

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</td>

<td>Use Matlab to erosion

<div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>imwrite(image, 'scene_ero.jpg');

extractmin = zeros(size(image), class(image));

for i = 1: time

ero_image = imread('scene_ero.jpg');

for col = (halfW + 1): (c - halfW)

for row = (halfH +1): (r -halfH)

pointDown = row-halfH;

pointUp = row+halfH;

pointLeft = col-halfW;

pointRight = col+halfW;

neighbor = ero_image(pointDown:pointUp,pointLeft:pointRight);

filter = neighbor(se);

extractmin(row, col) = min(filter);

end

imwrite(extractmin, "scene_ero.jpg");

end

</pre></div>

</td>

<td>

</td></tr>

<tr>

<td><a href="Opening_(morphology)" title="Opening (morphology)">Opening</a>

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</math><img src="./5350c22386c6f1c2c32769f4fc14ca3a0121a3ea.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:11.985ex; height:9.176ex;" alt="{\displaystyle {\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}}" loading="lazy">

</td>

<td>Use Matlab to Opening

<div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>imwrite(extractmin, "scene_opening.jpg")

extractopen = zeros(size(image), class(image));

for i = 1 : time

dil_image = imread('scene_opening.jpg');

for col = (halfW + 1): (c - halfW)

for row = (halfH + 1) : (r - halfH)

dpointD = row - halfH;

dpointU = row + halfH;

dpointL = col - halfW;

dpointR = col + halfW;

dneighbor = dil_image(dpointD:dpointU, dpointL:dpointR);

filter = dneighbor(se);

extractopen(row, col) = max(filter);

end

imwrite(extractopen, "scene_opening.jpg");

end

</pre></div>

</td>

<td>

</td></tr>

<tr>

<td><a href="Closing_(morphology)" title="Closing (morphology)">Closing</a>

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</td>

<td>Use Matlab to Closing

<div class="mw-highlight mw-highlight-lang-matlab mw-content-ltr" dir="ltr"><pre>imwrite(extractmax, "scene_closing.jpg")

extractclose = zeros(size(image), class(image));

for i = 1 : time

ero_image = imread('scene_closing.jpg');

for col = (halfW + 1): (c - halfW)

for row = (halfH + 1) : (r - halfH)

dpointD = row - halfH;

dpointU = row + halfH;

dpointL = col - halfW;

dpointR = col + halfW;

dneighbor = ero_image(dpointD:dpointU, dpointL:dpointR);

filter = dneighbor(se);

extractclose(row, col) = min(filter);

end

imwrite(extractclose, "scene_closing.jpg");

end

</pre></div>

</td>

<td>

</td></tr>

</tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<div role="note" class="hatnote navigation-not-searchable">Further information: <a href="Digital_imaging" title="Digital imaging">Digital imaging</a> and <a href="Applications_of_computer_vision" class="mw-redirect" title="Applications of computer vision">Applications of computer vision</a></div>

<div class="mw-heading mw-heading3"><h3 id="Digital_camera_images">Digital camera images</h3></div>

Digital cameras generally include specialized digital image processing hardware – either dedicated chips or added circuitry on other chips – to convert the raw data from their <a href="Image_sensor" title="Image sensor">image sensor</a> into a <a href="Color_correction" title="Color correction">color-corrected</a> image in a standard <a href="Image_file_formats" class="mw-redirect" title="Image file formats">image file format</a>. Additional post processing techniques increase edge sharpness or color saturation to create more naturally looking images.

<a href="Westworld_(film)" title="Westworld (film)">Westworld</a> (1973) was the first feature film to use the digital image processing to <a href="Pixellate" class="mw-redirect" title="Pixellate">pixellate</a> photography to simulate an android's point of view.<a href="#cite_note-42">[42]</a> Image processing is also vastly used to produce the <a href="Chroma_key" title="Chroma key">chroma key</a> effect that replaces the background of actors with natural or artistic scenery.

<div class="mw-heading mw-heading3"><h3 id="Face_detection">Face detection</h3></div>

<a href="Face_detection" title="Face detection">Face detection</a> can be implemented with <a href="Mathematical_morphology" title="Mathematical morphology">mathematical morphology</a>, the <a href="Discrete_cosine_transform" title="Discrete cosine transform">discrete cosine transform</a> (DCT), and horizontal <a href="Projection_(mathematics)" title="Projection (mathematics)">projection</a>.

General method with feature-based method

The feature-based method of face detection is using skin tone, edge detection, face shape, and feature of a face (like eyes, mouth, etc.) to achieve face detection. The skin tone, face shape, and all the unique elements that only the human face have can be described as features.

Process explanation

<ol><li>Given a batch of face images, first, extract the skin tone range by sampling face images. The skin tone range is just a skin filter.

<ol><li><a href="Structural_similarity" class="mw-redirect" title="Structural similarity">Structural similarity</a> index measure (SSIM) can be applied to compare images in terms of extracting the skin tone.</li>

<li>Normally, HSV or RGB color spaces are suitable for the skin filter. E.g. HSV mode, the skin tone range is [0,48,50] ~ [20,255,255]</li></ol></li>

<li>After filtering images with skin tone, to get the face edge, morphology and DCT are used to remove noise and fill up missing skin areas.

<ol><li>Opening method or closing method can be used to achieve filling up missing skin.</li>

<li>DCT is to avoid the object with skin-like tone. Since human faces always have higher texture.</li>

<li>Sobel operator or other operators can be applied to detect face edge.</li></ol></li>

<li>To position human features like eyes, using the projection and find the peak of the histogram of projection help to get the detail feature like mouth, hair, and lip.

<ol><li>Projection is just projecting the image to see the high frequency which is usually the feature position.</li></ol></li></ol>

<div class="mw-heading mw-heading3"><h3 id="Improvement_of_image_quality_method">Improvement of image quality method</h3></div>

Image quality can be influenced by camera vibration, over-exposure, gray level distribution too centralized, and noise, etc. For example, noise problem can be solved by <a href="Smoothing" title="Smoothing">smoothing</a> method while gray level distribution problem can be improved by <a href="Histogram_equalization" title="Histogram equalization">histogram equalization</a>.

<a href="Smoothing" title="Smoothing">Smoothing</a> method

In drawing, if there is some dissatisfied color, taking some color around dissatisfied color and averaging them. This is an easy way to think of Smoothing method.

Smoothing method can be implemented with mask and <a href="Convolution" title="Convolution">convolution</a>. Take the small image and mask for instance as below.

image is

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}2&5&6&5\\3&1&4&6\\1&28&30&2\\7&3&2&2\end{bmatrix}}}</annotation>

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</math><img src="./ba73023ac222584748d50094fd2b5c8ff4fb3fc4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:17.795ex; height:12.509ex;" alt="{\displaystyle {\begin{bmatrix}2&5&6&5\\3&1&4&6\\1&28&30&2\\7&3&2&2\end{bmatrix}}}" loading="lazy">

mask is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{bmatrix}1/9&1/9&1/9\\1/9&1/9&1/9\\1/9&1/9&1/9\end{bmatrix}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}1/9&1/9&1/9\\1/9&1/9&1/9\\1/9&1/9&1/9\end{bmatrix}}}</annotation>

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</math><img src="./9a61c215b24aa9c824f9615efbedb4edf03ab15c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:18.959ex; height:9.843ex;" alt="{\displaystyle {\begin{bmatrix}1/9&1/9&1/9\\1/9&1/9&1/9\\1/9&1/9&1/9\end{bmatrix}}}" loading="lazy">

After convolution and smoothing, image is

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<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}2&5&6&5\\3&9&10&6\\1&9&9&2\\7&3&2&2\end{bmatrix}}}</annotation>

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</math><img src="./855545cfa40bd44d635cbd904ae86c853209a8b7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:16.632ex; height:12.509ex;" alt="{\displaystyle {\begin{bmatrix}2&5&6&5\\3&9&10&6\\1&9&9&2\\7&3&2&2\end{bmatrix}}}" loading="lazy">

Observing image[1, 1], image[1, 2], image[2, 1], and image[2, 2].

The original image pixel is 1, 4, 28, 30. After smoothing mask, the pixel becomes 9, 10, 9, 9 respectively.

new image[1, 1] = <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{9}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{9}}}</annotation>

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</math><img src="./ca7fbb8c7af3dce2f4bb214f14a76358a32a49d2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{9}}}" loading="lazy"> * (image[0,0]+image[0,1]+image[0,2]+image[1,0]+image[1,1]+image[1,2]+image[2,0]+image[2,1]+image[2,2])

new image[1, 1] = floor(<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{9}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{9}}}</annotation>

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</math><img src="./ca7fbb8c7af3dce2f4bb214f14a76358a32a49d2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{9}}}" loading="lazy"> * (2+5+6+3+1+4+1+28+30)) = 9

new image[1, 2] = floor({<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{9}}}">

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new image[2, 1] = floor(<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{9}}}">

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</math><img src="./ca7fbb8c7af3dce2f4bb214f14a76358a32a49d2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{9}}}" loading="lazy"> * (3+1+4+1+28+30+7+3+2)) = 9

new image[2, 2] = floor(<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{9}}}">

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</math><img src="./ca7fbb8c7af3dce2f4bb214f14a76358a32a49d2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{9}}}" loading="lazy"> * (1+4+6+28+30+2+3+2+2)) = 9

Gray Level Histogram method

Generally, given a gray level histogram from an image as below. Changing the histogram to uniform distribution from an image is usually what we called <a href="Histogram_equalization" title="Histogram equalization">histogram equalization</a>.

In discrete time, the area of gray level histogram is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=0}^{k}H(p_{i})}">

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<annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{k}H(p_{i})}</annotation>

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</math><img src="./abf8541658f07b519e88ce11222fb7653e7066f5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:9.584ex; height:7.343ex;" alt="{\displaystyle \sum _{i=0}^{k}H(p_{i})}" loading="lazy">(see figure 1) while the area of uniform distribution is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=0}^{k}G(q_{i})}">

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<annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{k}G(q_{i})}</annotation>

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</math><img src="./3315d247848798770d0f3c21a86f1dd8c6d837e1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:9.215ex; height:7.343ex;" alt="{\displaystyle \sum _{i=0}^{k}G(q_{i})}" loading="lazy">(see figure 2). It is clear that the area will not change, so <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=0}^{k}H(p_{i})=\sum _{i=0}^{k}G(q_{i})}">

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<annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{k}H(p_{i})=\sum _{i=0}^{k}G(q_{i})}</annotation>

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From the uniform distribution, the probability of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q_{i}}">

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</math><img src="./2752dcbff884354069fe332b8e51eb0a70a531b6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.837ex; height:2.009ex;" alt="{\displaystyle q_{i}}" loading="lazy"> is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {N^{2}}{q_{k}-q_{0}}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\tfrac {N^{2}}{q_{k}-q_{0}}}}</annotation>

</semantics>

</math><img src="./65ade21483343c9cd5b40ec715577f6d5c16bf9a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:5.272ex; height:4.343ex;" alt="{\displaystyle {\tfrac {N^{2}}{q_{k}-q_{0}}}}" loading="lazy"> while the <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0<i<k}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 0<i<k}</annotation>

</semantics>

</math><img src="./a10b8f01bb97f7dc0f56d3f67f22c83944b2464b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.373ex; height:2.176ex;" alt="{\displaystyle 0<i<k}" loading="lazy">

In continuous time, the equation is <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \displaystyle \int _{q_{0}}^{q}{\tfrac {N^{2}}{q_{k}-q_{0}}}ds=\displaystyle \int _{p_{0}}^{p}H(s)ds}">

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</msubsup>

<mfrac>

<msup>

</mrow>

</msup>

<mrow>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mstyle>

</mrow>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</msubsup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \displaystyle \int _{q_{0}}^{q}{\tfrac {N^{2}}{q_{k}-q_{0}}}ds=\displaystyle \int _{p_{0}}^{p}H(s)ds}</annotation>

</semantics>

</math><img src="./13b3fefe6b5ce78e6247284089d22f16c60fc7b7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:25.697ex; height:6.343ex;" alt="{\displaystyle \displaystyle \int _{q_{0}}^{q}{\tfrac {N^{2}}{q_{k}-q_{0}}}ds=\displaystyle \int _{p_{0}}^{p}H(s)ds}" loading="lazy">.

Moreover, based on the definition of a function, the Gray level histogram method is like finding a function <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f}</annotation>

</semantics>

</math><img src="./132e57acb643253e7810ee9702d9581f159a1c61.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" loading="lazy"> that satisfies f(p)=q.

<th>Improvement method

</th>

<th>Issue

</th>

<th>Before improvement

</th>

<th>Process

</th>

<th>After improvement

</th></tr>

<tr>

<td>Smoothing method

</td>

<td>noise

with Matlab, salt & pepper with 0.01 parameter is added to the original image in order to create a noisy image.

</td>

<td>

</td>

<td>

<ol><li>read image and convert image into grayscale</li>

<li>convolution the grayscale image with the mask <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{bmatrix}1/9&1/9&1/9\\1/9&1/9&1/9\\1/9&1/9&1/9\end{bmatrix}}}">

<mrow>

<mtr>

<mtd>

</mrow>

</mtd>

<mtd>

</mrow>

</mtd>

<mtd>

</mrow>

</mtd>

</mtr>

<mtr>

<mtd>

</mrow>

</mtd>

<mtd>

</mrow>

</mtd>

<mtd>

</mrow>

</mtd>

</mtr>

<mtr>

<mtd>

</mrow>

</mtd>

<mtd>

</mrow>

</mtd>

<mtd>

</mrow>

</mtd>

</mtr>

</mtable>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}1/9&1/9&1/9\\1/9&1/9&1/9\\1/9&1/9&1/9\end{bmatrix}}}</annotation>

</semantics>

</math><img src="./9a61c215b24aa9c824f9615efbedb4edf03ab15c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:18.959ex; height:9.843ex;" alt="{\displaystyle {\begin{bmatrix}1/9&1/9&1/9\\1/9&1/9&1/9\\1/9&1/9&1/9\end{bmatrix}}}" loading="lazy"></li>

<li>denoisy image will be the result of step 2.</li></ol>

</td>

<td>

</td></tr>

<tr>

<td>Histogram Equalization

</td>

<td>Gray level distribution too centralized

</td>

<td>

</td>

<td>Refer to the <a href="Histogram_equalization" title="Histogram equalization">Histogram equalization</a>

</td>

<td>

</td></tr>

</tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Challenges">Challenges</h2></div>

<ol><li>Noise and <a href="Distortion" title="Distortion">Distortions</a>: Imperfections in images due to poor lighting, limited sensors, and file compression can result in unclear images that impact accurate image conversion.</li>

<li>Variability in Image Quality: Variations in image quality and resolution, including blurry images and incomplete details, can hinder uniform processing across a database.</li>

<li><a href="Object_detection" title="Object detection">Object Detection</a> and Recognition: Identifying and recognising objects within images, especially in complex scenarios with multiple objects and occlusions, poses a significant challenge.</li>

<li>Data Annotation and Labelling: Labelling diverse and multiple images for machine recognition is crucial for further processing accuracy, as incorrect identification can lead to unrealistic results.</li>

<li>Computational <a href="Resource_intensity" title="Resource intensity">Resource Intensity</a>: Accessing adequate computational resources for image processing can be challenging and costly, hindering progress without sufficient resources.</li></ol>

/* start https://en.wikipedia.org/ */

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</style><div class="div-col" style="column-width: 30em;">

<ul><li><a href="Digital_imaging" title="Digital imaging">Digital imaging</a></li>

<li><a href="Computer_graphics" title="Computer graphics">Computer graphics</a></li>

<li><a href="Computer_vision" title="Computer vision">Computer vision</a></li>

<li><a href="CVIPtools" title="CVIPtools">CVIPtools</a></li>

<li><a href="Digitizing" class="mw-redirect" title="Digitizing">Digitizing</a></li>

<li><a href="Fourier_transform" title="Fourier transform">Fourier transform</a></li>

<li><a href="Free_boundary_condition" title="Free boundary condition">Free boundary condition</a></li>

<li><a href="GPGPU" class="mw-redirect" title="GPGPU">GPGPU</a></li>

<li><a href="Homomorphic_filtering" title="Homomorphic filtering">Homomorphic filtering</a></li>

<li><a href="Image_analysis" title="Image analysis">Image analysis</a></li>

<li><a href="IEEE_Intelligent_Transportation_Systems_Society" class="mw-redirect" title="IEEE Intelligent Transportation Systems Society">IEEE Intelligent Transportation Systems Society</a></li>

<li><a href="Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li>

<li><a href="Medical_imaging" title="Medical imaging">Medical imaging</a></li>

<li><a href="Multidimensional_systems" class="mw-redirect" title="Multidimensional systems">Multidimensional systems</a></li>

<li><a href="Relaxation_labelling" title="Relaxation labelling">Relaxation labelling</a></li>

<li><a href="Remote_sensing_software" title="Remote sensing software">Remote sensing software</a></li>

<li><a href="Standard_test_image" title="Standard test image">Standard test image</a></li>

<li><a href="Superresolution" class="mw-redirect" title="Superresolution">Superresolution</a></li>

<li><a href="Total_variation_denoising" title="Total variation denoising">Total variation denoising</a></li>

<li><a href="Machine_Vision" class="mw-redirect" title="Machine Vision">Machine Vision</a></li>

<li><a href="Bounded_variation" title="Bounded variation">Bounded variation</a></li>

<li><a href="Radiomics" title="Radiomics">Radiomics</a></li>

<li><a href="Remote_sensing" title="Remote sensing">Remote sensing</a></li></ul></div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFSolomon,_C.J.Breckon,_T.P.2010" class="citation book cs1">Solomon, C.J.; Breckon, T.P. (2010). Fundamentals of Digital Image Processing: A Practical Approach with Examples in Matlab. Wiley-Blackwell. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F9780470689776">10.1002/9780470689776</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-470-84473-1</bdi>.</cite></li>

<li><cite id="CITEREFWilhelm_BurgerMark_J._Burge2007" class="citation book cs1">Wilhelm Burger; Mark J. Burge (2007). <a rel="nofollow" class="external text" href="http://www.imagingbook.com/">Digital Image Processing: An Algorithmic Approach Using Java</a>. <a href="Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-84628-379-6</bdi>.</cite></li>

<li><cite id="CITEREFR._FisherK_Dawson-HoweA._FitzgibbonC._Robertson2005" class="citation book cs1">R. Fisher; K Dawson-Howe; A. Fitzgibbon; C. Robertson; E. Trucco (2005). Dictionary of Computer Vision and Image Processing. John Wiley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-470-01526-1</bdi>.</cite></li>

<li><cite id="CITEREFRafael_C._GonzalezRichard_E._WoodsSteven_L._Eddins2004" class="citation book cs1">Rafael C. Gonzalez; Richard E. Woods; Steven L. Eddins (2004). Digital Image Processing using MATLAB. Pearson Education. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-81-7758-898-9</bdi>.</cite></li>

<li><cite id="CITEREFTim_Morris2004" class="citation book cs1">Tim Morris (2004). Computer Vision and Image Processing. Palgrave Macmillan. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-333-99451-1</bdi>.</cite></li>

<li><cite id="CITEREFVipin_Tyagi2018" class="citation book cs1">Vipin Tyagi (2018). Understanding Digital Image Processing. Taylor and Francis CRC Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-11-3856-6842</bdi>.</cite></li>

<li><cite id="CITEREFMilan_SonkaVaclav_HlavacRoger_Boyle1999" class="citation book cs1">Milan Sonka; Vaclav Hlavac; Roger Boyle (1999). Image Processing, Analysis, and Machine Vision. PWS Publishing. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-534-95393-5</bdi>.</cite></li>

<li><cite id="CITEREFGonzalezWoods2008" class="citation book cs1">Gonzalez, Rafael C.; Woods, Richard E. (2008). Digital image processing. Upper Saddle River, N.J.: Prentice Hall. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-13-168728-8</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/137312858">137312858</a>.</cite></li>

<li><cite id="CITEREFKovalevsky2019" class="citation book cs1">Kovalevsky, Vladimir (2019). Modern algorithms for image processing: computer imagery by example using C#. [New York, New York]. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4842-4237-7</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1080084533">1080084533</a>.</cite><code class="cs1-code">{{cite book}}</code>: CS1 maint: location missing publisher (link)</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://archive.org/details/Lectures_on_Image_Processing">Lectures on Image Processing</a>, by Alan Peters. Vanderbilt University. Updated 7 January 2016.</li>

<li><a rel="nofollow" class="external text" href="http://www.mathworks.com/discovery/digital-image-processing.html">Processing digital images with computer algorithms</a></li>

<li><a rel="nofollow" class="external text" href="https://www.informatika.web.id/2013/10/pengertian-citra-digital-pemahaman.html">Pengertian Citra Digital: Pemahaman Dasar dan Penerapannya dalam Teknologi</a></li></ul>

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</style><div id="Computer_vision148" style="font-size:114%;margin:0 4em"><a href="Computer_vision" title="Computer vision">Computer vision</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Categories</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>Datasets</li>

<li><a href="Digital_geometry" title="Digital geometry">Digital geometry</a></li>

<li>Commercial systems</li>

<li>Feature detection</li>

<li>Geometry</li>

<li>Image sensor technology</li>

<li>Learning</li>

<li><a href="Mathematical_morphology" title="Mathematical morphology">Morphology</a></li>

<li>Motion analysis</li>

<li>Noise reduction techniques</li>

<li>Recognition and categorization</li>

<li>Research infrastructure</li>

<li>Researchers</li>

<li>Segmentation</li>

<li>Software</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technologies</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Computer_stereo_vision" title="Computer stereo vision">Computer stereo vision</a></li>

<li><a href="Motion_capture" title="Motion capture">Motion capture</a></li>

<li><a href="Outline_of_object_recognition" title="Outline of object recognition">Object recognition</a>

<ul><li><a href="3D_object_recognition" title="3D object recognition">3D object recognition</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="3D_reconstruction21" scope="row" class="navbox-group" style="width:1%"><a href="3D_reconstruction" title="3D reconstruction">3D reconstruction</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="3D_reconstruction_from_multiple_images" title="3D reconstruction from multiple images">3D reconstruction from multiple images</a></li>

<li><a href="2D_to_3D_conversion" title="2D to 3D conversion">2D to 3D conversion</a></li>

<li><a href="Gaussian_splatting" title="Gaussian splatting">Gaussian splatting</a></li>

<li><a href="Neural_radiance_field" title="Neural radiance field">Neural radiance field</a></li>

<li><a href="Shape_from_focus" title="Shape from focus">Shape from focus</a></li>

<li><a href="Simultaneous_localization_and_mapping" title="Simultaneous localization and mapping">Simultaneous localization and mapping</a></li>

<li><a href="Structure_from_motion" title="Structure from motion">Structure from motion</a></li>

<li><a href="View_synthesis" title="View synthesis">View synthesis</a></li>

<li><a href="Visual_hull" title="Visual hull">Visual hull</a></li>

<li><a href="4D_reconstruction" title="4D reconstruction">4D reconstruction</a>

<ul><li><a href="Free_viewpoint_television" title="Free viewpoint television">Free viewpoint television</a></li>

<li><a href="Volumetric_capture" title="Volumetric capture">Volumetric capture</a></li></ul></li></ul>

</div></td></tr></tbody></table><div>

<ul><li><a href="3D_pose_estimation" title="3D pose estimation">3D pose estimation</a></li>

<li><a href="Activity_recognition" title="Activity recognition">Activity recognition</a></li>

<li><a href="Audio-visual_speech_recognition" title="Audio-visual speech recognition">Audio-visual speech recognition</a></li>

<li><a href="Automatic_image_annotation" title="Automatic image annotation">Automatic image annotation</a></li>

<li><a href="Automatic_number-plate_recognition" title="Automatic number-plate recognition">Automatic number-plate recognition</a></li>

<li><a href="Automated_species_identification" title="Automated species identification">Automated species identification</a></li>

<li><a href="Augmented_reality" title="Augmented reality">Augmented reality</a></li>

<li><a href="Bioimage_informatics" title="Bioimage informatics">Bioimage informatics</a></li>

<li><a href="Blob_detection" title="Blob detection">Blob detection</a></li>

<li><a href="Computer-aided_diagnosis" title="Computer-aided diagnosis">Computer-aided diagnosis</a></li>

<li><a href="Content-based_image_retrieval" title="Content-based image retrieval">Content-based image retrieval</a>

<ul><li><a href="Reverse_image_search" title="Reverse image search">Reverse image search</a></li></ul></li>

<li><a href="Eye_tracking" title="Eye tracking">Eye tracking</a></li>

<li><a href="Facial_recognition_system" title="Facial recognition system">Face recognition</a></li>

<li><a href="Foreground_detection" title="Foreground detection">Foreground detection</a></li>

<li><a href="Gesture_recognition" title="Gesture recognition">Gesture recognition</a></li>

<li><a href="Image_denoising" class="mw-redirect" title="Image denoising">Image denoising</a></li>

<li><a href="Image_restoration_by_artificial_intelligence" title="Image restoration by artificial intelligence">Image restoration</a></li>

<li><a href="Landmark_detection" title="Landmark detection">Landmark detection</a></li>

<li><a href="Medical_image_computing" title="Medical image computing">Medical image computing</a></li>

<li><a href="Object_detection" title="Object detection">Object detection</a>

<ul><li><a href="Moving_object_detection" title="Moving object detection">Moving object detection</a></li>

<li><a href="Small_object_detection" title="Small object detection">Small object detection</a></li></ul></li>

<li><a href="Optical_character_recognition" title="Optical character recognition">Optical character recognition</a></li>

<li><a href="Pose_tracking" title="Pose tracking">Pose tracking</a></li>

<li><a href="Remote_sensing" title="Remote sensing">Remote sensing</a></li>

<li><a href="Robotic_mapping" title="Robotic mapping">Robotic mapping</a></li>

<li><a href="Self-driving_car" title="Self-driving car">Autonomous vehicles</a></li>

<li><a href="Video_content_analysis" title="Video content analysis">Video content analysis</a></li>

<li><a href="Video_motion_analysis" title="Video motion analysis">Video motion analysis</a></li>

<li><a href="Artificial_intelligence_for_video_surveillance" title="Artificial intelligence for video surveillance">Video surveillance</a></li>

<li><a href="Video_tracking" title="Video tracking">Video tracking</a></li></ul></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>Main category</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Digital_signal_processing96" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Digital_signal_processing96" style="font-size:114%;margin:0 4em"><a href="Digital_signal_processing" title="Digital signal processing">Digital signal processing</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Detection_theory" title="Detection theory">Detection theory</a></li>

<li><a href="Discrete_time_and_continuous_time" title="Discrete time and continuous time">Discrete signal</a></li>

<li><a href="Estimation_theory" title="Estimation theory">Estimation theory</a></li>

<li><a href="Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon sampling theorem</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sub-fields</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Audio_signal_processing" title="Audio signal processing">Audio signal processing</a></li>

<li><a href="Speech_processing" title="Speech processing">Speech processing</a></li>

<li><a href="Statistical_signal_processing" class="mw-redirect" title="Statistical signal processing">Statistical signal processing</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Techniques</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Z-transform" title="Z-transform">Z-transform</a>

<ul><li><a href="Advanced_z-transform" title="Advanced z-transform">Advanced z-transform</a></li>

<li><a href="Matched_Z-transform_method" title="Matched Z-transform method">Matched Z-transform method</a></li></ul></li>

<li><a href="Bilinear_transform" title="Bilinear transform">Bilinear transform</a></li>

<li><a href="Constant-Q_transform" title="Constant-Q transform">Constant-Q transform</a></li>

<li><a href="Discrete_cosine_transform" title="Discrete cosine transform">Discrete cosine transform</a> (DCT)</li>

<li><a href="Discrete_Fourier_transform" title="Discrete Fourier transform">Discrete Fourier transform</a> (DFT)</li>

<li><a href="Discrete-time_Fourier_transform" title="Discrete-time Fourier transform">Discrete-time Fourier transform</a> (DTFT)</li>

<li><a href="Impulse_invariance" title="Impulse invariance">Impulse invariance</a></li>

<li><a href="Integral_transform" title="Integral transform">Integral transform</a></li>

<li><a href="Laplace_transform" title="Laplace transform">Laplace transform</a></li>

<li><a href="Post's_inversion_formula" class="mw-redirect" title="Post's inversion formula">Post's inversion formula</a></li>

<li><a href="Starred_transform" title="Starred transform">Starred transform</a></li>

<li><a href="Zak_transform" title="Zak transform">Zak transform</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Sampling_(signal_processing)" title="Sampling (signal processing)">Sampling</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aliasing" title="Aliasing">Aliasing</a></li>

<li><a href="Anti-aliasing_filter" title="Anti-aliasing filter">Anti-aliasing filter</a></li>

<li><a href="Downsampling_(signal_processing)" title="Downsampling (signal processing)">Downsampling</a></li>

<li><a href="Nyquist_rate" title="Nyquist rate">Nyquist rate</a> / <a href="Nyquist_frequency" title="Nyquist frequency">frequency</a></li>

<li><a href="Oversampling" title="Oversampling">Oversampling</a></li>

<li><a href="Quantization_(signal_processing)" title="Quantization (signal processing)">Quantization</a></li>

<li><a href="Sampling_rate" class="mw-redirect" title="Sampling rate">Sampling rate</a></li>

<li><a href="Undersampling" title="Undersampling">Undersampling</a></li>

<li><a href="Upsampling" title="Upsampling">Upsampling</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Information_processing141" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Information_processing141" style="font-size:114%;margin:0 4em"><a href="Information_technology" title="Information technology">Information processing</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Information processes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">information processes by function</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Perception" title="Perception">perception</a></li>

<li><a href="Attention" title="Attention">attention</a></li>

<li><a href="Social_influence" title="Social influence">influence</a></li>

<li><a href="Remote_control" title="Remote control">operating</a></li>

<li><a href="Communication" title="Communication">communication</a></li>

<li><a href="Reason" title="Reason">reasoning</a></li>

<li><a href="Learning" title="Learning">learning</a></li>

<li><a href="Information_storage" class="mw-redirect" title="Information storage">storing</a></li>

<li><a href="Decision-making" title="Decision-making">decision-making</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">information processing abstractions</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Event_processing" class="mw-redirect" title="Event processing">event processing</a></li>

<li><a href="Semiotics" title="Semiotics">sign processesing</a></li>

<li><a href="Signal" title="Signal">signal processing</a></li>

<li><a href="Data_processing" title="Data processing">data processing</a></li>

<li><a href="Stream_processing" title="Stream processing">stream processing</a></li>

<li><a href="Multi-agent_system" title="Multi-agent system">agent processing</a></li>

<li><a href="State_(computer_science)" title="State (computer science)">state processing</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Information processors</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">natural</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Natural_computing#Nature_as_information_processing" title="Natural computing">nature as information processing</a></li>

<li><a href="Information_processing_theory#Humans_as_Information_Processing_Systems" title="Information processing theory">humans as information processing systems</a></li>

<li><a href="Social_information_processing" title="Social information processing">society as information processing system</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">mixed</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mixed_reality" class="mw-redirect" title="Mixed reality">mixed reality</a></li>

<li><a href="Brain%E2%80%93computer_interface" title="Brain–computer interface">brain–computer interface</a></li>

<li><a href="Physical_computing" title="Physical computing">physical computing</a></li>

<li><a href="Human%E2%80%93computer_interaction" title="Human–computer interaction">human–computer interaction</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">artificial</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Processor_(computing)" title="Processor (computing)">processors</a> and <a href="Process_(computing)" title="Process (computing)">processes</a></li>

<li><a href="Bio-inspired_computing" title="Bio-inspired computing">bio-inspired computing</a></li>

<li><a href="Ubiquitous_computing" title="Ubiquitous computing">ubiquitous computing</a></li>

<li><a href="Artificial_brain" title="Artificial brain">artificial brain</a> and <a href="Mind_uploading" title="Mind uploading">mind uploading</a></li>

<li><a href="Virtual_reality" title="Virtual reality">virtual reality</a></li>

<li><a href="Virtual_world" title="Virtual world">virtual world</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Information processing theories and concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">in biology</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Computational_biology" title="Computational biology">computational</a> and <a href="Systems_biology" title="Systems biology">systems biology</a></li>

<li><a href="Genome_informatics" title="Genome informatics">genetic informatics</a> and <a href="Cellular_computing" class="mw-redirect" title="Cellular computing">cellular computing</a></li>

<li><a href="Computational_neuroscience" title="Computational neuroscience">computational neuroscience</a> and <a href="Neurocomputing" class="mw-redirect" title="Neurocomputing">neurocomputing</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">in cognitive psychology</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Information_processing_theory" title="Information processing theory">information processing theory</a></li>

<li><a href="Mind" title="Mind">mind</a> and <a href="Intelligence" title="Intelligence">intelligence</a></li>

<li><a href="Cognitive_informatics" class="mw-redirect" title="Cognitive informatics">cognitive informatics</a> and <a href="Neuroinformatics" title="Neuroinformatics">neuroinformatics</a></li>

<li><a href="Behavior_informatics" title="Behavior informatics">behavior informatics</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">in computer science</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Neural_computation" title="Neural computation">neural computation</a></li>

<li><a href="Theory_of_computation" title="Theory of computation">computation theory</a></li>

<li><a href="Algorithms" class="mw-redirect" title="Algorithms">algorithms</a> and <a href="Information_structure" title="Information structure">information structures</a></li>

<li><a href="Circuit_(computer_science)" title="Circuit (computer science)">computational circuits</a></li>

<li><a href="Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">in philosophy</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Computational_theory_of_mind" title="Computational theory of mind">computational theory of mind</a></li>

<li><a href="Philosophy_of_information" title="Philosophy of information">philosophy of information</a></li>

<li><a href="Philosophy_of_artificial_intelligence" title="Philosophy of artificial intelligence">philosophy of artificial intelligence</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">interdisciplinary</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Information_theory" title="Information theory">information theory</a></li>

<li><a href="Decision_theory" title="Decision theory">decision theory</a></li>

<li><a href="Systems_theory" title="Systems theory">systems theory</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Infosphere" title="Infosphere">infosphere</a></li>

<li><a href="Inforg" title="Inforg">inforg</a></li>

<li><a href="Decoding_the_Universe" title="Decoding the Universe">Decoding the Universe</a></li>

<li><a href="Information_overload" title="Information overload">information overload</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table></div>

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