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<title>Contextual image classification</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Contextual image classification</span></span>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>Contextual image classification</b>, a topic of <a href="Pattern_recognition" title="Pattern recognition">pattern recognition</a> in <a href="Computer_vision" title="Computer vision">computer vision</a>, is an approach of <a href="Classification_in_machine_learning" class="mw-redirect" title="Classification in machine learning">classification</a> based on contextual information in images. "Contextual" means this approach is focusing on the relationship of the nearby pixels, which is also called neighbourhood. The goal of this approach is to classify the images by using the contextual information.

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

<p>Similar as <a href="Natural_language_processing" title="Natural language processing">processing language</a>, a single word may have multiple meanings unless the context is provided, and the patterns within the sentences are the only informative segments we care about. For images, the principle is same. Find out the patterns and associate proper meanings to them.

</p><p>As the image illustrated below, if only a small portion of the image is shown, it is very difficult to tell what the image is about.

</p>

<p>Even try another portion of the image, it is still difficult to classify the image.

</p>

<p>However, if we increase the contextual of the image, then it makes more sense to recognize.

</p>

<p>As the full images shows below, almost everyone can classify it easily.

</p>

<p>During the procedure of <a href="Segmentation_(image_processing)" class="mw-redirect" title="Segmentation (image processing)">segmentation</a>, the methods which do not use the contextual information are sensitive to noise and variations, thus the result of segmentation will contain a great deal of misclassified regions, and often these regions are small (e.g., one pixel).

</p><p>Compared to other techniques, this approach is robust to noise and substantial variations for it takes the continuity of the segments into account.

</p><p>Several methods of this approach will be described below.

</p>

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

<div class="mw-heading mw-heading3"><h3 id="Functioning_as_a_post-processing_filter_to_a_labelled_image">Functioning as a post-processing filter to a labelled image</h3></div>

<p>This approach is very effective against small regions caused by noise. And these small regions are usually formed by few pixels or one pixel. The most probable label is assigned to these regions.

However, there is a drawback of this method. The small regions also can be formed by correct regions rather than noise, and in this case the method is actually making the classification worse.

This approach is widely used in <a href="Remote_sensing" title="Remote sensing">remote sensing</a> applications.

</p>

<div class="mw-heading mw-heading3"><h3 id="Improving_the_post-processing_classification">Improving the post-processing classification</h3></div>

<p>This is a two-stage classification process:

</p>

<ol><li>For each pixel, label the pixel and form a new feature vector for it.</li>

<li>Use the new feature vector and combine the contextual information to assign the final label to the</li></ol>

<div class="mw-heading mw-heading3"><h3 id="Merging_the_pixels_in_earlier_stages">Merging the pixels in earlier stages</h3></div>

<p>Instead of using single pixels, the neighbour pixels can be merged into homogeneous regions benefiting from contextual information. And provide these regions to classifier.

</p>

<div class="mw-heading mw-heading3"><h3 id="Acquiring_pixel_feature_from_neighbourhood">Acquiring pixel feature from neighbourhood</h3></div>

<p>The original spectral data can be enriched by adding the contextual information carried by the neighbour pixels, or even replaced in some occasions. This kind of pre-processing methods are widely used in <a href="Image_texture" title="Image texture">textured image</a> recognition. The typical approaches include mean values, variances, texture description, etc.

</p>

<div class="mw-heading mw-heading3"><h3 id="Combining_spectral_and_spatial_information">Combining spectral and spatial information</h3></div>

<p>The classifier uses the grey level and pixel neighbourhood (contextual information) to assign labels to pixels. In such case the information is a combination of spectral and spatial information.

</p>

<div class="mw-heading mw-heading3"><h3 id="Powered_by_the_Bayes_minimum_error_classifier">Powered by the Bayes minimum error classifier</h3></div>

<p>Contextual classification of image data is based on the Bayes minimum error classifier (also known as a <a href="Naive_Bayes_classifier" title="Naive Bayes classifier">naive Bayes classifier</a>).

</p><p><b>Present the pixel</b>:

</p>

<ul><li>A pixel is denoted as <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}">

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

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</math></span><img src="./86f21d0e31751534cd6584264ecf864a6aa792cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{0}}" loading="lazy"></span>.</li>

<li>The neighbourhood of each pixel <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}">

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

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</math></span><img src="./86f21d0e31751534cd6584264ecf864a6aa792cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{0}}" loading="lazy"></span> is a vector and denoted as <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N(x_{0})}">

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<annotation encoding="application/x-tex">{\displaystyle N(x_{0})}</annotation>

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</math></span><img src="./89ff7fe54b4fdb317feda7fe2d6e8b3da36f5df3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.257ex; height:2.843ex;" alt="{\displaystyle N(x_{0})}" loading="lazy"></span>.

<ul><li>The values in the neighbourhood vector is denoted as <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x_{i})}">

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

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</math></span><img src="./77bf16c9153b454dbdec165ad8160083202d7f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.217ex; height:2.843ex;" alt="{\displaystyle f(x_{i})}" loading="lazy"></span>.</li>

<li>Each pixel is presented by the vector</li></ul></li></ul>

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<annotation encoding="application/x-tex">{\displaystyle \xi =\left(f(x_{0}),f(x_{1}),\ldots ,f(x_{k})\right)}</annotation>

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</math></span><img src="./4cc7ca766cbbcdd03e871d44fc244439595238b7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.6ex; height:2.843ex;" alt="{\displaystyle \xi =\left(f(x_{0}),f(x_{1}),\ldots ,f(x_{k})\right)}" loading="lazy"></span></dd>

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<annotation encoding="application/x-tex">{\displaystyle x_{i}\in N(x_{0});\quad i=1,\ldots ,k}</annotation>

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</math></span><img src="./55296af153c897ca23c529c579588c279be29028.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.036ex; height:2.843ex;" alt="{\displaystyle x_{i}\in N(x_{0});\quad i=1,\ldots ,k}" loading="lazy"></span></dd></dl></dd></dl></dd></dl>

<ul><li>The labels (classification) of pixels in the neighbourhood <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N(x_{0})}">

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<annotation encoding="application/x-tex">{\displaystyle N(x_{0})}</annotation>

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</math></span><img src="./89ff7fe54b4fdb317feda7fe2d6e8b3da36f5df3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.257ex; height:2.843ex;" alt="{\displaystyle N(x_{0})}" loading="lazy"></span> are presented as a vector</li></ul>

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<annotation encoding="application/x-tex">{\displaystyle \eta =\left(\theta _{0},\theta _{1},\ldots ,\theta _{k}\right)}</annotation>

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</math></span><img src="./f1797c33abdd09d41de368fb99c160c4cfcd3135.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.758ex; height:2.843ex;" alt="{\displaystyle \eta =\left(\theta _{0},\theta _{1},\ldots ,\theta _{k}\right)}" loading="lazy"></span></dd>

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<annotation encoding="application/x-tex">{\displaystyle \theta _{i}\in \left\{\omega _{0},\omega _{1},\ldots ,\omega _{k}\right\}}</annotation>

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</math></span><img src="./4e6bf8f9c5f38b834734864a42ffb402ebb1a685.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.802ex; height:2.843ex;" alt="{\displaystyle \theta _{i}\in \left\{\omega _{0},\omega _{1},\ldots ,\omega _{k}\right\}}" loading="lazy"></span></dd>

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<annotation encoding="application/x-tex">{\displaystyle \omega _{s}}</annotation>

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</math></span><img src="./f9458d02624326fd1e59de34085a48f2167481b9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle \omega _{s}}" loading="lazy"></span> here denotes the assigned class.</dd></dl></dd></dl>

<ul><li>A vector presents the labels in the neighbourhood <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N(x_{0})}">

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<annotation encoding="application/x-tex">{\displaystyle N(x_{0})}</annotation>

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</math></span><img src="./89ff7fe54b4fdb317feda7fe2d6e8b3da36f5df3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.257ex; height:2.843ex;" alt="{\displaystyle N(x_{0})}" loading="lazy"></span> without the pixel <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}">

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

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</math></span><img src="./86f21d0e31751534cd6584264ecf864a6aa792cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{0}}" loading="lazy"></span></li></ul>

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<annotation encoding="application/x-tex">{\displaystyle {\hat {\eta }}=\left(\theta _{1},\theta _{2},\ldots ,\theta _{k}\right)}</annotation>

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</math></span><img src="./4ffd14faf700773c66024e5911c26c2e48d47b67.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.893ex; height:2.843ex;" alt="{\displaystyle {\hat {\eta }}=\left(\theta _{1},\theta _{2},\ldots ,\theta _{k}\right)}" loading="lazy"></span></dd></dl></dd></dl>

<p><b>The neighbourhood</b>:

Size of the neighbourhood. There is no limitation of the size, but it is considered to be relatively small for each pixel <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}">

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

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</math></span><img src="./86f21d0e31751534cd6584264ecf864a6aa792cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{0}}" loading="lazy"></span>.

A reasonable size of neighbourhood would be <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3\times 3}">

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</math></span><img src="./ddc0d4d6106875f8006be1d898512ca5843bad8e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.165ex; height:2.176ex;" alt="{\displaystyle 3\times 3}" loading="lazy"></span> of 4-<a href="Connectedness" title="Connectedness">connectivity</a> or 8-connectivity (<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}">

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<div class="gallerytext"><a href="4-connected_graph" class="mw-redirect" title="4-connected graph">4-connectivity</a> neighbourhood, </div>

</li>

<div class="gallerytext"><a href="8-connectivity" class="mw-redirect" title="8-connectivity">8-connectivity</a> neighbourhood</div>

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<p><b>The calculation</b>:

</p><p>Apply the minimum error classification on a pixel <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}">

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

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</math></span><img src="./86f21d0e31751534cd6584264ecf864a6aa792cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{0}}" loading="lazy"></span>, if the probability of a class <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{r}}">

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<annotation encoding="application/x-tex">{\displaystyle \omega _{r}}</annotation>

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</math></span><img src="./fcf70e3a6975ab8aaaa19a091ec2cdb04d299a3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.42ex; height:2.009ex;" alt="{\displaystyle \omega _{r}}" loading="lazy"></span> being presenting the pixel <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}">

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</math></span><img src="./86f21d0e31751534cd6584264ecf864a6aa792cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{0}}" loading="lazy"></span> is the highest among all, then assign <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{r}}">

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<annotation encoding="application/x-tex">{\displaystyle \omega _{r}}</annotation>

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</math></span><img src="./fcf70e3a6975ab8aaaa19a091ec2cdb04d299a3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.42ex; height:2.009ex;" alt="{\displaystyle \omega _{r}}" loading="lazy"></span> as its class.

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<annotation encoding="application/x-tex">{\displaystyle \theta _{0}=\omega _{r}\quad {\text{ if }}\quad P(\omega _{r}\mid f(x_{0}))=\max _{s=1,2,\ldots ,R}P(\omega _{s}\mid f(x_{0}))}</annotation>

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</math></span><img src="./6dad6745638a00cd0427399abb23c035d3b3804d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:53.348ex; height:4.343ex;" alt="{\displaystyle \theta _{0}=\omega _{r}\quad {\text{ if }}\quad P(\omega _{r}\mid f(x_{0}))=\max _{s=1,2,\ldots ,R}P(\omega _{s}\mid f(x_{0}))}" loading="lazy"></span></dd></dl>

<p>The contextual classification rule is described as below, it uses the feature vector <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1}}">

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</math></span><img src="./a8788bf85d532fa88d1fb25eff6ae382a601c308.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{1}}" loading="lazy"></span> rather than <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}">

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<annotation encoding="application/x-tex">{\displaystyle \theta _{0}=\omega _{r}\quad {\text{ if }}\quad P(\omega _{r}\mid \xi )=\max _{s=1,2,\ldots ,R}P(\omega _{s}\mid \xi )}</annotation>

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</math></span><img src="./dcdb0d0645aef1834fe34342402d1f6fe3dc50f1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.465ex; height:4.343ex;" alt="{\displaystyle \theta _{0}=\omega _{r}\quad {\text{ if }}\quad P(\omega _{r}\mid \xi )=\max _{s=1,2,\ldots ,R}P(\omega _{s}\mid \xi )}" loading="lazy"></span></dd></dl>

<p>Use the Bayes formula to calculate the posteriori probability <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(\omega _{s}\mid \xi )}">

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<annotation encoding="application/x-tex">{\displaystyle P(\omega _{s}\mid \xi )}</annotation>

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</math></span><img src="./246c4c14da84fb506006c32ad163a5c743a3b087.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.971ex; height:2.843ex;" alt="{\displaystyle P(\omega _{s}\mid \xi )}" loading="lazy"></span>

</p>

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</msub>

<mfrac>

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</mfrac>

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<annotation encoding="application/x-tex">{\displaystyle P(\omega _{s}\mid \xi )={\frac {p(\xi \mid \omega _{s})P(\omega _{s})}{p\left(\xi \right)}}}</annotation>

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</math></span><img src="./8b5b5d0f466b7f5ad0163570b65a427671edfdae.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:27.305ex; height:6.509ex;" alt="{\displaystyle P(\omega _{s}\mid \xi )={\frac {p(\xi \mid \omega _{s})P(\omega _{s})}{p\left(\xi \right)}}}" loading="lazy"></span></dd></dl>

<p>The number of vectors is the same as the number of pixels in the image. For the classifier uses a vector corresponding to each pixel <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}}">

<msub>

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

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</math></span><img src="./e87000dd6142b81d041896a30fe58f0c3acb2158.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle x_{i}}" loading="lazy"></span>, and the vector is generated from the pixel's neighbourhood.

</p><p><b>The basic steps of contextual image classification</b>:

</p>

<ol><li>Calculate the feature vector <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi }">

</mstyle>

</mrow>

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

</semantics>

</math></span><img src="./e0b461aaf61091abd5d2c808931c48b8ff9647db.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }" loading="lazy"></span> for each pixel.</li>

<li>Calculate the parameters of probability distribution <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p(\xi \mid \omega _{s})}">

<msub>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle p(\xi \mid \omega _{s})}</annotation>

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</math></span><img src="./ba5a22d7c47d9dd17de84bdd8db027e40482bf90.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:8.485ex; height:2.843ex;" alt="{\displaystyle p(\xi \mid \omega _{s})}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(\omega _{s})}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P(\omega _{s})}</annotation>

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</math></span><img src="./0285067316556987a44d4732ad11b91ef86d24bc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.004ex; height:2.843ex;" alt="{\displaystyle P(\omega _{s})}" loading="lazy"></span></li>

<li>Calculate the posterior probabilities <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(\omega _{r}\mid \xi )}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P(\omega _{r}\mid \xi )}</annotation>

</semantics>

</math></span><img src="./a42c44fa759689115e83e4674c9e1a0f76d3e00c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.942ex; height:2.843ex;" alt="{\displaystyle P(\omega _{r}\mid \xi )}" loading="lazy"></span> and all labels <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{0}}">

<msub>

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

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</math></span><img src="./18b67de6bf25dba7a24e66967ff6319858798734.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.145ex; height:2.509ex;" alt="{\displaystyle \theta _{0}}" loading="lazy"></span>. Get the image classification result.</li></ol>

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

<div class="mw-heading mw-heading3"><h3 id="Template_matching">Template matching</h3></div>

<p>The <a href="Template_matching" title="Template matching">template matching</a> is a "brute force" implementation of this approach.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The concept is first create a set of templates, and then look for small parts in the image match with a template.

</p><p>This method is computationally high and inefficient. It keeps an entire templates list during the whole process and the number of combinations is extremely high. For a <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m\times n}">

</mstyle>

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

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</math></span><img src="./12b23d207d23dd430b93320539abbb0bde84870d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.276ex; height:1.676ex;" alt="{\displaystyle m\times n}" loading="lazy"></span> pixel image, there could be a maximum of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{m\times n}}">

<msup>

</mrow>

</msup>

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle 2^{m\times n}}</annotation>

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</math></span><img src="./9297b7ff9b714bb2f0f3f8270ff633986de2f748.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.102ex; height:2.343ex;" alt="{\displaystyle 2^{m\times n}}" loading="lazy"></span> combinations, which leads to high computation. This method is a top down method and often called <a href="Lookup_table" title="Lookup table">table look-up</a> or <a href="Data_dictionary" title="Data dictionary">dictionary look-up</a>.

</p>

<div class="mw-heading mw-heading3"><h3 id="Lower-order_Markov_chain">Lower-order Markov chain</h3></div>

<p>The <a href="Markov_chain" title="Markov chain">Markov chain</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> also can be applied in pattern recognition. The pixels in an image can be recognised as a set of random variables, then use the lower order Markov chain to find the relationship among the pixels. The image is treated as a virtual line, and the method uses conditional probability.

</p>

<div class="mw-heading mw-heading3"><h3 id="Hilbert_space-filling_curves">Hilbert space-filling curves</h3></div>

<p>The <a href="Hilbert_curve" title="Hilbert curve">Hilbert curve</a> runs in a unique pattern through the whole image, it traverses every pixel without visiting any of them twice and keeps a continuous curve. It is fast and efficient.

</p>

<div class="mw-heading mw-heading3"><h3 id="Markov_meshes">Markov meshes</h3></div>

<p>The lower-order Markov chain and Hilbert space-filling curves mentioned above are treating the image as a line structure. The Markov meshes however will take the two dimensional information into account.

</p>

<div class="mw-heading mw-heading3"><h3 id="Dependency_tree">Dependency tree</h3></div>

<p>The <a href="Chow%E2%80%93Liu_tree" title="Chow–Liu tree">dependency tree</a><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> is a method using tree dependency to approximate probability distributions.

</p>

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

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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">G.T. Toussaint, "<a rel="nofollow" class="external text" href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.72.5050&rep=rep1&type=pdf">The Use of Context in Pattern Recognition</a>," Pattern Recognition, vol. 10, 1977, pp. 189–204.</span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">K. Abend, T.J. Harley, and L.N. Kanal, "<a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/abstract/document/1053827/">Classification of Binary Random Patterns</a>," IEEE Transactions on Information Theory, vol. 11, no. 4, October 1965, pp. 538–544.</span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">C.K. Chow and C.N. Liu, "<a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.133.9772&rep=rep1&type=pdf">Approximating Discrete Probability Distributions with Dependence Trees</a>," IEEE Transactions on Information Theory, vol.14, no. 3, May 1965, pp. 462–467.</span>

</li>

</ol></div></div>

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

<ul><li><a rel="nofollow" class="external text" href="http://www.inf.ed.ac.uk/teaching/courses/av/index.html">Advanced Vision homepage</a></li>

<li><a rel="nofollow" class="external text" href="http://www.bic.mni.mcgill.ca/~mallar/CS-644B/Intro.html">The Use of Context in Pattern Recognition</a></li>

<li><a rel="nofollow" class="external text" href="http://css.engineering.uiowa.edu/~dip/LECTURE/Understanding4.html">Image Analysis and Understanding: contextual image classification </a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20041210090608/http://css.engineering.uiowa.edu/~dip/LECTURE/Understanding4.html">Archived</a> 2004-12-10 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2023-12-22" href="https://en.wikipedia.org/wiki/?title=Contextual_image_classification&oldid=1191232249">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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