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Balanced histogram thresholding

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In <a href="Image_processing" class="mw-redirect" title="Image processing">image processing</a>, the balanced histogram thresholding method (BHT),<a href="#cite_note-1">[1]</a> is a very simple method used for automatic image <a href="Thresholding_(image_processing)" title="Thresholding (image processing)">thresholding</a>. Like <a href="Otsu's_Method" class="mw-redirect" title="Otsu's Method">Otsu's Method</a><a href="#cite_note-2">[2]</a> and the Iterative Selection Thresholding Method,<a href="#cite_note-3">[3]</a> this is a <a href="Histogram" title="Histogram">histogram</a> based thresholding method. This approach assumes that the image is divided in two main classes: The background and the foreground. The BHT method tries to find the optimum threshold level that divides the histogram in two classes.

This method weighs the histogram, checks which of the two sides is heavier, and removes weight from the heavier side until it becomes the lighter. It repeats the same operation until the edges of the <a href="Weighing_scale" title="Weighing scale">weighing scale</a> meet.

Given its simplicity, this method is a good choice as a first approach when presenting the subject of automatic image thresholding.

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

The following listing, in <a href="C_(programming_language)" title="C (programming language)">C</a> notation, is a simplified version of the Balanced Histogram Thresholding method:

<div class="mw-highlight mw-highlight-lang-c mw-content-ltr" dir="ltr"><pre>int BHThreshold(int[] histogram) {

i_m = (int)((i_s + i_e) / 2.0f); // center of the weighing scale I_m

w_l = get_weight(i_s, i_m + 1, histogram); // weight on the left W_l

w_r = get_weight(i_m + 1, i_e + 1, histogram); // weight on the right W_r

while (i_s <= i_e) {

if (w_r > w_l) { // right side is heavier

w_r -= histogram[i_e--];

if (((i_s + i_e) / 2) < i_m) {

w_r += histogram[i_m];

w_l -= histogram[i_m--];

}

} else if (w_l >= w_r) { // left side is heavier

w_l -= histogram[i_s++];

if (((i_s + i_e) / 2) >= i_m) {

w_l += histogram[i_m + 1];

w_r -= histogram[i_m + 1];

i_m++;

}

return i_m;

}

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The following, is a possible implementation in the <a href="Python_(programming_language)" title="Python (programming language)">Python</a> language:

<div class="mw-highlight mw-highlight-lang-python mw-content-ltr" dir="ltr"><pre>def balanced_histogram_thresholding(histogram, minimum_bin_count: int = 5, jump: int = 1) -> int:

"""

Determines an optimal threshold by balancing the histogram of an image,

focusing on significant histogram bins to segment the image into two parts.

Args:

histogram (list): The histogram of the image as a list of integers,

where each element represents the count of pixels

at a specific intensity level.

minimum_bin_count (int): Minimum count for a bin to be considered in the

thresholding process. Bins with counts below this

value are ignored, reducing the effect of noise.

jump (int): Step size for adjusting the threshold during iteration. Larger values

speed up convergence but may skip the optimal threshold.

Returns:

int: The calculated threshold value. This value represents the intensity level

(i.e. the index of the input histogram) that best separates the significant

parts of the histogram into two groups, which can be interpreted as foreground

and background.

If the function returns -1, it indicates that the algorithm was unable to find

a suitable threshold within the constraints (e.g., all bins are below the

minimum_bin_count).

"""

# Find the start and end indices where the histogram bins are significant

start_index = 0

while start_index < len(histogram) and histogram[start_index] < minimum_bin_count:

start_index += 1

end_index = len(histogram) - 1

while end_index >= 0 and histogram[end_index] < minimum_bin_count:

end_index -= 1

# Check if no valid bins are found

if start_index >= end_index:

return -1 # Indicates an error or non-applicability

# Initialize threshold

threshold = (start_index + end_index) // 2

# Iteratively adjust the threshold

while start_index <= end_index:

# Calculate weights on both sides of the threshold

weight_left = sum(histogram[start_index:threshold])

weight_right = sum(histogram[threshold:end_index + 1])

# Adjust the threshold based on the weights

if weight_left > weight_right:

start_index += jump

elif weight_left < weight_right:

end_index -= jump

else: # Equal weights; move both indices

start_index += jump

end_index -= jump

# Calculate the new threshold

return threshold

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

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<li id="cite_note-1"><a href="#cite_ref-1">^</a> A. Anjos and H. Shahbazkia. Bi-Level Image Thresholding - A Fast Method. BIOSIGNALS 2008. Vol:2. P:70-76.

</li>

<li id="cite_note-2"><a href="#cite_ref-2">^</a> Nobuyuki Otsu (1979). "A threshold selection method from gray-level histograms". IEEE Trans. Sys., Man., Cyber. 9: 62–66.

</li>

<li id="cite_note-3"><a href="#cite_ref-3">^</a> Ridler TW, Calvard S. (1978) Picture thresholding using an iterative selection method, IEEE Trans. System, Man and Cybernetics, SMC-8: 630-632.

</li>

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

<ul><li><a rel="nofollow" class="external text" href="http://w3.ualg.pt/~aanjos/prototype/BHThresholding_.jar">ImageJ Plugin</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131017205614/http://w3.ualg.pt/~aanjos/prototype/BHThresholding_.jar">Archived</a> 2013-10-17 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li>

This article is issued from <a class="external text" title="Last edited on 2025-02-11" href="https://en.wikipedia.org/wiki/?title=Balanced_histogram_thresholding&oldid=1275203927">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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