Balanced histogram thresholding: Difference between revisions

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{{short description|Type of image thresholding}}

In [[image processing]], the '''balanced histogram thresholding method''' (BHT),<ref>A. Anjos and H. Shahbazkia. Bi-Level Image Thresholding - A Fast Method. BIOSIGNALS 2008. Vol:2. P:70-76.</ref>, is a very simple method used for automatic image [[Thresholding (image processing)|thresholding]]. Like [[Otsu's Method]]<ref>Nobuyuki Otsu (1979). "A threshold selection method from gray-level histograms". IEEE Trans. Sys., Man., Cyber. 9: 62–66.</ref> and the '''Iterative Selection ThesholdingThresholding Method''',<ref>Ridler TW, Calvard S. (1978) Picture thresholding using an iterative selection method, IEEE Trans. System, Man and Cybernetics, SMC-8: 630-632.</ref>, this is a [[histogram]] 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.

[[File:Lovely spider.jpeg|thumb | 200px | right | Original image.]]

[[File:Lovely spider BHT.jpeg|thumb | 200px | right | Thresholded image.]]

[[File:BhaProgress3.gif|thumb | 200px | Evolution of the method.]]

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 [[weighing scale]] meet.

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==Algorithm==

The following listing, in [[C (programming language)|C]] notation, is a simplified version of the '''Balanced Histogram Thresholding''' method:

<syntaxhighlight lang="c">

<code>

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;

}

}</code>

</syntaxhighlight>

The following, is a possible implementation in the [[Python (programming language)|Python]] language:

[[File:BhaProgress3.gif|thumb | 200px | Evolution of the method.]]

<syntaxhighlight lang="python">

This method may have problems when dealing with very noisy images, because the ''weighing scale'' may be misplaced. The problem can be minimized by ignoring the extremities of the histogram.<ref>A. Anjos, R. Leite, M. L. Cancela, H. Shahbazkia. MAQ – A Bioinformatics Tool for Automatic Macroarray Analysis. International Journal of Computer Applications. 2010. Number 7 - Article 1.</ref>

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

threshold = (start_index + end_index) // 2

return threshold

</syntaxhighlight>

==References==

{{reflist}}

<!-- ==External links==

* [http://w3.ualg.pt/~aanjos/prototype/BHThresholdingBHThresholding_.jar ImageJ Plugin] {{Webarchive|url=https://web.archive.org/web/20131017205614/http://w3.ualg.pt/~aanjos/prototype/BHThresholding_.jar |date=2013-10->17 }}

* [https://www.youtube.com/watch?v=rKWK4O4dZQ8 Otsu ''vs''. BHT]

{{DEFAULTSORT:Balanced Histogram Thresholding}}

[[Category:Image processingsegmentation]]

[[Category:Articles with example Python (programming language) code]]

[[fa:آستانه گذاری هیستوگرام متقارن]]

[[pt:Limiarização por equilíbrio do histograma]]

[[ru:Алгоритм сбалансированного порогового отсечения гистограммы]]