Balanced histogram thresholding

In image processing, the balanced histogram thresholding method (BHT), is a very simple method used for automatic image thresholding. Like Otsu's Method and the Iterative Selection Thresholding Method, 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.

Original image.

Thresholded image.

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.

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

Algorithm

The following listing, in C notation, is a simplified version of the Balanced Histogram Thresholding method:

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;
}

The following, is a possible implementation in the Python language:

import numpy as np

def balanced_histogram_thresholding(histogram, minimum_bin_count: int = 5) -> int:
    """
    Determines an optimal threshold by balancing the histogram of an image, 
    focusing on significant histogram bins to segment the image into two parts.

    This function iterates through the histogram to find a threshold that divides 
    the histogram into two parts with a balanced sum of bin counts on each side. 
    It effectively segments the image into foreground and background based on this threshold. 
    The algorithm ignores bins with counts below a specified minimum, ensuring that 
    noise or very low-frequency bins do not affect the thresholding process.

    Args:
        histogram (np.ndarray): The histogram of the image as a 1D numpy array, 
                                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.

    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).

    """
    start_index = 0
    while histogram[start_index] < minimum_bin_count and start_index < len(histogram) - 1:
        start_index += 1
    
    end_index = len(histogram) - 1
    while histogram[end_index] < minimum_bin_count and end_index > 0:
        end_index -= 1

    if start_index >= end_index:
        return -1  # Indicates an error or non-applicability

    threshold = (start_index + end_index) // 2

    while True:
        weight_left = np.sum(histogram[start_index:threshold])
        weight_right = np.sum(histogram[threshold:end_index + 1])

        if weight_left > weight_right:
            end_index = threshold - 1
        else:
            start_index = threshold + 1

        new_threshold = (start_index + end_index) // 2

        if new_threshold == threshold:
            break
        else:
            threshold = new_threshold

    return threshold

External links

• ImageJ Plugin Archived 2013-10-17 at the Wayback Machine
• Otsu vs. BHT