Arrays have imcompateble size error

had an error about: imcompatable size etc.

ERROR:

Arrays have incompatible sizes for this operation.

Error in Q3>otsu_threshold (line 52)

variance = prob_background .* prob_foreground .* ((mean_background - mean_foreground).^2);

Error in Q3 (line 6)

binary_image1 = otsu_threshold(gray_image1);

Related documentation

CODE:

image1 = imread('Figure3_a.jpg');
gray_image1 = im2gray(image1);
% apply Otsu's thresholding to produce a binary image
binary_image1 = otsu_threshold(gray_image1);
% plot the original and binary images side by side
figure;
subplot(1, 2, 1); imshow(gray_image1); title('Original Image');
subplot(1, 2, 2); imshow(binary_image1); title('Binary Image');
% read the second image and convert it to grayscale
image2 = imread('Figure3_b.png');
gray_image2 = im2gray(image2);
% apply Otsu's thresholding to produce a binary image
binary_image2 = otsu_threshold(gray_image2);
% plot the original and binary images side by side
figure;
subplot(1, 2, 1); imshow(gray_image2); title('Original Image');
subplot(1, 2, 2); imshow(binary_image2); title('Binary Image');
function binary_image = otsu_threshold(source_image)
% calculate histogram of the input image
histogram = imhist(source_image);
% normalize the histogram so that its values lie in the range [0, 1]
histogram = histogram / numel(source_image);
% initialize variables for the maximum between-class variance and the optimal threshold value
max_variance = -inf;
optimal_threshold = 0;
% loop over all possible threshold values (1 to 255) and calculate the between-class variance for each
for t = 1:255
    % calculate the probability of the pixels below the threshold
    prob_background = sum(histogram(1:t));
    
    % calculate the probability of the pixels above the threshold
    prob_foreground = sum(histogram(t+1:end));
    
    % calculate the mean intensity of the pixels below the threshold
    mean_background = sum((0:t-1) .* histogram(1:t)) / prob_background;
    
    % calculate the mean intensity of the pixels above the threshold
    mean_foreground = sum((t:255) .* histogram(t+1:end)) / prob_foreground;
    
    % calculate the between-class variance for the current threshold
    variance = prob_background * prob_foreground * ((mean_background - mean_foreground).^2);
    
    % update the maximum between-class variance and the optimal threshold if necessary
    if variance > max_variance
        max_variance = variance;
        optimal_threshold = t;
    end
end
% use the optimal threshold to produce the binary image
binary_image = source_image >= optimal_threshold;
end

[Walter Roberson]

We need to see the code for function otsu_threshold

[Pratham Shah]

You need the change the way of obtaining mean_background and mean_background. You must be receiving an array in those variable.

One more thing, start the loop from i=2 as i=1 will result in 'divided by 0' error because prob_background is 0 for first iteration.

[Yigit Goktas]

function binary_image = otsu_threshold(source_image)
histogram = imhist(source_image);
% normalize the histogram so that its values lie in the range [0, 1]
histogram = histogram / numel(source_image);
% initialize variables for the maximum between-class variance and the optimal threshold value
max_variance = -inf;
optimal_threshold = 0;
% loop over all possible threshold values (1 to 255) and calculate the between-class variance for each
for t = 2:255
    % calculate the probability of the pixels below the threshold
    prob_background = sum(histogram(1:t));
    prob_foreground = sum(histogram(t+1:end));
    mean_background = sum((0:t-1) .* histogram(1:t)) / prob_background;
    mean_foreground = sum((t:255) .* histogram(t+1:end)) / prob_foreground;
    variance = prob_background * prob_foreground * ((mean_background - mean_foreground).^2);
    if variance > max_variance
        max_variance = variance;
        optimal_threshold = t;
    end
end
binary_image = source_image >= optimal_threshold;
end

Walter its the otsu_threshold function? I changed i=1 to 2 as Pratham said but don't know how to obtain mean_background as an array here

Answer 1

[Walter Roberson]

The problem you were encountering is that your variable named histogram is a column vector, but you were combining it with row vectors.

img = imread('cameraman.tif');

out = otsu_threshold(img);
imshow(img); title('original');

imshow(out); title('thresholded')

function binary_image = otsu_threshold(source_image)
histogram = imhist(source_image);
% normalize the histogram so that its values lie in the range [0, 1]
histogram = histogram / numel(source_image);
% initialize variables for the maximum between-class variance and the optimal threshold value
max_variance = -inf;
optimal_threshold = 0;
% loop over all possible threshold values (1 to 255) and calculate the between-class variance for each
for t = 2:255
    % calculate the probability of the pixels below the threshold
    prob_background = sum(histogram(1:t));
    prob_foreground = sum(histogram(t+1:end));
    mean_background = sum((0:t-1).' .* histogram(1:t)) / prob_background;
    mean_foreground = sum((t:255).' .* histogram(t+1:end)) / prob_foreground;
    variance = prob_background * prob_foreground * ((mean_background - mean_foreground).^2);
    if variance > max_variance
        max_variance = variance;
        optimal_threshold = t;
    end
end
binary_image = source_image >= optimal_threshold;
end