How can I compute the probability of a pixel intensity of the image in Matlab??

I have an enhanced image and I want to measure the amount of information in the enhanced image using the following metric:

where p(Ie) denotes the probability of a pixel intensity in the enhanced image Ie . now I want to know how to estimate the probability of a pixel intensity. Does anyone know how to do this in Matlab??

[Adam]

Which pixel intensity? The probablity of being exactly a given intensity or of being higher than a given intensity or lower? It doesn't make sense without additional context.of what Ie is

[ghada sandoub]

Ie is the enhanced image of dimmed image. Ie is color image. and I want to measure the amount of enhancement in the enhanced image by using DE which measures the amount of information in the enhanced image by estimating the probability of a pixel intensty in this image. but I didn't know how to make this in matlab.

Answer 1

[Image Analyst]

ghada:

Use histogram() with the 'Normalization' option of 'probability'.

You might also be interested in the entropy() function (which computes your formula directly from the image), or entropyfilt() function (which does an entropy computation in a moving window).

Demo below:

grayImage = imread('cameraman.tif');
subplot(2, 1, 1);
imshow(grayImage);
subplot(2, 1, 2);
histObject = histogram(grayImage, 256, 'Normalization', 'probability')
grid on;
xlabel('Gray Level', 'FontSize', 20);
ylabel('Probability', 'FontSize', 20);
% Extract probabililty of each gray level into a vector "p".
p = histObject.Values;

[ghada sandoub]

Thanks alot. but can I use the entropy() on the color image (enhanced image) directely and it will results in a correct operation or the entropy() applied on grayscale images only??

[Image Analyst]

You can use it on color images if you just want the entropy of every pixel regardless of what color it is. It's more of an interpretation issue than a functional/syntax/code issue.

[Aaron Charles Alday]

Your code didn't work to my matlab sorftware the command window shows this message....why?

"Error in imhist (line 60)

[a, n, isScaled, top, map] = parse_inputs(varargin{:});

Error in Test_Run_2 (line 8)

[pixelCounts, white_value] = imhist(grayImage, 256, 'Normalization', 'probability')"

[Image Analyst]

@Aaron Charles Alday, that's not my code. I didn't use imhist, I used histogram. imhist does not take those arguments.

Answer 2

[KALYAN ACHARJYA]

gray_image=rgb2gray(imread('test.jpg'));
[rows colm]=size(gray_image);
[pixelCounts, gray_value]=imhist(gray_image);
prob=pixelCounts(:)./(rows*colm);
prob=nonzeros(prob);
log_prob=log(prob);
DE=-sum(prob.*log_prob);
fprintf('\n The DE value is: %.2f',DE);

Command Window:

 The DE value is: 3.50>> 

[ghada sandoub]

Thanks alot

[KALYAN ACHARJYA]

Is the problem solved? I have written simple code based on your question. If not. Check the comment of Image Anaalyst sir

Answer 3

[Ganesha Thondilege]

I hope this will help you.

grayImage = imread('cameraman.jpg');
subplot(1,2, 1);
imshow(grayImage);
subplot(1,2, 2);
imhist(grayImage);

[Walter Roberson]

This does not give probability as requested. It also does not give entropy which is what the user formula was for.

[Ganesha Thondilege]

Try this to get the probabilities of each gray_value

grayImage = imread('cameraman.jpg');
[l,m]=size(grayImage);
subplot(1,2, 1);
imshow(grayImage);
[pixelCounts, gray_value]=imhist(grayImage);
prob=pixelCounts(:)./(l*m);
subplot(1,2,2);
plot(gray_value,prob);

[Walter Roberson]

what advantages would this have compared to https://www.mathworks.com/matlabcentral/answers/450942-how-can-i-compute-the-probability-of-a-pixel-intensity-of-the-image-in-matlab#answer_366112