Histogram

Histogram of a monochrome image with $L$ possible gray levels, $l = 0, 1, ..., L-1$ .

$P(l) = n_l / n$ ,
$n_l$ is the number of pixels with gray level $l$ .
$n$ is the total number of pixels in the image.

Histogram Calculation (Sample Matlab Script)

function h = histogram(imgname) 
img = imread(imgname);  
figure; imshow(img);

% method 1
h = zeros(256,1); 
for l = 0:255
    for i = 1:N,
        for j = 1:M,
            if img(i, j) == l,  
                h(l + 1) = h(l + 1) + 1;
            end     
        end
    end 
end

figure; bar(h);

% method 2
img = double(img); h = zeros(256,1); 
for i=1:M,
    for j=1:N,  
        f = img(i,j);  
        h(f+1) = h(f+1) + 1;
    end 
end

% method 3
h = zeros(256,1); 
for l = 0 : 255,
    h(l + 1)=sum(sum(img == l)); 
end

Photoshop has extensive histogram display tools
Matlab: imhist( ): can compute and display histograms
Python: matplotlib.pyplot.hist( ), numpy.histogram( )

See: Histogram Equalization