Reduce the Number of Intensity Levels of a Grayscale Image in MATLAB

Question

I have written a Matlab script to reduce the number of intensity levels of each pixel of a grayscale image from 256 to some power of 2.

img_color = imread('photo.jpg');
img_gray = rgb2gray(img_color);
imshow(img_gray);
[rows, cols] = size(img_gray);
noOfDesiredIntensityLevels = 2; // test data. will check for 4,8,16,32,etc.
bitsNeededToRepresentIntensityLevels = log2(noOfDesiredIntensityLevels);
new_img = img_gray;
for i = 1 : rows
    for j = 1 : cols
        new_img(i,j) = floor(img_gray(i,j)/(2^(8-bitsNeededToRepresentIntensityLevels)));
    end
end
figure
imshow(new_img);

On execution, the script returns a black image. My expectation was that the image will be turned into black-and-white (intensity value for each pixel will be either a 0 or a 1).

What am I missing here?

P.S: I am a novice in Matlab and Image Processing. So, please ignore any mistakes in my understanding.

Answer 1

I think by number of levels you want the image full scale grey-scale to be divided piece-wise into given number of levels. For example: -

• If number of levels = 2, then you want only two grey-scales in your image i.e. (0 and 128) or (128 and 255) depending upon if you are using floor or ceil within the range
• If number of levels = 4, then you want 4 different levels in your image i.e. (0, 64, 124, 192)

Solution - This operation can be done in a single line

new_img = ceil(img_gray./step)*step;

Here I have divide the entire range into desired number of parts (levels) with size as step and used ceil function to restrict the result to the upper bounds (you can use floor for lower bounds)

Full Code -

img_color = imread('peppers.png');
img_gray = rgb2gray(img_color);
imshow(img_gray);

[rows, cols] = size(img_gray);
noOfDesiredIntensityLevels = 2;
step = ceil(255/(noOfDesiredIntensityLevels - 1));

new_img = ceil(img_gray./step)*step;

figure
imshow(new_img);


% optional code to show the levels
allSteps = 0;
currStep = 0;
while(currStep < 255)
    currStep = currStep + step;
    allSteps = [allSteps currStep];
end

allSteps

Edit 1 - I have included few extra lines which shows you the different levels (steps) in an array. Its just optional but nice to know the exact values of the levels.

Answer 2

This is one way to do it

img_color = imread('peppers.png');
img_gray = rgb2gray(img_color);
figure(1); imshow(img_gray);

nLevels = 4; % change this to the desired level 2 or more
maxLevel = 256;
threshGap = maxLevel / nLevels;
thresholds = zeros(1, nLevels);
thresholds(nLevels) = maxLevel-1;
thresholds(1) = floor(threshGap);
for i = 2:nLevels-1
    thresholds(i) = floor(thresholds(i-1) + threshGap);
end

grayGap = maxLevel / (nLevels - 1);
grayLevels = zeros(1, nLevels);
grayLevels(nLevels) = maxLevel - 1;
for i = 2:nLevels-1
    grayLevels(i) = floor(grayLevels(i-1) + grayGap);
end

new_img = img_gray;
[rows, cols] = size(img_gray);


for i = nLevels:-1:1
    %new_img(img_gray < thresholds(i)) = grayLevels(i); % you can use this line of
    % code and remove the next double nested loops

    for x=1:rows
        for y =1:cols
            if img_gray(x, y) < thresholds(i)
                new_img(x, y) = grayLevels(i);
            end
        end
    end
end

figure(2); imshow(new_img);

Here is a result with 4 gray-levels:

Note: The code is pretty straightforward but If you don't understand something just comment.

Answer 3

With Matlab, you don't need to loop other all pixels. Being matrix-based (hence "MatLab"), you can divide a whole image directly. Then, imshow can be tricky on images that are not on 8 bits. Instead imagesc can scales images.

clear all;
noOfDesiredIntensityLevels = 2; 
bitsIntialToRepresentIntensityLevels = 8; 

img_color = (imread('peppers.png'));
img_gray = double(rgb2gray(img_color));

bitsNeededToRepresentIntensityLevels = log2(noOfDesiredIntensityLevels);
if ~isequal(bitsNeededToRepresentIntensityLevels,floor(bitsNeededToRepresentIntensityLevels))
    error('Number of intensity levels is not a power of two')
end
new_img = floor(img_gray/(2^(bitsIntialToRepresentIntensityLevels-bitsNeededToRepresentIntensityLevels)));

figure(1)
subplot(1,2,1)
imagesc(img_gray);
subplot(1,2,2)
imagesc((2^(bitsIntialToRepresentIntensityLevels-bitsNeededToRepresentIntensityLevels))*new_img);