Increase image contrast using look up table in MATLAB

Question

I am trying to do some image processing for which I am given an 8-bit grayscale image. I am supposed to change the contrast of the image by generating a lookup table that increases the contrast for pixel values between 50 and 205. I have generated a look up table using the following MATLAB code.

a = 2;
x = 0:255;
lut = 255 ./ (1+exp(-a*(x-127)/32));

When I plot lut, I get a graph shown below:

So far so good, but how do I go about increasing the contrast for pixel values between 50 and 205? Final plot of the transform mapping should be something like:

Answer 1

Judging from your comments, you simply want a linear map where intensities that are < 50 get mapped to 0, intensities that are > 205 get mapped to 255, and everything else is a linear mapping in between. You can simply do this by:

slope = 255 / (205 - 50); % // Generate equation of the line - 
                          % // y = mx + b - Solve for m
intercept = -50*slope; %// Solve for b --> b = y - m*x, y = 0, x = 50
LUT = uint8(slope*(0:255) + intercept); %// Generate points
LUT(1:51) = 0; %// Anything < intensity 50 set to 0
LUT(206:end) = 255; %// Anything > intensity 205 set to 255

The LUT now looks like:

plot(0:255, LUT);
axis tight;
grid;

Take note at how I truncated the intensities when they're < 50 and > 205. MATLAB starts indexing at index 1, and so we need to offset the intensities by 1 so that they correctly map to pixel intensities which start at 0.

To finally apply this to your image, all you have to do is:

out = LUT(img + 1); 

This is assuming that img is your input image. Again, take note that we had to offset the input by +1 as MATLAB starts indexing at location 1, while intensities start at 0.

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Minor Note

You can easily do this by using imadjust, which basically does this for you under the hood. You call it like so:

outAdjust = imadjust(in, [low_in; high_in], [low_out; high_out]);

low_in and high_in represent the minimum and maximum input intensities that exist in your image. Note that these are normalized between [0,1]. low_out and high_out adjust the intensities of your image so that low_in maps to low_out, high_in maps to high_out, and everything else is contrast stretched in between. For your case, you would do:

outAdjust = imadjust(img, [0; 1], [50/255; 205/255]);

This should stretch the contrast such that the input intensity 50 maps to the output intensity 0 and the input intensity 205 maps to the output intensity 255. Any intensities < 50 and > 205 get automatically saturated to 0 and 255 respectively.

Answer 2

You need to take each pixel in your image and replace it with the corresponding value in the lookup table. This can be done with some nested for loops, but it is not the most idiomatic way to do it. I would recommend using arrayfun with a function that replaces a pixel.

new_image = arrayfun(@(pixel) lut(pixel), image);

It might be more efficient to use the code that generates lut directly on the image. If performance is a concern and you don't need to use a lookup table, try comparing both methods.

new_image = 255 ./ (1 + exp(-image * (x-127) / 32));

Note that the new_image variable will no longer be of type uint8. If you need to display it again (say, with imshow) you will need to convert it back by writing uint8(new_image).