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.