Create a LUT Table by Euclidean Distance

Hello,

I have a list of N vectors in 3D space (Points in RGB color space). We'll call that our Dictionary.

The whole data M is in 3D Space ({0, 1, ..., 255} x {0, 1, ..., 255} x {0, 1, ..., 255}).

I want to create a LUT which works in the following way, each point in the Space will be mapped to the point dictionary according to Euclidean Distance.

This can be also seen as a quantization process of an image. I want to create a LUT Table s.t. is pixel will be quantized into a value of the Code Book which is the most similar to it in the L2 / Euclidean sense.

How can I do it in a vectorized, efficient manner?

This is a sample code I created using loops:

function [ mRgbLut ] = CreateRgbLUT( mCodeBook )

mRgbLut     = zeros(256, 256, 256);
numLevels   = size(mCodeBook, 1);

for iRValue = 0:255
    redIdx = iRValue + 1;
    for jGValue = 0:255
        grennIdx = jGValue + 1;
        for kBValue = 0:255
            blueIdx = kBValue + 1;

              vCurrColor = [iRValue, jGValue, kBValue];

              vRgbDistance = sum(((repmat(vCurrColor, [numLevels, 1]) - mCodeBook) .^ 2), 2);
              [minRgbDist, codeBookIdx] = min(vRgbDistance);

              mRgbLut(redIdx, grennIdx, blueIdx) = sub2ind([256, 256, 256], mCodeBook(codeBookIdx, 1), mCodeBook(codeBookIdx, 2), mCodeBook(codeBookIdx, 3));
          end
      end
  end

end

Thank You.

Answer 1

[Royi Avital]

Ok, I created something using the ' allcomb ' function from File Exchange.

Here is the code:

function [ mRgbLut ] = CreateRgbLUT( mCodeBook )

numLevels   = size(mCodeBook, 1);

vBaseValues = [0:255];

mCombValues         = allcomb(vBaseValues, vBaseValues, vBaseValues);
mCombValues         = [mCombValues(:, 3), mCombValues(:, 2), mCombValues(:, 1)];
mCodeBookReshaped   = reshape(mCodeBook.', [1, 3, numLevels]);

mRgbDistance = bsxfun(@minus, mCombValues, mCodeBookReshaped) .^ 2;
mRgbDistance = sum(mRgbDistance, 2);

[minRgbDist, codeBookIdx] = min(mRgbDistance, [], 3);

mRgbLut = reshape(codeBookIdx, [256, 256, 256]);

end

I hope this might assist someone (It something like the step in K Means).