# Create a LUT Table by Euclidean Distance

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Royi Avital on 26 Jun 2015
Answered: Royi Avital on 29 Jun 2015
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.

Royi Avital on 29 Jun 2015
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).

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