2015 Fall ECE 438 Boutin Implementation of Quantization Yitong Wang - Rhea

1. Introduction (Implementation of Max Quantization)

Quantization is an operation to compress a signal by reducing a range of values to a single value. Color quantization is a process to reduce the number of colors in an image in order to reduce the size. This slecture will describe the color quantization using kmean function in matlab.

2. Background

• The brightness of a photo at each pixel is typically distributed among integers from 0 to 255. However, since some images are desired to limit the number of colors, the brightness value has to be rounded off to fit the size of the image.
• During the procedure of quantization, there must be some loss of data. To avoid high error percentage and remain quality as good as possible, using kmean function is a good choice.

• Max quantizier

3. Theory

• [ind,color] = kmean(input,k) function performs k-means clustering to partition the observations of the n-by-m data matrix input into k clusters, and returns an n-by-1 vector which represent the index of the values of colors after operation. The operation uses the squared Euclidean distance measure.
• To start the operation, the image have to be reshaped into a X-3 matrix that contains R,G and B as we used in lab 5. Where X is the number of pixels in each row.

%Seperate the image matrix into R G and B R = rgb(:,:,1); G = rgb(:,:,2); B = rgb(:,:,3); %reform a image matrix in size-3 matrix img(:,1) = R(:); img(:,2) = G(:); img(:,3) = B(:);

• Operate the kmean function to get the

$ X = double(input) $

After this, we can do the quantization.

• Substract X with $ Min(X) $ (To see the difference of value between the pixel and the least bright pixel)
• Divide the result by Δ and round it to integer
• Add the result to $ Min(X) $

To make the step simple, we can make a quantization function respect to input X and quantization level N. However, the image signal is in matrix, so just simply use x(:), which convert the matrix into a vactor.

function [y] = Uquant(x,N)

delta = (max(x(:))-min(x(:)))/(N-1); % calculate delta

y = round((x-min(x(:)))/delta).*delta + min(x(:)); % round the quantized value then add with min(x)

end

File:Bit4.jpg

4. Conclusion (Replace by appropriate section title)

Text of fourth section goes here.

5. References

• Reference 1
• reference 2

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