Difference between revisions of "2015 Fall ECE 438 Boutin Implementation of Quantization Yitong Wang" - Rhea

Revision as of 21:00, 29 November 2015

Implementation of Color Quantization

A slecture by ECE student Yitong Wang

Partly based on the ECE438 Fall 2015 lecture material of Boutin.

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

Questions and comments

If you have any questions, comments, etc. please post them here.

Back to 2015 Fall ECE 438 Boutin

@@ Line 5: / Line 5: @@
-<center><font size= 4>Max Quantizer on Image</font size>
+<center><font size= 4>Implementation of Color Quantization</font size>
 A [http://www.projectrhea.org/learning/slectures.php slecture] by [[ECE]] student Yitong Wang
@@ Line 14: / Line 14: @@
 ----
 ==1. Introduction (''Implementation of Max Quantization'')==
-Quantization is an operation to compress a signal by reducing a range of values to a single value. We tried Max quantizer on voice sigal in lab5. This slecture will describe the image quantization through max quantizer and the difference between it and uniform quantizier.
+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.
-<math> f(x)= \frac{1}{5} \sin x \int_{-\infty}^\alpha \pi^y dy</math>
 ----
 ==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 take only several values, the brightness value has to be rounded off to fit the size of the image.
+*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.
-*Since the quantization will obviously cause loss of data, we should try the quantization in different levels and the analyse the error.
+*Max quantizier
 ==3. Theory ==
-To operate an uniform quantization, the first things is to determine the uniform quantization step Δ. Although there are 256 values to represent the brightness, the Δ depends on the range of the brightness of image instead of 0 to 255.
+*[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
- <math> Δ = \frac{Max(X) - Min(X)}{N-1} </math>
-Where X is the signal to be quantized and N is the number of quantization levels.
-The quantization step Δ is the range of values will to be quantized. Since the input image is not type double, it can't be processed in mathematical operation in Matlab. It should be converted to type double.