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

1. Introduction (Implementation of Quantization)

Quantization is an operation to compress a signal by reducing a range of values to a single value. This slecture will describe the implementation of image quantization $ f(x)= \frac{1}{5} \sin x \int_{-\infty}^\alpha \pi^y dy $

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.

• Since the quantization will obviously cause loss of data, we should try the quantization in different levels and the analyse the error.

3. Theory

To operate an uniform quantization, the first things is to determine the uniform quantization step Δ.

$  Δ = \frac{Max(X) - Min(X)}{N-1}  $

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.

$ 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

function [y] = Uquant(x,N) delta = (max(x(:))-min(x(:)))/(N-1); y = round((x-min(x(:)))/delta).*delta + min(x(:)); end

4. Conclusion (Replace by appropriate section title)

Text of fourth section goes here.

5. References

• Reference 1
• reference 2

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