FINALREPORT
DCT Transform
Haar Wavelet Transform
quantization
methods
results
conclusions
QUANTIZATION
During quantization each pixel of the transformed digital image is mapped to a discrete number. Each integer in the range of numbers used in the mapping symbolizes a color.
Haar Wavelet Quantiztion:
If the image to be quantized has N x M pixels and the new color scale is to have G = 2m numbers, then, the number of bits required to store the quantized image is N x M x m. The images we used in this project are 256 x 256 pixels. In order to uniformly quantize the image we would need 256x256xm bits
In the case of transformed digital image, all of the energy resides in a particular section of the array. Adaptive quantization methods can take advantage of foreknowledge of smooth regions by using fewer quantization levels in these areas. The fewer the color levels used the smaller the number of bits required. Likewise, neighborhoods of the digital image with high energy should be represented with more quantization levels. More bits will be used in these regions, but if the neighborhoods are small, then the overall reduction in bits will be greater that that achieved by uniform quantization.
Statistical quantization methods can improve on adaptive techniques. Generally the same number of quantization levels are used in adaptive and statistical quantization so there is no savings there. However, statictical methods consider the distribution of the data in each section when determining the breakdown of the quantization levels. Therefore, the improvement lies in better definition of each quantization level.
Uniform quantization, adaptive quantization and statistical quantization were all computed for the Haar wavelet transform and comparisons of the methods can be found in the results section.
DCT Quantization:
After the image is DCT transformed, it is divided into 8x8 blocks. These blocks are then encoded individually. The blocks on the top left corner would be encoded with more bits to keep the important information or energies. As we move away from the upper left hand corner, the blocks are encoded with fewer and fewer bits. Eventually hitting the bottom right corner, the blocks are encoded with few if any bitsl. This is the usual DCT quantization method.
In this project we kept a certain number of 8x8 blocks in the top left hand corner and multiplied the rest of our DCT coefficients with 0. This would simplify our code, improve compression, but lower the quality of the compressed image. This “mask” matrix determined what dimension of the upper left-hand corner of DCT coefficients would be kept and the rest of the coefficients multiplied by 0. We used masks of size 4x4 8x8 and 16x16. As the mask size increased, so did the quality of the image.
Contact the authors:
nofences@rice.edu
heidit@caam.rice.edu
hard@rice.edu
bwang@rice.edu