CS 195 - 5 : Machine Learning Problem Set 5

Let’s begin by briefly reviewing the Matlab routines required for VQ-based image compression. First, note that the VQ parameters are set on lines 13-19 of prob1.m. The general VQ framework is implemented by learnVQ.m, which uses the subroutine kmeans.m to implement the k-means algorithm. (Note that, as recommended, we use findnn.m and lpnorm.m within the k-means implementation to allow flexible nearest-neighbor selection under a general Lp-norm.) Applying VQ to imagePS5.png demonstrates that this algorithm can achieve significant compression ratios. First, note that the original image has dimensions 510×768 pixels and is represented using 24-bit color (i.e., 3 bytes per pixel). As a result, imagePS5.png requires 510·768·24 = 9,400,320 bits to store. In contrast, the VQ cluster means (using k = 256 and m = 3) only require 256·3·3·24 = 55,296 bits to store. In order to reconstruct the original image we must assign an 8-bit index into the VQ cluster means “codebook” for each 3×3 block, which requires an additional (510/3)·(768/3)·8 = 348,160 bits. As a result, the compressed image requires a total of 403,456 bits to store, leading to the following compression ratio.