Image compression using BTC-PF Algorithm for Gray Scale images and its performance analysis

In this paper, a novel Gray Scale image compression method (BTC algorithm using Pattern fitting) based on block truncation coding (BTC) and Vector quantization (VQ) is proposed. This method inherits the advantages of both BTC and vector quantization. The BTC-PF method has some controlling parameters through which we can control the bit-rate and quality. The BTC-PF method is also successfully employed to handle low bit-rate coding. The performance of proposed image compression method is quite good. As the decoding methods are mainly based on table look up, decoding module of these methods are faster than that of the state-of-the-art techniques. The effectiveness of the proposed schemes is established by comparing the performance with that of the existing methods. Keywords— Image Processing, Compression, BTC Scheme, storage, resolution, decoding, transmission, MSE, PSNR, mean. I. BLOCK TRUNCATION CODING Block truncation coding (BTC) is a simple, fast, lossy and fixed length compression technique for gray scale images. This is a block-adaptive binary encoding scheme based on moment preserving quantization. The concept is introduced by Delp and Mitchell [2,8,38]. In BTC method, an image is divided into n×n blocks (in general n=4) and each block is coded separately. Gray levels of each block is quantized by Q level quantizer and these quantizer levels are chosen such that a few low order moments are preserved in the quantized output. In the simplest form of BTC, the first two moments are preserved and blocks are represented by two quantization levels. By incorporating additional constraints, higher order moments can be preserved. Suppose k (=n) be the number of pixels in a block and also suppose f(xi), xi ∈ C are the gray values of the pixels in a block of the original image where C represents the set of coordinates of pixels in the block, i.e., . The first two sample moments and are given by is the sample mean and the sample variance of image block is given by Then a two level quantization is performed on the block. The pixels with intensity greater than the quantization threshold are quantized to value b, and the other pixels are quantized to value a. Here, the sample mean is set as the quantization threshold and suppose the quantization partition of C with respect to the threshold gives two sets of pixels and , such that [10,11,12], C = ∪ and ∩ = ∅ where, and The quantization partition of C can be represented by a binary-pattern P. The binary pattern or bit-plane P is defined as The partition of C is defined as The quantization levels a and b are used to preserve first two sample moments. Then and solving for a and b yields International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 12, December 2015 4338 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR Thus a compressed image block is represented by the triplet (a, b, P). For 8-bit gray scale image, the straightforward BTC needs bits per pixel. An example of BTC method is shown in Fig. 1. Figure 1: An example of BTC: (a) original block, m1 = 7.94, σ = 4.91, (b) corresponding bit-pattern, k0 =7, (c) reconstructed block with a=2 and b=12. The steps for encoding a block by BTC are:  Perform quantization (determination of threshold, and quantization levels)  Coding of the quantization levels (i.e., a and b)  Coding of the bit-pattern P BTC method is simple and results into high quality reconstructed image, but the compression ratio is low. In literature, there are several modifications of BTC to improve the performance [1,2,5]. The original BTC uses threshold = and preserves the first and second order moments. This method can be extended to preserve third order moments also. To preserve third order moment, the is determined such a way that number of pixels greater than is given by: