Wavelet Based Image Coding Schemes : A Recent Survey <s> The GW (Geometric Wavelet) Coding <s> For low bit-rate compression applications, segmentation-based coding methods provide, in general, high compression ratios when compared with traditional (e.g., transform and subband) coding approaches. In this paper, we present a new segmentation-based image coding method that divides the desired image using binary space partitioning (BSP). The BSP approach partitions the desired image recursively by arbitrarily oriented lines in a hierarchical manner. This recursive partitioning generates a binary tree, which is referred to as the BSP-tree representation of the desired image. The most critical aspect of the BSP-tree method is the criterion used to select the partitioning lines of the BSP tree representation, In previous works, we developed novel methods for selecting the BSP-tree lines, and showed that the BSP approach provides efficient segmentation of images. In this paper, we describe a hierarchical approach for coding the partitioning lines of the BSP-tree representation. We also show that the image signal within the different regions (resulting from the recursive partitioning) can be represented using low-order polynomials. Furthermore, we employ an optimum pruning algorithm to minimize the bit rate of the BSP tree representation (for a given budget constraint) while minimizing distortion. Simulation results and comparisons with other compression methods are also presented. <s> BIB001 </s> Wavelet Based Image Coding Schemes : A Recent Survey <s> The GW (Geometric Wavelet) Coding <s> This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image <s> BIB002 </s> Wavelet Based Image Coding Schemes : A Recent Survey <s> The GW (Geometric Wavelet) Coding <s> Geometric wavelet is a recent development in the field of multivariate nonlinear piecewise polynomials approximation. The present study improves the geometric wavelet (GW) image coding method by using the slope intercept representation of the straight line in the binary space partition scheme. The performance of the proposed algorithm is compared with the wavelet transform-based compression methods such as the embedded zerotree wavelet (EZW), the set partitioning in hierarchical trees (SPIHT) and the embedded block coding with optimized truncation (EBCOT), and other recently developed "sparse geometric representation" based compression algorithms. The proposed image compression algorithm outperforms the EZW, the Bandelets and the GW algorithm. The presented algorithm reports a gain of 0.22 dB over the GW method at the compression ratio of 64 for the Cameraman test image. <s> BIB003
Geometric wavelet is a recent advancement in the field of multivariate nonlinear piecewise polynomials approximation proposed by Deckel et.al BIB002 . It is a new and efficient method best suited for low bit-rate image coding. It combines the binary space partition tree approximation BIB001 with geometric wavelet (GW) coding so as to efficiently capture curve singularities and thus providing a sparse representation of the image. The GW method successfully competes with advanced wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. A gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp) is achieved. The GW technique also outperforms other recent segmentation methods that are based on "sparse geometric representation". Table 5 shows the PSNR values for Lena test image using the GW approach. Table 5 . PSNR values for Lena image of size 512x512 using GW, compared with other state-ofthe-art methods An improvement over the geometric wavelet (GW) image coding method by using the slope intercept representation of the straight line in the binary space partition scheme is proposed by Chopra and Pal BIB003 . The performance of this algorithm is compared with other classical wavelet transform-based compression methods such as EZW, the SPIHT and the EBCOT algorithms. The proposed image compression algorithm outperforms the EZW and SPIHT algorithm, as shown in Table 6 . The PSNR results for Lena image using the improved GW method for compression ratios of 64, 128 and 256 are given in Table 6 . These results are also compared with other algorithms. Table 6 . PSNR values for Lena image of size 512x512 using improved GW, compared with other state-of-the art-methods