Multiresolution image VQ compression by color codebook reordering

In this paper, a method to reach multiresolution VQ is proposed. A reordering process of color vectors from the codebook is performed. This yields to obtain an index image very close to the initial luminance image that can be obtained from any color image, but at a lower resolution. That way, the VQ technique can be applied once again on this new index image. In other words, a hierarchical and multiresolution VQ is defined. At each stage of the VQ compressed image, one is able to reconstruct it using the initial color codebook and the index one. A comparison of the proposed method and classical Hierarchical VQ (HVQ) scheme at different compression levels is performed to judge the performance and the robustness of the hybrid method. B oth objective and subjective measures are used. This work is a preliminary work to compress high dimension images at different levels. Introduction From all existing lossy compression techniques, the Vector Quantization (VQ) technique has been widely used in the last two decades. This technique is a generalization of the scalar quantization process to the quantization of a vector belonging to a set in which one partial order is provided at least. This compression technique has been selected among others since theoretically no other coding technique can do better than VQ. Actually, we enumerate the set of binary words produced by the coding system as indexes 1,2, . . . ,N. For the ith binary word, let the decoded output of the given coding system be vector yi. Then, a VQ decoder achieves equivalent performance to the decoder of any given coding system and a VQ encoder can be defined to be identical to the encoder of any given coding system [1]. The higher the dimension of vectors and the fewer the number of indexes, the higher the compression rate. Nevertheless, for high dimension vectors, the reconstructed images usually suffer from visible block structure. Various improvements of the VQ techniques have been developed in order to achieve the best trade-off between compression rate and reconstructed image quality. Two main approaches have been investigated : 1) the reduction of the address bits and 2) the reduction of the bit rate of smooth regions [2]. In the first approach, one tries to design an optimal subset of the codebook by evaluating the correlation of the adjacent pixels across block boundaries. A typical technique is the finite state vector quantization. The second approach is based on the emphazis of the features of the different regions in an image, such as the variable block vector quantization, and the hierarchical multirate vector quantization where the blocks with different grayscale transition features are assigned into different layers. One way to reach the optimal quality-compression rate tradeoff is the development of hierarchical techniques for the design of vector quantizer (VQ) encoders implemented by table lookups rather than by a minimum distortion search [2]. In a table lookup encoder, input vectors to the encoder are used directly as addresses in code tables to choose the channel symbol codewords. In order to preserve manageable table sizes for large dimension VQs, hierarchical structures are used to quantize the signal successively in stages. The encoder of a hierarchical VQ (HVQ) consists of several stages, each stage being a VQ implemented by a lookup table. Since both the encoder and the decoder are implemented by table lookups, there are no arithmetic computations required in the final VQ implementation [3]. In such a way, hierarchical does not mean multiresolution. In this paper, a new method to reach multiresolution VQ is presented. The main idea is to reorder color vectors from the codebook to obtain an index image very close to the initial luminance image that can be obtained from any color image, but at a lower resolution. In that case, the VQ technique can be applied once again on this new index image. That way, a hierarchical and multiresolution VQ is defined. At each stage of the VQ compressed image, one is able to reconstruct it using the initial color codebook and the index one. This global scheme is shown in Fig. 1. Specification of the VQ VQ maps a vector x of dimension k to another vector y of dimension k that belongs to a finite set C (codebook) of output vectors (codewords). Thus, the vector quantizer Q is defined as follows