A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission.

Introduces a new image coding scheme using lattice vector quantization. The proposed method involves two steps: biorthogonal wavelet transform of the image, and lattice vector quantization of wavelet coefficients. In order to obtain a compromise between minimum distortion and bit rate, we must truncate and scale the lattice suitably. To meet this goal, we need to know how many lattice points lie within the truncated area. We investigate the case of Laplacian sources where surfaces of equal probability are spheres for the L(1) metric (pyramids) for arbitrary lattices. We give explicit generating functions for the codebook sizes for the most useful lattices like Z(n), D(n), E(s), wedge(16).

We propose a new wavelet compression algorithm based on the rate-distortion optimization for densely sampled triangular meshes. This algorithm includes the normal remesher, a wavelet transform, and an original bit allocation optimizing the quantization of the wavelet coefficients. The allocation process minimizes the reconstruction error for a given bit budget. As distortion measure, we use the mean square error of the normal mesh quantization, expressed according to the quantization error of each subband. We show that this metric is a suitable criterion to evaluate the reconstruction error, i.e. the geometric distance between the input mesh and the quantized normal one. Moreover, to design a useful bit allocation, we propose a model-based approach, depending on the wavelet coefficient distributions. The proposed algorithm achieves results better than state-of-the-art methods, up to +2.5 dB compared to the original zerotree coder for normal meshes.