Analysis of vector transformation for image coding.

摘要

Vector Transform Coding (VTC) is a new technique in image coding. Since its first presentation to the literature, it has been getting a big interest by people. Studies showed that it is a very powerful technique in performing image coding. VTC includes two major steps. The first is vector transformation (VT) and the second is vector quantization (VQ). VT is true generalization of scalar transform. Image is transformed to the vector transform domain and VQ is performed in the vector transform domain. VQ demands for high correlated elements inside the vectors and less correlation between the vectors to perform better. Because VT tends to keep the correlation inside the vectors and to reduce the correlation between the vectors, VTC performs better than the well known scalar transform plus VQ schemes. This study can be summarized in two parts: (1) Optimum Vector Transform study and (2) Comparison of Vector Transforms. Optimum case for VT if VQ performed in the transform domain has been studied. In case of taking the image as a group of column vectors, two attributes have been introduced. Under these two attributes optimum transform for the case of column vectors has been formulated and derived. For the case of square matrices, the formulation has been given. In comparison of VTs, intrinsic coupling factor (ICF) values as a measure of preserving the inter-vector correlation have been calculated and compared, and energy compaction of the vector transforms and average values of off-diagonal elements of correlation matrices have been calculated and compared.