Visual Optimization of Dct Quantization Matrices for Individual Images

Many image compression standards (JPEG, MPEG, H.261) are based on the Discrete Cosine Transform (DCT). However, these standards do not specify the actual DCT quantization matrix. We have previously provided mathematical formulae to compute a perceptually lossless quantization matrix. Here I show how to compute a matrix that is optimized for a particular image. The method treats each DCT coefficient as an approximation to the local response of a visual "channel." For a given quantization matrix, the DCT quantization errors are adjusted by contrast sensitivity, light adaptation, and contrast masking, and are pooled non-linearly over the blocks of the image. This yields an 8x8 "perceptual error matrix." A second non-linear pooling over the perceptual error matrix yields total perceptual error. With this model we may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix. 1. JPEG DCT QUANTIZATION The JPEG image compression standard provides a mechanism by which images may be compressed and shared among users 1, 2. The image is first divided into blocks of size {8,8}. Each block is transformed into its DCT, which we write cijk , where i,j indexes the DCT frequency (or basis function), and k indexes a block of the image. Each block is then quantized by dividing it, coefficient by coefficient, by a quantization matrix (QM) ij q , and rounding to the nearest integer uijk = Round ijk c ij q [ ] . (1) The quantization error ijk e in the DCT domain is then ijk e = ijk c − ijk u qij . (2) 2. IMAGE-INDEPENDENT PERCEPTUAL