Multiresolution vector quantization

Multiresolution source codes are data compression algorithms yielding embedded source descriptions. The decoder of a multiresolution code can build a source reproduction by decoding the embedded bit stream in part or in whole. All decoding procedures start at the beginning of the binary source description and decode some fraction of that string. Decoding a small portion of the binary string gives a low-resolution reproduction; decoding more yields a higher resolution reproduction; and so on. Multiresolution vector quantizers are block multiresolution source codes. This paper introduces algorithms for designing fixed- and variable-rate multiresolution vector quantizers. Experiments on synthetic data demonstrate performance close to the theoretical performance limit. Experiments on natural images demonstrate performance improvements of up to 8 dB over tree-structured vector quantizers. Some of the lessons learned through multiresolution vector quantizer design lend insight into the design of more sophisticated multiresolution codes

Rate-distortion adaptive vector quantization for wavelet imagecoding

We propose a wavelet image coding scheme using rate-distortion adaptive tree-structured residual vector quantization. Wavelet transform coefficient coding is based on the pyramid hierarchy (zero-tree), but rather than determining the zero-tree relation from the coarsest subband to the finest by hard thresholding, the prediction in our scheme is achieved by rate-distortion optimization with adaptive vector quantization on the wavelet coefficients from the finest subband to the coarsest. The proposed method involves only integer operations and can be implemented with very low computational complexity. The preliminary experiments have shown some encouraging results: a PSNR of 30.93 dB is obtained at 0.174 bpp on the test image LENA (512×512

Compressed Random-Access Trees for Spatially Coherent Data

International audienceAdaptive multiresolution hierarchies are highly efficient at representing spatially coherent graphics data. We introduce a framework for compressing such adaptive hierarchies using a compact randomly-accessible tree structure. Prior schemes have explored compressed trees, but nearly all involve entropy coding of a sequential traversal, thus preventing fine-grain random queries required by rendering algorithms. Instead, we use fixed-rate encoding for both the tree topology and its data. Key elements include the replacement of pointers by local offsets, a forested mipmap structure, vector quantization of inter-level residuals, and efficient coding of partially defined data. Both the offsets and codebook indices are stored as byte records for easy parsing by either CPU or GPU shaders. We show that continuous mipmapping over an adaptive tree is more efficient using primal subdivision than traditional dual subdivision. Finally, we demonstrate efficient compression of many data types including light maps, alpha mattes, distance fields, and HDR images

Rate-distortion optimized geometrical image processing

Since geometrical features, like edges, represent one of the most important perceptual information in an image, efficient exploitation of such geometrical information is a key ingredient of many image processing tasks, including compression, denoising and feature extraction. Therefore, the challenge for the image processing community is to design efficient geometrical schemes which can capture the intrinsic geometrical structure of natural images. This thesis focuses on developing computationally efficient tree based algorithms for attaining the optimal rate-distortion (R-D) behavior for certain simple classes of geometrical images, such as piecewise polynomial images with polynomial boundaries. A good approximation of this class allows to develop good approximation and compression schemes for images with strong geometrical features, and as experimental results show, also for real life images. We first investigate both the one dimensional (1-D) and two dimensional (2-D) piecewise polynomials signals. For the 1-D case, our scheme is based on binary tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly and is called prune-join algorithm. This allows to achieve the correct exponentially decaying R-D behavior, D(R) ~ 2-cR, thus improving over classical wavelet schemes. We also show that the computational complexity of the scheme is of O(N logN). We then extend this scheme to the 2-D case using a quadtree, which also achieves an exponentially decaying R-D behavior, for the piecewise polynomial image model, with a low computational cost of O(N logN). Again, the key is an R-D optimized prune and join strategy. We further analyze the R-D performance of the proposed tree algorithms for piecewise smooth signals. We show that the proposed algorithms achieve the oracle like polynomially decaying asymptotic R-D behavior for both the 1-D and 2-D scenarios. Theoretical as well as numerical results show that the proposed schemes outperform wavelet based coders in the 2-D case. We then consider two interesting image processing problems, namely denoising and stereo image compression, in the framework of the tree structured segmentation. For the denoising problem, we present a tree based algorithm which performs denoising by compressing the noisy image and achieves improved visual quality by capturing geometrical features, like edges, of images more precisely compared to wavelet based schemes. We then develop a novel rate-distortion optimized disparity based coding scheme for stereo images. The main novelty of the proposed algorithm is that it performs the joint coding of disparity information and the residual image to achieve better R-D performance in comparison to standard block based stereo image coder