Blending Models for Image Enhancement and Coding
Joceli Mayer, Glen G. Langdon · 2015
We propose practical algorithms for efficient representation of images. Polynomial blending functions provide an interesting surface representation. These functions are well known in graphics applications. However, they are seldom used for image coding or enhancement. We use this surface model to represent image regions resulting in high perceived quality. We show that the image artifacts originated by quantization can be drastically reduced by using a representation based on blending functions. We describe two O(n) enhancement algorithms based on Bezier blending functions. They are designed to mitigate the quantization noise generated by lossy image coding techniques like JPEG-DCT and JPEG-LS. One technique uses a fixed order Bezier blending surface and the other technique uses variable order surfaces with a distance transform. Both techniques need an activity estimator to separate smooth regions from edges, noises and textures. We propose a very efficient estimator based on the quantization step used by the coding algorithm. Both techniques provide a significant image enhancement for the images degraded by the lossy coding algorithms. A new recursive triangular partitioning (RTP) is proposed to represent an image by triangular blending surfaces. Efficient triangular blending models are proposed. We compare this partitioning with the traditional quadtree. Analysis and results clearly indicate a superior performance for the RTP. The partitioning information is efficiently encoded and provides a much smaller overhead as compared to free shape boundary coding techniques like chain coding. We combine our technique with Laplacian pyramid and wavelets decomposition because low order blending functions do not represent textures and edges very well. This combination addresses the representation of edges and textures. The performance, measured as a tradeoff between bitrate and distortion, is considerably improved by this combination. The proposed algorithm becomes competitive to the state-of-art algorithms based on JPEG-DCT and wavelets. We investigate the problem of optimally quantizing the control points which define the blending surfaces. Due to the dependence among neighboring triangular surfaces, it turns out to be an exponentially complex problem. Traditional optimization techniques like Lagrangian and Lloyd-Max quantization cannot address this dependence. We propose an O( n · log(n)) greedy algorithm based on priority queues. This greedy algorithm provides an additional improvement in both quality and compression ratio. We extend this greedy algorithm to quantize 3D coordinates representing objects described in VRML. We use a sphere generated by triangles for evaluation purposes. The greedy quantized version presents very little perceived distortion and needs about half the size of the VRML file compressed by algorithms based on Lempel-Ziv (“zip”), the popular approach. The main contribution of the thesis is the novel and the practical algorithms based on blending surfaces applied to image coding and enhancement of lossy compressed images. Both encoding and enhancement using blending functions provide results competitive to the state-of-art algorithms. Emphasis is given to the practical aspects of the problem, where the perceived quality and algorithm complexity are the most interesting issues.