Low Bit Rate Image Coding in the Scale Space

Scale-space representation has been extensively studied in the computer vision community for analyzing image structures at di erent scales. This paper borrows and develops useful mathematical tools from scale-space theory to facilitate the task of image compression. Instead of compressing the original image directly, we propose to compress its scale-space representation obtained by the forward di usion with a Gaussian kernel at the chosen scale. The major con tribution of this w ork is a no vel solution to the ill-posed inverse di usion problem. We analytically derive a nonlinear lter to deblur Gaussian blurring for 1D ideal step edges. The generalized 2D edge enhancing lter only requires the knowledge of local minimum/maximum and preserves the geometric constraint of edges. When combined with a standard wavelet-based image coder, the forward and inverse di usion can be viewed as a pair of pre-processing and post-processing stages used to select and preserve important image features at the given bit rate. Experiment results ha ve sho wn that the proposed di usion-based tec hniques can dramatically improve the visual quality of reconstructed images at low bit rate (below 0:25bpp).