Image Compression with Anisotropic Diffusion

Abstract

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for remov- ing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widelyused JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec.

Edge-Based Image Compression with Homogeneous Diffusion

“…It should be noted that contours can be encoded more efficiently than the same number of individual pixels, and they avoid visually unpleasant singularities of the fundamental solution of the Laplace equation. Moreover, by using homogeneous diffusion, our method is simpler and potentially faster than recent compression methods based on nonlinear anisotropic diffusion processes [16].…”

Image compression with B-tree coding algorithm enhanced by data modelling with Burrows-Wheeler transformation

“…Results of compression method explained in this article (Burrows-Wheeler Transform + Range Coding + Context Mixing or shorter EEDC-BWT) will be compared to EEDC [6], JPEG and JPEG2000 on four images of 257x257 elements. Compression was done on five different degrees of compression: 0.8, 0.4, 0.2, 0.1 and 0.05 bpp.…”

“…The interpolation methods are described in section 2 and as a conclusion edgeenhancing diffusion is selected due to its lowest AAE score. Edge Enhancing Diffusion is useful for scattered data interpolation and this method can be used for image reconstruction [6,7]. For compression purposes interpolation quality is not enough if the image data is too expensive to encode.…”

“…Both perform on various compression ratios so in order to achieve better compression, a novel approach to image compression must be used. In this research partial differential equations (PDEs) are discussed and explained because the PDEs are nowadays successfully applied to problems in image denoising, enhancement, inpainting, segmentation and also image compression [6,7,10,14].…”

“…The basic idea of PDE-based interpolation will be described in the following section. Afterwards the new compression model and its compression results will be presented and compared to EEDC [6], JPEG [12] and JPEG 2000 [16].…”