Edge-Based Image Compression with Homogeneous Diffusion

Abstract

Abstract. It is well-known that edges contain semantically important image information. In this paper we present a lossy compression method for cartoon-like images that exploits information at image edges. These edges are extracted with the Marr-Hildreth operator followed by hysteresis thresholding. Their locations are stored in a lossless way using JBIG. Moreover, we encode the grey or colour values at both sides of each edge by applying quantisation, subsampling and PAQ coding. In the decoding step, information outside these encoded data is recovered by solving the Laplace equation, i.e. we inpaint with the steady state of a homogeneous diffusion process. Our experiments show that the suggested method outperforms the widely-used JPEG standard and can even beat the advanced JPEG2000 standard for cartoon-like images.

Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion

“…With respect to its intention to reconstruct an image from a small set of characteristic data, our paper has some relations to publications where edge information is used to represent the main image content. This has been done in many different formulations [78,19,36,50,1,5,26,29,75,48]. Methods of this type can be seen as representatives of second-generation coding approaches that exploit perceptually relevant features such as edge contours [42].…”

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

“…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].…”

Three-Dimensional Data Compression with Anisotropic Diffusion

“…With JPEG 2000 [9] and DICOM [7] for medical imaging, both the 2-D and 3-D setting are dominated by transform-based approaches. However, a new family of image compression algorithms based on partial differential equations (PDE) has recently emerged [1,6,8]. Those methods have successfully challenged and in some cases surpassed the quality of the established codecs.…”

“…PDE-based approaches [1,6,8] rely on the common idea to store only a small, systematically chosen subset of the image efficiently and reconstruct the missing parts by PDE-based interpolation. Methods based on edge-enhancing diffusion (EED) [1,8] restrict the selection of known data for the sake of storage efficiency and compensate this with the powerful interpolation capacities of EED.…”

“…Methods based on edge-enhancing diffusion (EED) [1,8] restrict the selection of known data for the sake of storage efficiency and compensate this with the powerful interpolation capacities of EED. Compression using edge information and homogeneous diffusion [6] is mostly efficient on cartoon-like recommended for submission to YRF2012 by Prof. Joachim Weickert images. Our 3-D compression algorithm is modelled after R-EED [8], an algorithm that chooses sparse data with a rectangular subdivision scheme and fills in missing image parts with EED-based interpolation.…”