Image Compression with Anisotropic Diffusion
Reads0
Chats0
TLDR
This paper introduces a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion, and shows that this anisotropic diffusion equation with a diffusion tensor outperforms many other PDEs when sparse scattered data must be interpolated.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 removing 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 widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec.read more
Citations
More filters
Journal ArticleDOI
iPiano: Inertial Proximal Algorithm for Nonconvex Optimization
TL;DR: An algorithm for solving a minimization problem composed of a differentiable and a convex function and the algorithm iPiano combines forward-backward splitting with an inertial force yields global convergence of the function values and the arguments.
Posted Content
iPiano: Inertial Proximal Algorithm for Non-Convex Optimization
TL;DR: In this paper, a non-smooth split version of the Heavy-ball method from Polyak is proposed for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex function.
Proceedings ArticleDOI
Object segmentation in video: A hierarchical variational approach for turning point trajectories into dense regions
Peter Ochs,Thomas Brox +1 more
TL;DR: A variational method to obtain dense segmentations from sparse trajectory clusters by propagating information with a hierarchical, nonlinear diffusion process that runs in the continuous domain but takes superpixels into account.
Book
Scale space and variational methods in computer vision : Second International Conference, SSVM 2009, Voss, Norway, June 1-5, 2009 : proceedings
Ssvm,Xue-Cheng Tai +1 more
TL;DR: This paper presents a meta-analysis of the reconstruction of Image Segmentation using a variety of techniques and approaches, including the use of nanofiltration, as well as some new approaches based on the principles of “novelty” and “convexity”.
Book ChapterDOI
From box filtering to fast explicit diffusion
TL;DR: A novel class of algorithms that combine the advantages of both worlds are presented: They are based on simple explicit schemes, while being more efficient than semi-implicit approaches.
References
More filters
Journal ArticleDOI
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Journal ArticleDOI
Scale-space and edge detection using anisotropic diffusion
Pietro Perona,Jitendra Malik +1 more
TL;DR: A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced, chosen to vary spatially in such a way as to encourage intra Region smoothing rather than interregion smoothing.
Journal ArticleDOI
Determining optical flow
TL;DR: In this paper, a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image, and an iterative implementation is shown which successfully computes the Optical Flow for a number of synthetic image sequences.
Proceedings ArticleDOI
Determining Optical Flow
TL;DR: In this article, a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image, and an iterative implementation is shown which successfully computes the Optical Flow for a number of synthetic image sequences.
Journal ArticleDOI
A Method for the Construction of Minimum-Redundancy Codes
TL;DR: A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized.