Structure and Geometry in Partial Differential Equations for Image Processing and Analysis
Abstract
We first describe results on shape-base image contrast enhancement. This work shows how to perform local contrast enhancement while preserving the shapes in the image. We have transferred this software to Dr. Szymczak from Physical Acoustics at the Naval Research Laboratory for testing on underwater laser images (LIDAR). We then show a novel approach to anisotropic diffusion. This approach is based on robust statistics, and in particular, in the theory of influence functions. This technique is, for example, of particular significance for image denoising prior to segmentation. We conclude this document with a description of a novel technique of incorporating prior information in anisotropic diffusion. The idea is to use Bayes rule to compute posterior distributions, and then, regularize those distributions via partial differential equations before the MAP is computed. Although a number of results have already been obtained in these areas, the work described in this document is still in progress. As was mentioned above, we want to extend the work on shape-preserving contrast enhancement to include additional definitions of shape and adapt it to specific applications. We are also planing to extend the robust framework for anisotropic diffusion to vector-valued data, and investigate fast implementations. We plan to further investigate the underlying theory of the posterior diffusion work, and to apply it to additional problems. The work described in this document opens a number of theoretical questions that we plan to address as well.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 20, 1997
- Accession Number
- ADA330540
Entities
People
- Guillermo Sapiro
Organizations
- University of Minnesota