ChapterZero

One of the reasons I’m so fascinated with image processing is the fact that you easily get direct feedback about the usefulness of your analysis. Among other things, this means that papers in this area are fun for browsing: even if you can’t follow the analysis, you can look at the pictures and get a sense of how worthwhile the results are. And if the papers are written well, you can duplicate the results. Here are links to three particularly interesting papers: Isophote-based Interpolation, Image Processing via the Beltrami operator, A General Framework for Low Level Vision.

The first presents the idea of interpolating using curvature driven evolution of isophotes (curves of constant image intensity), to preserve the geometry of the image; the results for the given test images– given as comparisons with bicubic, nearest neighbor, and linear interpolation– look encouraging. An interesting question is whether there is some analogous idea for multichannel images.

The remaining two papers present a geometric approach to scale-space image processing based on the Polyakov action from high energy physics. The idea is to represent images as surfaces and the processing of them as a minimization of the surface area; this approach has several advantages. In particular, it applies as directly to vector images as it does to scalar images. The second paper has two beautiful examples of this approach used on color images, but doesn’t justify the use of the Polyakov action and surface area minimization approach. The third paper goes into the details of the mathematics.

Possibly relevant posts:

• Hyperspectral imaging (5/12/2006)
• PDEs and functionals (5/6/2007)
• Analysis of non-rigid shapes (11/15/2007)