J. Andrew Bangham, J. R. Hidalgo, Richard Harvey, Gavin C. Cawley,
The Segmentation of Images via Scale-Space Trees, British Machine
Vision Conference, 1998.
Topological analysis of parametric images, submitted.
Abstract: Homology theory is not broadly used in image processing. One of the reasons is that homology theory studies sets, i.e., binary images. Meanwhile, images typically seen in practical applications, such as color photos, have parameters. We will discuss a simple approach to homology theory of images with parameters and its applications in image processing.
Talk, Homology of color images, Sept 21, 2006, MSRI, workshop Applications of topology in science and engineering. Note: The formula in slide 19 (an important one!) is incorrect. Video from MSRI is here. Quality is so-so.
Talk, Low level vision through topological glasses (extension of the one at MSRI), Oct. 19, 2006, Mathematics Colloquium, flyer.
Preprint, submitted. Note: Soon after it was submitted, I realized that a couple of important references are missing:
P. Monasse and F. Guichard. Fast computation of a contrast invariant image representation.
The papers take some similar approaches to the problem. The differences are quite important. They don't use homology. This makes their approach only partially applicable to 3D images. Color images are not discussed. Object counting is not addressed. Image simplification is very similar though.