18th

Date: Fri., 16 Nov. 2012 at 16:00 -

Venue: Conference Room, Reseach Center for Frontier Medical Engineering, Chiba University

（千葉大学ＣＦＭＥ Ｂ号棟１階会議室）

Discrete geometry: computational and mathematical tools for biomedical image computing

Dr. Yukiko Kenmochi (CNRS research associate, LIGM, Universite' Paris-Est)

Mr. Yongchao Xu (PhD student, LIGM, Universite' Paris-Est)

After the brief introduction of the recent activities of our research group, A3SI (Algorithms, architectures, analysis and synthesis of images), of LIGM (Laboratoire d'Informatique Gaspard-Monge), we focus our talk on the following two subjects related to medical image computing.

Connected operators are filtering tools that act by merging elementary regions of an image. They have very good contour-preservation properties. A popular strategy to define the connected operators relies on tree-based representations of input image, i.e., a tree with each node weighted by some shape-based attribute, then the filtering can be seen as a thresholding of the tree, seen as a nodes weighted graph. Rather than being satisfied with a mere thresholding, we propose to expand on this idea, and to apply connected filters on this latest graph. Consequently, the filtering is done on the space of shapes build from the image. Such a processing is a generalization of the existing tree-based connected operators. Indeed, the framework includes the classical existing connected operators by attributes. It also allows us to propose a class of novel connected operators from the leveling family, based on shape attributes. Finally, we also propose a novel class of self-dual connected operators that we call morphological shapings. Some application examples including retinal image analysis will be illustrated to show the interest of the proposed approach.

A geometric transformation in the Euclidean space R^n is a bijective transformation preserving some geometric structure; for example, a rigid transformation preserves distances (isometry). However, such important property is generally lost when we consider a geometric transformation in digital images, i.e., in the grid space Z^n, due to the discontinuities induced by the digitization process from R^n to Z^n. In this talk, we focus on 2D rigid transformations. We first study rigid transformations on 2D digital images as fully discrete processes; more precisely the combinatorial structure modeling the whole space of discrete rigid transformations on a finite subset of Z^2 is represented by a finite graph. This graph allows us to understand the above problem due to the transformation discontinuities in Z^2, and to involve topology preservation of digital images under rigid transformations (we generally lose geometric structures of digital images, but we can characterize their topological invariances), which is highly desired in medical image computing.