My research activities are in the areas of computational topology and imaging science. In the domain of computational topology, my research objectives are to develop efficient algorithms for
- the computation of topological invariants and structures such as the homologies and cohomologies of spaces and maps, and
- the computation, the characterization, and the representation of critical points and critical regions in scalar and vector fields by means of Morse theory and Conely index theory.
Topological invariants such as homology have been used recently in a wide variety of applications in domains such as dynamical systems, and image processing and recognition. In dynamics, typical problems are translated into problems in topology where invariants such as the Conley index are computed using homology algorithms. In digital image analysis, topological invariants are useful in shape description, indexation, and classification. Scalar and vector fields are used to represent data in different applications areas like geographic information systems and the charaterization of the critical points of the data constitutes a fundamental technique for the study of the important features of the data and its visualization. Other areas of applications include computer graphics, computer aided-design (CAD) and electrical engineering to name but a few. The necessity of improved algorithms for the computation of the structures mentioned above appears evident as new applications of computational topology arise in research for very large data sets. Although several algorithms and software packages have been developed for this purpose, there is still a lot of room for improvement as processing very large data sets is often very time and memory-consuming.
I currently supervise (and co-supervise with colleagues from the Université de Sherbrooke) a group of MSc and Ph.D. students working on these problems and on other problems directly related to computer vision such as shape description and recognition and segmentation using deformable models techniques. I am interested in expanding my research team and I welcome new students interested in working on these issues. I provide for my students an exciting research environment with lab facilities at Bishop’s University and at Université de Sherbrooke where I am a member of two research groups
- The Imaging and Vision Group – MOIVRE (MOdélisation en Imagerie, Vision et RÉseaux de neurones), and
- The Computational Topology Group – GRTC (Groupe de recherche en topologie computationnelle).