Ordinary and partial differential equations have found wide applicability in computer vision, graphics, and imaging, including diverse problems such as anisotropic diffusion for image and surface smoothing, estimation of rigid and deformable transformations between images and surfaces for alignment, and curve and surface evolutions for image segmentation, reconstruction from unorganized points, and multi-view stereo.

In this talk, I will present our research activities of applying differential equations in various biomedical computer vision and image/video analysis applications. In our work, the differential equations result from deriving energy minimizing flows using mathematical tools from variational calculus, physics, probability theory, and machine learning via statistical shape distributions. I will describe methods developed for image enhancement, image/volume segmentation using various intensity and information-theoretic measures, image and surface registration/morphing, and tracking of surgical instruments in video. If time permits, I will additionally present a brief overview of our earlier 3D scene reconstruction work.