UBC Mathematics Department
Recent advances in computer vision, based on geometrically invariant nonlinear diffusion processes, have underscored the importance of Lie groups in the equations of image processing and object recognition. In this talk, I will survey how the differential invariants of Lie groups are used to construct both invariant differential equations and invariant signatures for objects in images. New, noise-resistant, invariant numerical schemes for approximating differential invariants, based on joint invariants, will be presented. Finally, practical applications to image processing, including multi-scale resolution, denoising, edge detection, segmentation, and object recognition, will be illustrated, with particular emphasis on medical image processing, including ultrasound and magnetic resonance imaging.