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Peng-Wen Chen

2011-10-28
15:00:00 - 17:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, I will discuss convex relaxation approaches for imagine processing tasks, focusing on imaging segmentation and imaging matching problems. Many imaging models are proposed based on variation methods. However, these models produce nonconvex minimization problems, which implies that the global optimal solutions cannot be obtained numerically. Recently, researchers have discovered an equivalent convex minimization problem for piecewise constant segmentation model. The second part of the talk is the imaging matching problem. I will start with shape matching problem, which is highly nonconvex. Due to the spacial monotonicity requirement, dynamical programming is a common tool to ensure the optimality. To derive some possible equivalent convex model, I will discuss the well-known convex minimization problem, Monge-Kantorovich mass tranport problem. According to the optimality condition of mass transport problem, the global optimal transformation can be computed via solving a convex minimization problem, if it preserves the cyclical monotonicity, i.e., a gradient. Based on the observation, we present a new registration method for solving point set matching problems. In application, we employed this method to match two sets of pulmonary vascular tree branch points whose displacement is caused by the lung volume changes of the same human subject (a joint work with Ching-Long Lin and I-Liang Chern).