Mathematical Methods in Visual Computing

This course provides a comprehensive overview on the mathematical techniques and methods used in visual computing applications. The course contains two central themes: inverse problems in image processing; and statistical visual information analysis. The first theme introduces linear and non-linear inverse problems related to imaging and their solutions. This includes regularization methods for ill-posed problems and solutions to large scale inverse problems. The second theme introduces basic statistical methods of image restoration and analysis. This covers modeling of image intensity distribution, local smoothing filters, wiener filters, image segmentation, and shape analysis. The materials in this course emphasize the theoretical mathematical foundations of image processors as well as the practical implementation and numerical case studies of real imaging problems.