References:
(1). Mathematical Problems in Image Processing - PDE and the Calculus of Variations, by Gilles Aubert and Pierre Kornprobst;
(2). Measure Theory and Fine Properties of Functions by L.C.Evans and R.F.Gariepy
(3). Geometric Level Set Methods, Stanley Osher and Nikos Paragios.
(4). The Handbook of Mathematical Models in Computer Vision, Nikos Paragios, Yunmei Chen, and Olivier Faugeras;
(5). Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods Tony F. Chan and Jianhong (Jackie) Shen;
(6). Paper reading.

Meeting Time and Room: MWF 5 at LIT235

Office Hours: MWF 4 or by appointment

Course Outline:
This course is the continuation of "Introduction to PDE based methods for image analysis: Modeling and algorithms". In this course We will focus on the problems of image segmentation and registration. We will study the mathematical models to solve these problems, the mathematical theories for the well-posedness of the models, and the numerical solutions of the models. Students will gain practical experience by applying algorithms to real world problems.

Arrangement of the course:

Unit 1: Futher discussions on image segmentation
Edge and region based active contours for segmentation
Geodesic active contour and its variation
Region based active contour with parametric density estimatior
Region based active contour with non-parametric density estimatior
Fuzzy/ soft segmentation methods

Unit 2: Futher discussions on image registration
Intensity based image registration using intensity statistics
Parametric density functions, Mutual information, joint entropy based image registration
Inverible and deformable registration
Optical flow for image registration

Unit 3: Statistical shape knowledge in segmentation
Shape representation, shape metrix, alignment of training contours
Linear Shape Statistics in Segmentation: Principal component analysis, Gaussian Model in Shape Space
Nonlinear Shape Statistics in Segmentation: Mercer kernel methods, kernel principal component analysis, probabilistic modeling in feature space
Segmentation with shape prior, simultaneous segmentation and registration

Unit 4: Existence of solutions in Sobolev and BV spaces
Sobolev space and BV space, strong and weak convergences
Convexity, low-semicontinuty and direct method in calculus of variation

Grading:
Students will be required to present a paper and do numerical and theoretical projects related to the course content. These projects may be related to problems of particular interest to the individual student. Grades will be assigned on the basis of these projects.