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 4 at LIT221

Office Hours: MWF 5 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: Review on level set method
1. Curve representation and basic geometry
2. Classical level set method, Variational level set method

Unit 2: Review on image de-noising
Variation method in image denoising
(1). Isotropic smoothing, Total variation based smoothing, P(x)-energy minimization
(2). Differences and connections between these methods

Unit 3: Image segmentation
1. Active contour method in segmentation
(1). Edge based method:
Snake model
Geodesic active contour model
(2). Region based method:
Mumford-Shah's model and CV model
Region based active contour with parametric density estimatior
Region based active contour with non-parametric density estimatior
2. Fuzzy/ soft segmentation methods
3. Incorporating prior information into image segmentation

Unit 4: Image registration
1. Intensity based image registration:
Rigid and deformable segmentation
Mutual information, joint entropy
Monomodality and multimodality image registration
2. Feature based image registration
3. Joint segmentation and registration

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.