Texts:

1. Required: The Statistical Theory of Shape, Christopher G. Small,  Springer Series in Statistics,  1996.
2. Other Material: Class notes and papers from the following: IEEE Trans. Medical Imaging and other journals

Office hours: T 5th and 6th period, R 6th period or by appointment.

Grading:

1. Homeworks (biweekly): 25%.
2. Midterm: 25%.
   
3. Two individual projects: 25% each.
   

1. Prerequisites: A familiarity with basic concepts in calculus, vector spaces and probability theory. A partial list of basic requirements follows. Calculus: Differentiation, chain rule, integration. Vector spaces: Euclidean spaces, groups of transformations. Probability theory: Expectations, distribution functions.
   
2. Homeworks/programs will be assigned bi-weekly. If you do not have any prior numerical computing experience, I suggest you use MATLAB for the programs.
3. The midterm will be given approximately at the middle of the semester.
   
4. A set of notes including homework assignment notices which will evolve with the course can be found here.
   

 

1. Introduction to shape analysis with applications in medical imaging and computer vision.
2. Transformations on Euclidean Space, differential geometry. (Chapter 2 of Small).
3. Correspondence problem and automated homology in various manifestations: Point-sets, curves and surfaces.
4. Shape spaces, thin-plate splines, atlases and distributions on manifolds (Chapters 3 and 4 of Small).
5. Examples of shape analysis (Chapter 6 of Small and papers from the literature).