EE913a: Advanced Topics in Medical Imaging and Computer Vision

Instructor: Hemant Tagare. Phone: 737 4271. Email: hemant.tagare@yale.edu
Time and Location: Tuesday-Thursday 2:30 p.m.- 3:45 p.m.BML-333
Office Hours:  I have not decided on office hours yet. Send me email if you want to
                      meet with me.
Teaching Assistant: There is no official T.A. for the course. However, Jing Yang
                    has temporarily agreed to help out with grading etc. You can reach
                    her at  Email: j.yang@yale.edu (Tel: 785 4905).
Contents: This year we will study differential geometry and its applications to
imaging.
Note: I expect to do some travelling this semester, so we might have to reschedule
          a few classes. Please be flexible.


 

Date

Topic
Sep 4.
Overview of the course. Mathematical Preliminaries. Vector spaces
Functions. Continuity. Differentiability. 
Sep. 9-11
(Need to reschedule)
Curves. Definition. Implicit function theorem. Arc length parameterization.
Frenet Equations.
Sep. 16-18
Curve congruence. Local structure of curves. Frame fields. Connection
Equations.
Sep. 23-25
Surfaces. Definition. Tangent plane. First fundamental form. Examples.
Sept 30-Oct. 2
Orientable surfaces. Gauss map. Shape operator. Second fundamental form.
Oct. 7-Oct.9
Gaussian and mean curvatures. Calculations. Special curves on surfaces.
Oct. 14-16
Structural equations of a surface. Bonnet'ss theorem. Intrinsic geometry of surfaces.
Oct. 21
Gauss' theorem. Geodesics. Parallel transport
 Oct. 23  Mid-term
Nov. 4-6
Gauss Bonnet theorem + Slack time in case we fall behind.
Nov. 11-13
Introduction to manifolds. Tangent spaces. 
Nov. 18-20
Differential forms or Applications
Nov. 25-27
Thanksgiving break.
Dec. 2- Dec. 4
Applications.
Dec. 9 - Dec.11
Applications.
 Dec. 16  Final Exam

Textbook: Differential Geometry of Curves and Surfaces, Manfredo P. Do Carmo, Prentice Hall. (Should be available at the Yale Bookstore)
References: [1] Elementary Differential Geometry, Barret O'Neil, Academic Press.
[2] Solid Shape, Jan Koenderink. MIT Press.

Grading Policy

Homework: 30 %
Mid-term: 30%
Final: 30%
Class Participation: 10%


Class Notes
Will be posted here on the morning of the day of the class.
You are expected to download and print them and bring
your set to class.

Lecture 1 is here. The file has some images, and if it is slow
to download, a smaller version without the images is here.

Lecture 2 is here.

Lecture 3 is here.

Lecture 4 is here.

Lecture 5 is here.

Lecture 6 is here.

Lecture 7 is here.

Lecture 8 is here.

Lecture 9 is here.

Lecture 10 is here.

Lecture 11 is here.

Lecture 12 is here.

Lecture 13 is here.

Lecture 14 is here.

Lecture 16 is here.

Lecture 17 is here.
 
 

Homework Solutions: To be posted.