MTH 5050
Mathematical Methods for Image processing II
Fall 2004
Professor : Gnana Bhaskar Tenali (gtenali@fit.edu )
Office: S-317 (Crawford Building) Telephone No: 674-7213 Class Room: S 230
Class Timings: TR 6.30pm- 7.45pm Office Hours : TR 2pm-3pm or by Appointment.
Course Contents:
Calculus of Variations: Variational Derivative- Invariance of Euler’s equation –
Variational problems in parametric form – General variation of a functional – Canonical
form of the Euler equation – Hamilton Jacobi Equation- Front propagation - Second
variation – Variational problems involving multiple integrals.
Linear Image Analysis : The Heat Equation, Existence and Uniqueness, directional
averages and directional heat equations, curve evolution by heat equation.
Contrast Invariant Image analysis-Generalized level lines and topographic map, contrast
invariant equations.
Viscosity Solutions : Definition, properties, uniqueness. Contrast Invariance and viscosity
solutions.
References : Due to the nature of the course, we do not have an assigned text book. The
following books are cited as references, and you are not required to buy any of them.
Students are encouraged to make their own notes based on the lectures. I will provide
lecture notes as well as list of problems for practice, whenever necessary. You are also
encouraged to borrow any of the books from me for occasional reading.
1. G. Aupert and P. Kornprobst, Mathematical Problems in Image Processing, PDE
and the Calculus of Variations, Springer, 2002.
2. L.C. Evans, Partial Differential Equations, AMS, 2000.
3. I.M. Gelfand and SV Fomin, Calculus of Variations, Prentice Hall, 1963.
4. C. Caratheodory, Calculus of Variations and PDE of the first order, AMS Chelsea
Publishing, Second/Third Ed. 1982/1999.
Several research papers that I will inform during the semester.
Grading Policy: There will be two mid term examinations and a final project. The final
project consists of two parts: a formal write-up of at least 5 pages (60%), and a 10-to-15
minute presentation to your classmates (40%). The write-up should be self-contained,
with a concise abstract and introduction, a clear definition of the problem (a small
discovery? an improvement? a generalization of known results? an application to your
own field? etc.), a detailed explanation of your own effort, numerical results (if any), and
a conclusion. The presentation will be accommodated into the last two weeks, and the
write-up must be in my office by 5:00pm, Tuesday, November 30. The topic must be
related to the course. By 4th November, you should have your topic ready. If you cannot
find your favorite topic, talk to me during 25-29, October. I will be glad to help you
choose a topic.. The project must be carried by you. To be uniform and fair in grading,
collaboration is not encouraged for the final project (though important for scientific
research).