Instructor: W. Mio	Email: mio@math.fsu.edu
Office: 111 LOV	Phone: 644-5596
Web page: http://www.math.fsu.edu/~mio/
Office Hours: TR 10:30-11:20 am, or by appointment.

Prerequisites: Multivariable Calculus and elements of Linear Algebra.

Text: No textbook will be adopted. We will cover material from several different sources, including several recent, yet unpublished results in shape analysis. A few references are given below.

Course objectives: This course is an introduction to shape theory and is aimed at a broad audience of mathematics, science and engineering students. The typical discussion will include theory, computational models, and applications to problems arising in computer vision and pattern recognition. We will begin with a discussion of Kendall's theory based on landmark representations of shapes and then consider recent continuous extensions of the model, which in turn lead to several new discrete analogues of the classical theory. The discussion will also include multi-resolution representations of shapes and techniques to align and match the geometric features of curves in Euclidean space, which is an important step in making several of the algorithms more useful in practice. Time permitting, we will discuss the important case of surfaces in 3D space and also give an overview of recent developments in the construction of shape spaces of curves equipped with several different shape metrics. Due to the diverse background of the expected audience, we will also cover some basic topics in Fourier series, Hilbert spaces and Sobolev spaces needed for the development of the shape models.

Grading: The evaluation will be based on class participation and several different types of assignments. Due to the interdisciplinary nature of the subject, students will have the option of choosing a combination of computer projects, oral presentations, or other projects. Further details will be discussed in class.

Honor code: The Academic Honor System at The Florida State University is based on the premise that each student has the responsibility 1) to uphold the highest standards of academic integrity in the student's own work, 2) to refuse to tolerate violations of academic integrity in the University community, and 3) to foster a high sense of integrity and social responsibility on the part of the University community.

American Disabilities Act: Students with disabilities needing academic accommodations should register with and provide documentation to the Student Disability Resource Center (SDRC), and bring a letter from the SDRC to the instructor indicating their needs. This should be done within the first week of class.

References: 1. D. Kendall, Shape manifolds, Procrustean metrics and complex projective spaces, Bull. London Math. Soc. 16 (1984), 81-121. 2. I. Dryden and K. Mardia, Statistical Shape Analysis, Wiley, 1998. 3. D. Kendall, D. Barden, T. Carne, and H. Le, Shape and Shape Theory, Wiley, 1999.