CIS 610, Summer 1, 2009

Brief description:

The purpose of this course is to present geometric methods used in computer vision, robotics and computer graphics. The treatment will be rigorous but I will try very hard to convey intuitions and to give many examples illustrating all these concepts.


This time, I intend to discuss two kinds of topics:
  1. Affine and Euclidean geometry, spectral theorems, SVD, pseudo-inverses and PCA,
  2. Convex sets, polytopes, polyhedra and basics of linear programming

The material in (2) provides firm foundations for linear programming and convex programming.

  1. Basics of Affine Geometry (Chapter 1-2 of GMA)
  2. Euclidean Geometry (Chapters 6 and 7 of GMA)
  3. Spectral theorems in Euclidean geometry and Hermitian spaces, (Chapter 11 of GMA)
  4. Singular value decomposition and polar forms (Chapters 12 and 13 of GMA)
  5. Convex sets and Polytopes
    (Chapter 3 of GMA + Notes)
  6. Foundations of Linear Programming

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Jean Gallier