FFTs in Graphics and Vision

Course Description

In this course, we will study the Fourier Transform from the perspective of representation theory. We will begin by considering the standard transform defined by the commutative group of rotations in 2D and translations in two- and three-dimensions, and will proceed to the Fourier Transform of the non-commutative group of 3D rotations. Subjects covered will include correlation of images, shape matching, computation of invariances, and symmetry detection.

Source Code

The code you will be using is packed in the 660.660.zip archive. The archive contains Visual Studio 2013 solution files as well as a Makefile that should allow you to compile the code. For windows uers, the FFTW .lib and .dll files are already includes. For Linux users, you will need to download/install those so the compiler can find them. Also, the Makefile assumes that libjpeg is already installed on your system.


Date Subject Notes Misc
Week 1 01/26/15 Introduction Notes
01/28/15 Fast String Matching and Math Review Notes Fast Pattern Matching in Strings
Week 2 02/02/15 More Math Review Notes
02/04/15 Groups and Representations Notes
Week 3 02/09/15 Moving Dot Products Notes
02/11/15 The Fast Fourier Transform Notes An Algorithm for the Machine Calculation of Complex Fourier Series
Week 4 02/16/15 Alignment, Invariance, and Pattern Matching Notes
02/18/15 Rotational and Reflective Symmetry Detection Notes
Week 5 02/23/15 Differential Equations Notes
02/25/15 Homogenous Polynomials and Irreducible Representations Notes
Week 6 03/02/15 Class Cancelled
Week 7 03/09/15 The Laplace Operator Notes
03/11/15 Spherical Harmonics Notes
03/16/15 Spring Break
Week 8 03/23/15 Spherical Harmonics and Legendre Polynomials Notes
03/25/15 The Spherical Laplacian Notes
Week 9 03/30/15 Invariance of Shape Descriptors Notes
04/01/15 Representing Rotations Notes
Week 10 04/06/15 Class Cancelled -- Passover
Week 11 04/13/15 Spherical Convolution and Axial Symmetry Detection Notes
04/15/15 Correlation of Spherical Functions Notes
Week 12 04/20/15 Symmetry Detection Notes
04/22/15 Fast Spherical Alignment Notes
Week 13 04/27/15 Characters and Representations Notes