FFTs in Graphics and Vision
(600.660)


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 packaged in two zip files: In order to get the code to compile and link correctly, you will need to install the FFTW libraries and .h files on your machine. In case you have trouble converting the .def files to .lib stubs, you can download the necessary .lib files from here.
Additionally, I have also include the .zip file Include.zip which should contain all the header files that are required to get the code in Source.zip to compile correctly.

Updates

Assignments

Date Subject Notes Misc
Week 1 9/04/12 Introduction Notes
9/06/12 Fast String Matching & Math Review Notes Fast Pattern Matching in Strings
Week 2 9/11/12 Inner Product Spaces Notes
9/13/12 Groups and Representations Notes
Week 3 9/18/12 Class Cancelled -- Rosh HaShana
9/20/12 Moving Dot Products Notes
Week 4 9/25/12 The FFT Notes An Algorithm for the Machine Calculation of Complex Fourier Series
9/27/12 Allignment, Invariance, and Pattern Matching Notes
Week 5 10/02/12 Class Cancelled -- Sukkot
10/04/12 Symmetry Detection Notes
Week 6 10/09/12 Class Cancelled -- Simhat Torah
10/11/12 EM Connectomics Workshop
Week 7 10/16/12 Class Cancelled -- Fall Break
10/18/12 Differential Equations Notes Videos: Heat Dissipation Wave Propogation
Week 8 10/23/12 Polynomials and Circular Functions Notes
10/25/12 Class Cancelled
Week 9 10/30/12 Class Cancelled (Hurricane Sandy)
11/01/12 Finding Sub-Representations Notes
Week 10 11/06/12 The Spherical Harmonics Notes
11/08/12 Spherical Harmonics and Legendre Polynomials Notes
Week 11 11/13/12 Sub-Representations and the Laplacian Notes
11/15/12 The Spherical Laplacian Notes Videos: Heat Dissipation Wave Propogation 1 Wave Propogation 2
Week 12 11/20/12 Descriptor Invariance Notes
11/22/12 Class Cancelled -- Thanksgiving
Week 13 11/27/12 Representing Rotations Notes
11/29/12 Convolution and Axial Symmetry Notes
Week 14 12/04/12 Aligning Spherical Functions Notes
12/06/12 Symmetry Detection Notes
Week 14 12/06/12 Fast Rotational Alignment & Surface Reconstruction Notes