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:

Packages.zip: This includes code for reading and writing .bmp and .jpeg files, the spherical harmonics package, and some code for parsing command line arguments.
Source.zip: This contains the template classes that you will be using to interface with the different Fourier transforms.

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

(11/16/06) The source distribution for computing the Fourier transforms has undergone some major revision. The code has been updated and a new version of Source.zip has replaced the old one.
(10/09/06) A bug has been found in the complex.inl that affected how addition and multiplication of complex numbers was performed. The code has been updated and a new version of Source.zip has replaced the old one.
(10/10/06) Because the C++ code relies on templates, it will not compile under Visual Studios 6.0. If you need a more up-to-date compiler, see the CS staff for a copy of Viusal Studios 2005.
(10/12/06) There was a small bug in the code relating the to the indexing of arrays (a method that should have been declared constant was not). The code has been updated and a new version of Source.zip has replaced the old one.
(10/16/06) There was a bug in the code effecting the linear interpolation of values when the overloaded ::operator( ) method was called. The bug related to how negative integers were rounded and has been resolved. The code has been updated and a new version of Source.zip has replaced the old one.

Assignments

The FFT and Image Processing: (10/13/06)
Pattern/Symmetry Detection and Wave Propagation: (11/03/06)
Spherical Functions: (12/17/06)

Date	Subject	Notes	Misc
9/11/05	Introduction	Notes
9/13/06	Fast String Matching & Math Review	Notes	Fast Pattern Matching in Strings
9/18/06	Inner Product Spaces	Notes
9/20/06	Representations	Notes
9/25/06	Moving Dot Products	Notes
9/27/06	The FFT	Notes	An Algorithm for the Machine Calculation of Complex Fourier Series
10/02/06	Yom Kippur -- Class Cancelled
10/04/06	Allignment, Invariance, and Pattern Matching	Notes
10/09/06	Symmetry Detection	Notes
10/11/06	Differential Equations	Notes
10/16/06	Fall Break
10/18/06	Polynomials and Circular Functions	Notes
10/23/06	Finding Sub-Representations	Notes
10/25/06	Sub-Representations and the Laplacian	Notes
10/30/06	The Spherical Harmonics	Notes
11/01/06	Class Canceled
11/06/06	Spherical Laplcian	Notes
11/08/06	Descriptor Invariance	Notes
11/13/06	Representing Rotations	Notes
11/15/06	Convolution and Axial Symmetry	Notes
11/20/06	Aligning Spherical Functions	Notes
11/22/06	Thanksgiving Eve -- Class Cancelled
11/27/06	Symmetry Detection	Notes
11/29/06
12/04/06
12/06/06
12/11/06

FFTs in Graphics and Vision (600.660)

Course Description

Source Code

Assignments

FFTs in Graphics and Vision
(600.660)