Design of Multi-Parameter Steerable Functions Using Cascade Basis Reduction

A new cascade basis reduction method of computing the optimal least-squares set of basis functions to steer a given function locally is presented. The method combines the Lie group-theoretic and the singular value decomposition approaches such that their respective strengths complement each other. Since the Lie group-theoretic approach is used, the sets of basis and steering functions computed can be expressed in analytic form. Because the singular value decomposition method is used, these sets of basis and steering functions are optimal in the least-squares sense. Most importantly, the computational complexity in designing the basis functions for transformation groups with large numbers of parameters is signi cantly reduced. The e ciency of the cascade basis reduction method is demonstrated by designing a set of basis functions to steer a Gabor function under the four-parameter linear transformation group.

• Type: Conference
• Year: 1998
• Where: ICCV
• Authors: Patrick C. Teo, Yacov Hel-Or
• Keywords: Basis Functions, Basis Reduction Method, Cascade Basis Reduction, Computer Vision, ICCV 1998, Singular Value Decomposition, Value Decomposition Method