Design of MultiParameter Steerable Functions Using Cascade Basis Reduction.pdfVIP

Design of MultiParameter Steerable Functions Using Cascade Basis Reduction y z Patrick C Teo and Yacov HelOr y Department of Computer Science z NASA Ames Research Center Stanford University Stanford CA Moett Field CA teowhiteStanfordEDU tokywhiteStanf ordEDU Abstract A new cascade basis reduction metho d of computing the optimal leastsquares set of basis functions steering a given function is presented The metho d combines the Lie grouptheoretic and the singular value decomp osition approaches in such a way that their resp ective strengths complement each other Since the Lie grouptheoretic approach is used the set of basis and steering functions computed can b e expressed analytically Because the singular value decomp osition metho d is used this set of basis and steering functions is optimal in the leastsquares sense Furthermore the computational complexity in designing basis functions for transformation groups with large numb ers of parameters is signicantly reduced The eciency of the cascade basis reduction metho d is demonstrated by designing a set of basis functions that steers a Gab or function under the fourparameter linear transformation group Intro duction A function is called steerable if transformed versions of this function can always b e expressed as linear combinations of a xed set of basis functions These functions have b een used widely in image pro cessing computer vision and recently even in computer graphics One of the main problems in designing steerable functions lies in det