Fast algorithm for lapped nonorthogonal transform: application to the image Gabor transform

Michel Poize; Marc Renaudin; Patrick Venier

doi:10.1117/12.131509

1 November 1992 Fast algorithm for lapped nonorthogonal transform: application to the image Gabor transform

Michel Poize, Marc Renaudin, Patrick Venier

Proceedings Volume 1818, Visual Communications and Image Processing '92; (1992) https://doi.org/10.1117/12.131509
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

A fast algorithm to solve the problem of the expansion of a one or two-dimensional finite and discrete signal into a lapped non-orthogonal time-modulated set of functions is described, thus providing a solution to the particular problem of the Gabor transform of images. Starting with current methods, such as Bastiaan's auxiliary functions and the ZAK transform, we describe a new algorithm resulting in a significant decrease in CPU time for image Gabor coefficients with only a slight approximation. The complexity of this algorithm is equivalent to the block Fourier transform plus 2 to 4 operations for each pixel. The global complexity is thus in O(M) compared with the most rapid current method in O(M logM). This algorithm is presented in two formalisms: the transform and the filtering formalisms in order to show the interdependence of the two approaches. Finally, theoretical results are demonstrated by an implementation study of the new fast algorithm.

Citation Download Citation

Michel Poize, Marc Renaudin, and Patrick Venier "Fast algorithm for lapped nonorthogonal transform: application to the image Gabor transform", Proc. SPIE 1818, Visual Communications and Image Processing '92, (1 November 1992); https://doi.org/10.1117/12.131509

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