<title>Wavelets, tomography, and line-segment image representations</title>

摘要

Conventional scale dependent wavelet analysis represents a signal or iniage as a superposition of translated differently scaled versions of the same basis function. When the basis function for time series analysis is a chirp with linear frequency modulation a scale dependent wavelet representation is equivalent to a sequence of projections of the signal timefrequency distribution along differently rotated lines and reconstruction of the signal from its chirped wavelet representation is analogous to tomographic reconstruction from time frequency projections. The same analogy applies in two dimensions if scaled basis functions are replaced by rotated ones such that an image is represented by a superposition of translated differently rotated versions of the same basis function. For rotation dependent wavelet analysis basis functions consisting of very long line segments yield a tomographic representation while shorter line segments yield a line segment image representation as in the primate visual cortex. Applications include binocular robot vision and synthetic aperture radar.