Geometric invariance in space-variant vision systems: the exponential chirp transform

Outlines a method to derive geometric invariance kernels which may be applied to a space-variant sensor architecture. The basic idea as to transform a kernel with desired symmetry properties (e.g. the Fourier kernel) in the domain to the range of the transform. By combining this transformed kernel with the Jacobian of the transformation, the authors obtain a new integral transform, in the range, which has similar properties to the original transform. The authors illustrate this idea with a variant of the Mellin-Fourier transform, applied to an image which has been transformed by a log-polar mapping. The kernel obtained, which the authors call an “exponential chirp” has properties (unlike the Mellin-Fourier transform) which are both consistent with the spatial nature of human vision and can be applied directly in the space-variant image plane. The authors outline applications to visual template matching and auto-correlation, and show a one-dimensional example of a generalization of cepstral auto-correlation using this method