Abstract

A new rotationally invariant matched filter has been developed. The principle is based on the extraction from the target of the information based on rotation-invariant principal components. For this purpose, the Karhunen-Loeve expansion applied to the target f(r, θ) sampled on angular radii yields its representation with a set of radial eigenfunctions ordered by decreasing eigenvalues: where Ψ_k(θ) denotes the kth eigenvector of the angular covariance matrix. The inverse Karhunen-Loeve transform using a reduced number of radial eigenfunctions yields the synthesis of a new pseudoobject defined by The similarity between the original and the reconstructed targets depends on both the order and the number of the radial eigenfunctions used in the inverse transform. A rotationally invariant filter is then obtained by performing the circular harmonic expansion of the reconstructed pseudoobject.

© 1988 Optical Society of America