Maximum likelihood orientation estimation of 1-D patterns in Laguerre-Gauss subspaces

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Elio D Di ClaudioAlberto Laurenti

Abstract

A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

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Citations

May 4, 2011·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Elio D Di ClaudioAlberto Laurenti
Sep 30, 2017·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Elio D Di Claudio, Giovanni Jacovitti

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IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Elio D Di ClaudioAlberto Laurenti
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