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IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Signal Processing
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Image Processing
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IEEE Transactions on Image Processing
Local orientation analysis in images by means of the Hermite transform
IEEE Transactions on Image Processing
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IEEE Transactions on Image Processing
The finite ridgelet transform for image representation
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Analysis of Superimposed Oriented Patterns
IEEE Transactions on Image Processing
Interconversion Between Truncated Cartesian and Polar Expansions of Images
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Gauss-Laguerre-Hermite method of keypoint extraction
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Gauss-laguerre keypoints extraction using fast hermite projection method
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Pattern Recognition and Image Analysis
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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.