Angular Accuracy of Steerable Feature Detectors
| Autor: | Arash Amini, John Paul Ward, Michael Unser, Julien Fageot, Zsuzsanna Püspöki |
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| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
reconstruction steerable wavelets Computer science Computer Science - Information Theory General Mathematics design edge 02 engineering and technology Tracking (particle physics) wavelets estimation of orientation Wavelet steerable filters 0202 electrical engineering electronic engineering information engineering Computer vision business.industry Information Theory (cs.IT) Applied Mathematics junction detection tracking filters statistics cramer-rao lower bounds 020201 artificial intelligence & image processing Enhanced Data Rates for GSM Evolution Artificial intelligence business |
| Zdroj: | SIAM Journal on Imaging Sciences. 12:344-371 |
| ISSN: | 1936-4954 |
| Popis: | The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated in the literature, and their localization and detection properties are well known. In this paper, we study the complementary topic of local orientation estimation, which has not received similar attention. Simply stated, the problem that we address is the following: estimate the angle of rotation of a pattern with steerable filters centered at the same location, where the image is corrupted by colored isotropic Gaussian noise. For this problem, we use a statistical framework based on the Cram\'{e}r-Rao lower bound (CRLB) that sets a fundamental limit on the accuracy of the corresponding class of estimators. We propose a scheme to measure the performance of estimators based on steerable filters (as a lower bound), while considering the connection to maximum likelihood estimation. Beyond the general results, we analyze the asymptotic behaviour of the lower bound in terms of the order of steerablility and propose an optimal subset of components that minimizes the bound. We define a mechanism for selecting optimal subspaces of the span of the detectors. These are characterized by the most relevant angular frequencies. Finally, we project our template to a basis of steerable functions and experimentally show that the prediction accuracy achieves the predicted CRLB. As an extension, we also consider steerable wavelet detectors. Comment: 13 pages, 3 figures |
| Databáze: | OpenAIRE |
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