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Edge detection with polynomial frames on the sphere
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DOI：10.1016/j.jat.2025.106279.png)
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Abstract
En 中文
In a recent article, we have shown that a variety of localized polynomial frames, including isotropic as well as directional spherical systems, are suitable for detecting jump discontinuities that lie along circles on the sphere. More precisely, such edges can be identified in terms of their position and orientation by the asymptotic decay of the frame coefficients in an arbitrary small neighborhood. In this paper, we will extend these results to discontinuities which lie along general smooth curves. In particular, we prove upper and lower estimates for the frame coefficients when the analysis function is concentrated in the vicinity of such a singularity. The estimates are given in an asymptotic sense, with respect to some dilation parameter, and they hold uniformly in a neighborhood of the smooth curve segment under consideration. (c) 2025 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Keywords:
Detection of singularities
Analysis of edges
Wavelets on the sphere
Polynomial frames
Directional wavelets
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IF:
0.6
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30
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