Monotonic Sampling of a Continuous Closed Curve with Respect to Its Gauss Digitization: Application to Length Estimation

In many applications of geometric processing, the border of a continuous shape and of its digitization (i.e., its pixelated representation) should be matched. Assuming that the continuous-shape boundary is locally turn bounded , we prove that there exists a mapping between the boundary of the digiti...

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Bibliographic Details
Published in:Journal of mathematical imaging and vision 2022-10, Vol.64 (8), p.869-891
Main Authors: Le Quentrec, É., Mazo, L., Baudrier, É., Tajine, M.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computer Science
Convergence
Digitization
Estimators
Image Processing and Computer Vision
Mapping
Mathematical Methods in Physics
Signal,Image and Speech Processing
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Summary:In many applications of geometric processing, the border of a continuous shape and of its digitization (i.e., its pixelated representation) should be matched. Assuming that the continuous-shape boundary is locally turn bounded , we prove that there exists a mapping between the boundary of the digitization and the one of the continuous shape such that these boundaries are traveled together in a cyclic order manner. Then, we use this mapping to prove the multigrid convergence of perimeter estimators that are based on polygons inscribed in the digitization. Furthermore, convergence speed is given for this class of estimators. If, moreover, the continuous curves also have a Lipschitz turn, an explicit error bound is calculated.
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-022-01098-8