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Extraction of the Level Lines of a Bilinear Image

Abstract : We detail precisely an algorithm for the extraction of the level lines of a bilinear image, which is a continuous function interpolating bilinearly a discrete image. If we discard the levels of the discrete image, where topological difficulties arise, a level line is a concatenation of branches of hyperbolas. The algorithm tracks these branches and provides a sampling of the level lines in the form of closed polygons. If the level line contains a saddle point, the hyperbola degenerates to orthogonal segments, where an arbitrary but consistent choice is adopted for the tracking at the bifurcation. In any case, the extracted polygons are disjoint and enclose a bounded region. This allows to order the level lines in an enclosure tree hierarchy, which may be used for a variety of filters. Recovering this tree is a simple post-processing of the extraction algorithm. Source Code The ANSI C++ 03 implementation of the code that we provide is the one which has been peer reviewed and accepted by IPOL. The source code, the code documentation, and the online demo are accessible at the IPOL web page of the article 1. Compilation and usage instructions are included in the README.txt file of the archive. The code is sensibly the same as the one used for computing the mean curvature map of an image [5]. The demo just outputs the level lines and their hierarchy.
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Soumis le : mardi 27 août 2019 - 10:30:55
Dernière modification le : samedi 15 janvier 2022 - 03:58:50
Archivage à long terme le : : samedi 11 janvier 2020 - 02:19:33


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Pascal Monasse. Extraction of the Level Lines of a Bilinear Image. Image Processing On Line, IPOL - Image Processing on Line, 2019, 9, pp.205-219. ⟨10.5201/ipol.2019.269⟩. ⟨hal-02271680⟩



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