Circular arc reconstruction of digital contours with chosen Hausdorff error

Authors:
Bertrand Kerautret;Jacques-Olivier Lachaud;Thanh Phuong Nguyen
Affiliations:
LORIA (UMR CNRS 7503) Nancy University, France and LAMA (UMR CNRS 5127), University of Savoie, France;LAMA (UMR CNRS 5127), University of Savoie, France;LORIA (UMR CNRS 7503) Nancy University, France
Venue:
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Year:
2011

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Abstract

We address the problem of constructing an approximate continuous representation of a digital contour with guarantees on the Hausdorff error between the digital shape and its reconstruction. Instead of polygonalizing the contour, we propose to reconstruct the shape with circular arcs. To do so, we exploit the recent curvature estimators. From their curvature field, we introduce a new simple and efficient algorithm to approximate a digital shape with as few arcs as possible at a given scale, specified by a maximal admissible Hausdorff distance. We show the potential of our reconstruction method with numerous experiments and we also compare our results with some recent promising approaches. Last, all these algorithms are available online for comparisons on arbitrary shapes.