Generalized Perpendicular Bisector and exhaustive discrete circle recognition

Authors:
Eric Andres;Gaëlle Largeteau-Skapin;Marc Rodríguez
Affiliations:
Laboratory XLIM-SIC, University of Poitiers, BP 30179, UMR CNRS 6712, 86962 Futuroscope Chasseneuil Cedex, France;Laboratory XLIM-SIC, University of Poitiers, BP 30179, UMR CNRS 6712, 86962 Futuroscope Chasseneuil Cedex, France;Laboratory XLIM-SIC, University of Poitiers, BP 30179, UMR CNRS 6712, 86962 Futuroscope Chasseneuil Cedex, France
Venue:
Graphical Models
Year:
2011

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Abstract

This paper presents a generalization of the notion of circumcenter as the intersection of perpendicular bisectors. We define Generalized Perpendicular Bisectors between two regions as an area where each point is the center of at least one circle crossing both regions. This allows us to determine all the possible discrete circle centers that cross a given set of pixels. The possible radii can then easily be determined. This exhaustive digital circle parameter computation is adapted to various types of circles/digitization schemes such as Naive, Pythagorean and standard/supercover circles.