Space of circles: its applications in image processing
Jean-Marie Becker, Stéphane Grousson, Didier Guieu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
The 'space of circles' (Gamma) 2 is a representation space in which circles are considered as points. This paper first presents the main properties of this space, with special attention paid to its rich pseudo-euclidean structure, equivalent to duality with respect to a certain paraboloid. The interest of (Gamma) 2 for image processing is demonstrated by two applications regarding a finite set of points in the plane: its associated Voronoi tessellation, and a second one which deals with an efficient description of the circumscribed circle (minimal size surrounding circle) of the given set.