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.

Abstract. This paper presents a theoretical generalization of the circumcenter as the intersection of generalized perpendicular bisectors. We define generalized bisectors between two regions as an area where each point is the center of at least one circle crossing each of the two regions. These new notions should allow the design of new circle recognition algorithms.

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International audienceThis paper deals with the Simplified Generalized Perpendicular Bisector (SGBP) presented in [15,1]. The SGPB has some interesting properties that we explore. We show in particular that the SGPB can be used for the recognition and exhaustive parameter estimation of noisy discrete circles. A second application we are considering is the error estimation for a class of rotation reconstruction algorithms

Abstract. This paper addresses the problem of the maximal recognition of hyperplanes for an invertible reconstruction of 3D discrete objects. kcuspal cells are introduced as a three dimensional extension of discrete cusps defined by R.Breton. With k-cuspal cells local non planarity on discrete surfaces can be identified in a very straightforward way.