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 Naïve, Pythagorean and standard/supercover circles.