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By Hans Grauert

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This technique has been implemented and Fig. b illustrates the segmentation of a part of a digital ellipse into DCAs. For each DCA, the circle drawn is the smallest separating circle. 5 Conclusion A simple, online and linear-time algorithm is introduced to cope with three constrained problems: recognition of digital circular arcs coming from the digitization of a disk having either a given radius, a boundary that is incident to a given point or a center that is on a given straight line. In addition to its theoretical interest, solving such constrained problems is valuable for the recognition of digital circular arcs.

A digital contour C is a digital circle iff there exists a Euclidean disk D(ω, r) that contains B but no points of ¯ B. Definition 2 is the analog of Definition 1 for parts of C. Definition 2 (Circular arc (Fig. c)). A part (Ci Cj ) of C (with i < j) is a circular arc iff there exists a Euclidean disk D(ω, r) that contains B(Ci Cj ) but ¯(C C ) . no points of B i j This definition is equivalent to the one of Kovalevsky [9]. Cj Ck Ci Ck+1 (a) (b) Cj (c) Ci (d) Fig. 2. (a) An elementary part. (b) A digital circle.

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