Arc Segmentation in Linear Time

A linear algorithm based on a discrete geometry approach is proposed for the detection of digital arcs and digital circles using a new representation of them. It is introduced by inspiring from the work of Latecki [1]. By utilizing this representation, we transform the problem of digital arc detection into a problem of digital straight line recognition. We then develop a linear method for arc segmentation of digital curves.

[1]  Peter Damaschke.  The linear time recognition of digital arcs , 1995, Pattern Recognit. Lett..

[2]  Y. Gerard,et al.  An Elementary Algorithm for Digital Ar , 2007 .

[3]  Steve Fisk.  Separating Point Sets by Circles, and the Recognition of Digital Disks , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Eric Andres,et al.  Discrete circles, rings and spheres , 1994, Comput. Graph..

[5]  V. Kovalevsky,et al.  New definition and fast recognition of digital straight segments and arcs , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[6]  Longin Jan Latecki,et al.  Shape Similarity Measure Based on Correspondence of Visual Parts , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Marcel Worring,et al.  Digitized Circular Arcs: Characterization and Parameter Estimation , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Laure Tougne,et al.  On Three Constrained Versions of the Digital Circular Arc Recognition Problem , 2009, DGCI.

[9]  Chul E. Kim,et al.  Digital Disks , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Chul E. Kim,et al.  Digital disks and a digital compactness measure , 1984, STOC '84.

[11]  Peter Sauer,et al.  On the Recognition of Digital Circles in Linear Time , 1993, Comput. Geom..

[12]  Isabelle Debled-Rennesson,et al.  Optimal blurred segments decomposition of noisy shapes in linear time , 2006, Comput. Graph..

[13]  Akira Nakamura,et al.  Digital circles , 1984, Comput. Vis. Graph. Image Process..

[14]  Nimrod Megiddo,et al.  Linear Programming in Linear Time When the Dimension Is Fixed , 1984, JACM.