Chord-to-point distance accumulation and planar curvature: a new approach to discrete curvature

Abstract In this paper we present a method of calculating a property – which can be regarded as a discrete curvature – of planar digital boundaries. Chord-to-point distance accumulation is computed by accumulating the distance from a point in the boundary to a chord specified by moving end points. According to the shape of the boundary, positive or negative distances are obtained. The values are accumulated as the chord is moved. The distance accumulation is robust with respect to change of chord length compared to planar curvature. The scale space image of the distance accumulation showed that the zero crossings of distance accumulation are quite stable. Experimental results with simulated and real images showed its robustness. Analysis of its relation to planar curvature matched very well with experimental results.

[1]  Philippe Saint-Marc,et al.  Adaptive Smoothing: A General Tool for Early Vision , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Roland T. Chin,et al.  Scale-Based Detection of Corners of Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Arnold W. M. Smeulders,et al.  Length estimators for digitized contours , 1987, Comput. Vis. Graph. Image Process..

[4]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[5]  Longin Jan Latecki,et al.  Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution , 1999, Comput. Vis. Image Underst..

[6]  Michael Brady,et al.  The Curvature Primal Sketch , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Kim L. Boyer,et al.  Robust Contour Decomposition Using a Constant Curvature Criterion , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Marcel Worring,et al.  The accuracy and precision of curvature estimation methods , 1992, Proceedings., 11th IAPR International Conference on Pattern Recognition. Vol. III. Conference C: Image, Speech and Signal Analysis,.

[9]  Farzin Mokhtarian,et al.  Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Roland T. Chin,et al.  On the Detection of Dominant Points on Digital Curves , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  James C. Bezdek,et al.  Curvature and Tangential Deflection of Discrete Arcs: A Theory Based on the Commutator of Scatter Matrix Pairs and Its Application to Vertex Detection in Planar Shape Data , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Robert C. Bolles,et al.  Perceptual Organization and Curve Partitioning , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.