A 3-D Contour Segmentation Scheme Based on Curvature and Torsion

The Darboux vector contains both the curvature and torsion of a three-dimensional (3-D) image as its components. Curvature measures how sharply a curve is turning while torsion measures the extent of its twist in 3-D space. Curvature and torsion completely define the shape of a 3-D curve. A scheme is presented that uses the length of this vector, also called the total curvature, for the segmentation of 3-D contours. A quintic B-spline is used in this formulation to obtain the total curvature for noisy data. Examples of nonnoisy and noisy data illustrate the merit of the scheme. >

[1]  Alex Pentland,et al.  On describing complex surface shapes , 1986, Image Vis. Comput..

[2]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Donald S. Fussell,et al.  Computer rendering of stochastic models , 1982, Commun. ACM.

[4]  N. Kehtarnavaz,et al.  Recognition Of 3D Curves Based On Curvature And Torsion , 1988, Defense, Security, and Sensing.

[5]  Robert M. Haralick,et al.  Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Theodosios Pavlidis,et al.  Segmentation of Plane Curves , 1974, IEEE Transactions on Computers.

[7]  Theodosios Pavlidis,et al.  Waveform Segmentation Through Functional Approximation , 1973, IEEE Transactions on Computers.

[8]  R. Voss.  Random Fractal Forgeries , 1985 .

[9]  Herbert Freeman,et al.  Computer Processing of Line-Drawing Images , 1974, CSUR.

[10]  Theodosios Pavlidis,et al.  A Hierarchical Syntactic Shape Analyzer , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[12]  Nasser Kehtarnavaz,et al.  A syntactic/Semantic technique for surface reconstruction from cross-sectional contours , 1988, Comput. Vis. Graph. Image Process..

[13]  Larry S. Davis,et al.  Understanding Shape: Angles and Sides , 1977, IEEE Transactions on Computers.

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

[15]  Nasser Kehtarnavaz,et al.  A framework for surface reconstruction from 3D contours , 1988, Comput. Vis. Graph. Image Process..

[16]  Rui J. P. de Figueiredo,et al.  Waveform Feature Extraction Based on Tauberian Approximation , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Rui J. P. de Figueiredo,et al.  A general moment-invariants/attributed-graph method for three-dimensional object recognition from a single image , 1986, IEEE J. Robotics Autom..