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