A new decomposition scheme for three-dimensional contours based on curvature and torsion

This paper presents a new scheme for segmentation of three-dimensional (3D) contours based on a criterion involving their curvature and torsion properties. Curvature indicates how sharply a curve is turning while torsion measures the extent of its twist in 3D space. Also, curvature and torsion completely define a curve in 3D space. For these reasons, the two together have been chosen here as a set of intrinsic and complete structural features of a contour. The Darboux vector Ω contains both these features as its components. We use the length ∥Ω∥ of the Darboux vector, also known as total curvature, as the criterion for segmentation of the contour. Specifically we choose the zero-crossings of d²∥Ω∥/ds², where s = arc length, as the breakpoints in the segmentation of the contour. The segmentation scheme is described by means of a block diagram which includes filters for calculation of d²∥Ω∥/ds²in terms of appropriate distributional derivatives resulting from the contour parametric equations.