Interactive generation of feature contours on surfaces: A minimal paths approach

The interactive specification of curves on surfaces having specific properties presents a number of technical challenges including the geometric representation of surface and curve models; the specification of desirable curve properties and the incorporation of user direction and supervision. Existing techniques for generating curves on surfaces are either completely automated, and therefore limit the range of resulting curves, or completely user driven, which makes the precise specification of certain feature curves impractical. We introduce the novel use of 2D image processing techniques for generating shortest paths, crest lines, minimal paths and iso-contours on surfaces. Feature curves are characterized as geodesics with respect to a Riemannian metric defined on the surface. This representation allows the user to easily specify intrinsic or extrinsic surface features through the specification of a scalar field over the surface. Our interactive method, based on the 2D method called Live-wire, allows the user to adaptively moderate the precision with which they specify the curve, and the automatic control that they relegate to the algorithm. This allows for a seamless transition between user specification of free-form contours and the automated computation of optimal feature contours on a surface. This technique was designed for computer aided surgical planning and simulation, where precise surface based measurements and the detailed specification of surgical cutting operations are required. We demonstrate the effectiveness of our new method by generating feature curves on the surfaces of several geometric and biological shapes.