Differential Invariants as the Base of Triangulated Surface Registration

The paper addresses the problem of 3D model reconstruction from overlapping triangulated range images. A technique for automatic matching of curved freeform surfaces exploiting curvilinear differential structures of the surfaces is presented. We propose a hybrid registration algorithm that combines advantages of working with small amounts of interest points (to attain computational speed), estimates the Euclidean transform matching both surfaces, and uses all available points and the iterative closest reciprocal point algorithm to refine the estimate and finally match surfaces (to attain high precision, good initial estimation avoids local minima). The method works in a bottom-up manner using the hierarchy: points → differential structures (i.e., curvilinear line segments) → surface. The registration is automatic. The only parameter set by the user is the required level of mean curvature. The approach is demonstrated through examples.