Geometric modeling of rigid and non-rigid 3D shapes using the global geodesic function
In this paper, we present a novel intrinsic geometric representation of 3D objects. We add the proposed modeling of objects to their topological graphs to ensure a full and compact description necessary for shape-based retrieval, recognition and analysis of 3D models. In our approach, we address the challenges due to pose variability, computational complexity and noisy data by intrinsically and simply describing a 3D object by a global geodesic function. We exploit the geometric features contained in the dense set of iso-levels of this function. Using Whitney easy embedding theorem, we embed the manifold of the geodesic iso-levels in Ropf3 and obtain a single space curve as our geometry descriptor. 3D shape comparison is then reduced to comparing the resulting modeling curves. To quantify the dissimilarities between them we simply compute an L2 distance between classical Euclidian invariants applied to space curves. The experimental results show that in addition to being straightforward and easy to compute, our modeling technique achieves a high level of discrimination, and appears to be robust to both noise and decimation.