2012 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (2008)
Anchorage, AK, USA
June 23, 2008 to June 28, 2008
David W. Dreisigmeyer , Los Alamos National Laboratory, NM 87545, USA
Hamid Krim , North Carolina State University, Electrical and Computer Engineering Department, Raleigh, 27695-7911, USA
Djamila Aouada , North Carolina State University, Electrical and Computer Engineering Department, Raleigh, 27695-7911, USA
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 ℝR<sup>3</sup> 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 L<sup>2</sup> 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.
David W. Dreisigmeyer, Hamid Krim, Djamila Aouada, "Geometric modeling of rigid and non-rigid 3D shapes using the global geodesic function", 2012 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, vol. 00, no. , pp. 1-8, 2008, doi:10.1109/CVPRW.2008.4563075