@article{aouada_krim_2010, title={Squigraphs for Fine and Compact Modeling of 3-D Shapes}, volume={19}, ISSN={["1941-0042"]}, DOI={10.1109/TIP.2009.2034693}, abstractNote={We propose to superpose global topological and local geometric 3-D shape descriptors in order to define one compact and discriminative representation for a 3-D object. While a number of available 3-D shape modeling techniques yield satisfactory object classification rates, there is still a need for a refined and efficient identification/recognition of objects among the same class. In this paper, we use Morse theory in a two-phase approach. To ensure the invariance of the final representation to isometric transforms, we choose the Morse function to be a simple and intrinsic global geodesic function defined on the surface of a 3-D object. The first phase is a coarse representation through a reduced topological Reeb graph. We use it for a meaningful decomposition of shapes into primitives. During the second phase, we add detailed geometric information by tracking the evolution of Morse function's level curves along each primitive. We then embed the manifold of these curves into ¿3, and obtain a single curve. By combining phase one and two, we build new graphs rich in topological and geometric information that we refer to as squigraphs. Our experiments show that squigraphs are more general than existing techniques. They achieve similar classification rates to those achieved by classical shape descriptors. Their performance, however, becomes clearly superior when finer classification and identification operations are targeted. Indeed, while other techniques see their performances dropping, squigraphs maintain a performance rate of the order of 97%.}, number={2}, journal={IEEE TRANSACTIONS ON IMAGE PROCESSING}, author={Aouada, Djamila and Krim, Hamid}, year={2010}, month={Feb}, pages={306–321} }
 @article{aouada_krim_2009, title={NOVEL SIMILARITY INVARIANT FOR SPACE CURVES USING TURNING ANGLES AND ITS APPLICATION TO OBJECT RECOGNITION}, ISBN={["978-1-4244-2353-8"]}, ISSN={["1520-6149"]}, DOI={10.1109/icassp.2009.4959824}, abstractNote={We present a new similarity invariant signature for space curves. This signature is based on the information contained in the turning angles of both the tangent and the binormal vectors at each point on the curve. For an accurate comparison of these signatures, we define a Riemannian metric on the space of the invariant. We show through relevant examples that, unlike classical invariants, the one we define in this paper enjoys multiple important properties at the same time, namely, a high discrimination level, independence of any reference point, uniqueness property, as well as a good preservation of the correspondence between curves. Moreover, we illustrate how to match 3D objects by extracting and comparing the invariant signatures of their curved skeletons.}, journal={2009 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS 1- 8, PROCEEDINGS}, author={Aouada, Djamila and Krim, Hamid}, year={2009}, pages={1277–1280} }
 @article{aouada_dreisigmeyer_krim_2008, title={Geometric modeling of rigid and non-rigid 3D shapes using the global geodesic function}, DOI={10.1109/cvprw.2008.4563075}, abstractNote={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.}, journal={Pattern Recognition}, author={Aouada, D. and Dreisigmeyer, D. W. and Krim, H.}, year={2008}, pages={935–942} }