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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...
To simplify the matching and recognition of 3D objects, we propose to decompose a complex 3D shape into simpler primitive parts. Our partitioning of objects relies on their topological Reeb graphs. Taking advantage of the properties of Morse theory, we detect the critical points of the global geodesic function. These points define the levels at which the segmentation happens. To preserve the geometry...
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...
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...
This paper presents a novel classification strategy for 3D objects. Our technique is based on using a global geodesic function to intrinsically describe the surface of an object. The choice of the global geodesic function ensures the invariance of the classification procedure to scaling and all isometric transformations. Using the Jensen-Shannon divergence, feature parameters are extracted from the...
A new integro-differential invariant for curves in 3D transformed by affine group action is presented in this paper. The derivatives involved are of the first order, and therefore this invariant is significantly less sensitive to noise than classical affine differential invariants, the simplest of which involves derivatives of order 5. A classification procedure based on characteristic curves of an...
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