3D Shape Correspondence Under Topological Noise

In this work, we present a new approach for the problem of 3D shape correspondence under topological noise. Topological noise can be easily encountered in 3D models acquired by various ways such as motion capture technology. In our proposed approach, the pair of 3D shapes is brought to comparable topology before doing matching. We remove the connections leading to topological changes by moving the shape surface inward along the surface normal with a velocity relative to the curvature at each point. We employ coarse matching under the isometry assumption after bringing the shapes to comparable topology. Our method successfully performed on MIT samba sequence, SHREC10 and SHREC11 datasets.


3D Correspondence by Breadth First Search Frontiers
Sahillioğlu, Yusuf (null; 2009-06-01)
This paper presents a novel, robust, and fast 3D shape correspondence algorithm applicable to the two snapshots of the same object in arbitrary deformation. Given two such frames as triangle meshes with fixed connectivity, our algorithm first classifies vertices into Breadth-First Search (BFS) frontiers according to their unweighted shortest path distance from a source vertex. This is followed by the rigid or non-rigid alignment of the corresponding frontiers of two meshes as the second and final step. This...
3D Shape Correspondence by Isometry Driven Greedy Optimization
Sahillioğlu, Yusuf (null; 2010-06-01)
We present an automatic method that establishes 3D correspondence between isometric shapes. Our goal is to find an optimal correspondence between two given (nearly) isometric shapes, that minimizes the amount of deviation from isometry. We cast the problem as a complete surface correspondence problem. Our method first divides the given shapes to be matched into surface patches of equal area and then seeks for a mapping between the patch centers which we refer to as base vertices. Hence the correspondence is...
Extended dynamical symmetries of Landau levels in higher dimensions
Kürkcüoğlu, Seçkin; YURDUŞEN, İSMET (Springer Science and Business Media LLC, 2020-02-14)
Continuum models for time-reversal (TR) invariant topological insulators (Tis) in d >= 3 dimensions are provided by harmonic oscillators coupled to certain SO(d) gauge fields. These models are equivalent to the presence of spin-orbit (SO) interaction in the oscillator Hamiltonians at a critical coupling strength (equivalent to the harmonic oscillator frequency) and leads to flat Landau Level (LL) spectra and therefore to infinite degeneracy of either the positive or the negative helicity states depending on...
Quantum Hall effect on odd spheres
Coskun, U. H.; Kürkcüoğlu, Seçkin; Toga, G. C. (2017-03-22)
We solve the Landau problem for charged particles on odd dimensional spheres S2k-1 in the background of constant SO(2k - 1) gauge fields carrying the irreducible representation (I/2,I/2, . . . , I/2). We determine the spectrum of the Hamiltonian, the degeneracy of the Landau levels and give the eigenstates in terms of the Wigner D-functions, and for odd values of I, the explicit local form of the wave functions in the lowest Landau level (LLL). The spectrum of the Dirac operator on S2k-1 in the same gauge f...
Coarse-to-Fine Combinatorial Matching for Dense Isometric Shape Correspondence
Sahillioğlu, Yusuf; Yemez, Y. (2011-08-01)
We present a dense correspondence method for isometric shapes, which is accurate yet computationally efficient. We minimize the isometric distortion directly in the 3D Euclidean space, i.e., in the domain where isometry is originally defined, by using a coarse-to-fine sampling and combinatorial matching algorithm. Our method does not require any initialization and aims to find an accurate solution in the minimum-distortion sense for perfectly isometric shapes. We demonstrate the performance of our method on...
Citation Formats
A. Genctav, Y. Sahillioğlu, and Z. S. Tarı, “3D Shape Correspondence Under Topological Noise,” 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54163.