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## Consistent shape maps via semidefinite programming

Venue: | In Computer Graphics Forum |

Citations: | 21 - 3 self |

### Citations

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Algebraic connectivity of graphs.
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(Show Context)
Citation Context ...ere they are random graphs. Deterministic setting. A straightforward relaxation of (5.1) is given by λmax(LGfalses ) ≤ λ2(LG)/2, 1 ≤ s ≤ m. (10) where λ2(LG) is also called the algebraic connectivity =-=[Fie73]-=- of graph G. As the largest eigenvalue of a graph Laplacian is bounded by two times of the maximum (weighted) degree of its vertices, we arrive at the following relaxed exact recovery condition: 9 Cor... |

546 | Robust principal component analysis?” - Candes, Li, et al. - 2011 |

284 | Scape: shape completion and animation of people, - Anguelov, Srinivasan, et al. - 2005 |

114 | Möbius voting for surface correspondence
- Lipman, Funkhouser
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Citation Context ...f m samples and a distance matrix dS(·, ·) that describes all pair-wise distances between these samples. Given a triangular mesh M , we generate such a representation using the procedure described in =-=[LF09]-=-, which first detects extremals of Gaussian curvatures, and then applies furthest point sampling to add the remaining samples . The distance matrix dS(·, ·) stores geodesic distances on M . Map. A poi... |

76 | Reassembling fractured objects by geometric matching - Huang, Flöry, et al. |

67 | Blended intrinsic maps.
- Kim, Lipman, et al.
- 2011
(Show Context)
Citation Context ...ted differently. Following the setup in [KLF11, HZG∗12], we choose 11 categories from SHREC07, where point-based maps are meaningful, and evaluate against sparse manual correspondences as provided in =-=[KLF11]-=-. Input maps. We use blended intrinsic maps [KLF11] to establish initial maps between pairs of shapes. As blended intrinsic maps generate dense vertex-based correspondences, we snap them into point-to... |

62 | Alternating direction augmented Lagrangian methods for semidefinite programming.
- Wen, Goldfarb, et al.
- 2010
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Citation Context ...Numerical optimization. For numerical optimization, we employ the alternating direction method of multipliers technique (ADMM) [BPC∗11]. Our current implementation applies the ADMMmethod described in =-=[WGY10]-=- for solving semidefinite programs. Due to space constraint, we defer the explicit expressions Appendix B. Rounding strategy. As X can take real values in (7), it is possible that the optimal solution... |

47 | Functional maps: A flexible representation of maps between shapes - OVSJANIKOV, BEN-CHEN, et al. - 2012 |

42 | Exploring collections of 3d models using fuzzy correspondences - KIM, LI, et al. - 2012 |

35 | M.: Disambiguating visual relations using loop constraints
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(Show Context)
Citation Context ...tiple shape matching appears as a crucial step in many scientific problems including fusing partially overlapping range scans [Hub02], assembling fractured surfaces [HFG∗06] and structure from motion =-=[ZKP10]-=-. As it is beyond the scope of this paper to review all existing works, we only discuss approaches that can be applied to 3D shapes. To facilitate the discussion, we employ the terminology of a model ... |

33 | Automatic Three-dimensional Modeling from Reality
- Huber
- 2002
(Show Context)
Citation Context ...W∗11,KLM∗12,HZG∗12] on these datasets. 1.1 Related work The problem of multiple shape matching appears as a crucial step in many scientific problems including fusing partially overlapping range scans =-=[Hub02]-=-, assembling fractured surfaces [HFG∗06] and structure from motion [ZKP10]. As it is beyond the scope of this paper to review all existing works, we only discuss approaches that can be applied to 3D s... |

28 | GUIBAS L.: An optimization approach to improving collections of shape maps - NGUYEN, BEN-CHEN, et al. |

24 | An optimization approach for extracting and encoding consistent maps - Huang, Zhang, et al. - 2012 |

20 | Exact and stable recovery of rotations for robust synchronization
- Wang, Singer
- 1211
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Citation Context ...und truth maps. In contrast, the proposed approach admits precise theoretical guarantees. Experimentally, it also modestly outperforms [KLM∗12] and [HZG∗12] on benchmark datasets. In independent work =-=[WS12]-=-, Wang and Singer analyzed a semidefinite programming formulation to the problem of recovering consistent rotational transforms between rigid shapes. Their approach also recognizes the fact that the m... |

15 | Spectral distributions of adjacency and Laplacian matrices of random graphs, The Annals of Applied Probability
- Ding, Jiang
(Show Context)
Citation Context ...(i, j) ∈ E , 1 ≤ s ≤ m are also generated independently with probability q ∈ (0, 1). It is easy to see that Gfalses , 1 ≤ s ≤ m also satisfy the Erdös-Rényi model but with probability pq. As shown in =-=[DJ10]-=-, under the Erdös-Rényi model, as the number of shapes n→∞, the second smallest and the largest eigenvalues of the Laplacian of a random graph G all converge to np with probability 1, i.e., λ2(LG)/np→... |

14 |
Ovsjanikov M, Guibas L. A concise and provably informative multi-scale signature based on heat diffusion. Comput Graph Forum 2009;28(5):1383–92
- Sun
(Show Context)
Citation Context ...e similar to each other (e.g., TOSCA and SCAPE). Alternatively, this setting is also relevant when we focus on maps between extremal points which can be obtained consistently across the shapes (c.f., =-=[SOG09]-=-). In this case, the output consists of cycle-consistent maps between the input shapes Φout = {φij : Si → Sj |1 ≤ i < j ≤ n}. Generalized setting. The generalized setting is used in the case, where in... |

11 |
Chazelle B and Dobkin D: Shape distributions
- Osada, Funkhouser
(Show Context)
Citation Context ...: Consistent correspondences across the Human dataset. Matched points share the same color and radius. with its k-nearest neighbor shapes (k = 5 in this paper) in terms of the intrinsic D2-descriptor =-=[OFCD02]-=- (a histogram of squared geodesic distances between pairs of points). Sampling. Shapes in each category of TOSCA and SCAPE represent the same object, so we place m = 64 samples on each shape and compu... |

9 |
Terence Tao, Decoding by linear programming
- Candes
(Show Context)
Citation Context ...nalyze the optimality condition of the relaxed convex problem to obtain exact recovery conditions. In a broader picture, the proposed approach follows the general methodologies of compressive sensing =-=[CT05]-=- and low-rank matrix recovery [CR09,CLMW11], which analyze and solve difficult optimization problems using their convex relaxations. It is quite challenging to convert the multiple shape matching prob... |

1 | PARABOSCHI L.: Shrec: shape retreval contex: Watertight models track - GIORGI, BIASDTTI - 2007 |