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## Registration of 3D Point Clouds and Meshes: A Survey From Rigid to Non-Rigid

Citations: | 32 - 4 self |

### Citations

3066 |
A method for registration of 3-d shapes
- Besl, McKay
- 1998
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Citation Context ...Type Examples Distance and Angle SC [46], [47] Preserving Properties TransformationLower-Bounding DC [48] Induced Affine Ratio T [4] Constraints Principal Axes T [49] Closest Point Criterion DC [14], =-=[50]-=-, [51] Spin Images SC [52] Curvature SC [53], [54] Features Moments & Spherical Geometry Scale-Space SC SC [54] [17] Integral Descriptors Feature Scale-Space SC SC [46], [48], [55] [48] DCT-DFT Coeffi... |

785 |
Object Modeling by Registration of Multiple Range Images
- Chen, Medioni
- 1991
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Citation Context ...xamples Distance and Angle SC [46], [47] Preserving Properties TransformationLower-Bounding DC [48] Induced Affine Ratio T [4] Constraints Principal Axes T [49] Closest Point Criterion DC [14], [50], =-=[51]-=- Spin Images SC [52] Curvature SC [53], [54] Features Moments & Spherical Geometry Scale-Space SC SC [54] [17] Integral Descriptors Feature Scale-Space SC SC [46], [48], [55] [48] DCT-DFT Coefficients... |

698 | Efficient Variants of the ICP Algorithm
- Rusinkiewicz, Levoy
- 2001
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Citation Context ...valuations and finally, consider future directions and trends guided by our analysis of the core components and data fitting. 1.1 Comparsion to other surveys Among all the existing surveys (Table 1), =-=[11]-=-–[15] focus on rigid registration only. Our survey tries TABLE 1 Existing Surveys of Surface Registration Ref Rigid NonRigid Focus [10] ̌ ̌ surface registration for medical imaging [11] ̌ systematic b... |

569 | Using spin images for efficient object recognition in cluttered 3D scenes
- Johnson, Hebert
- 1999
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Citation Context ... Angle SC [46], [47] Preserving Properties TransformationLower-Bounding DC [48] Induced Affine Ratio T [4] Constraints Principal Axes T [49] Closest Point Criterion DC [14], [50], [51] Spin Images SC =-=[52]-=- Curvature SC [53], [54] Features Moments & Spherical Geometry Scale-Space SC SC [54] [17] Integral Descriptors Feature Scale-Space SC SC [46], [48], [55] [48] DCT-DFT Coefficients SC [17] Cluster Sig... |

372 | A graduated assignment algorithm for graph matching
- Gold, Rangarajan
- 1996
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Citation Context ...of convergence, and robustness—see the earlier survey in [15]. Recent improvements explicitly model inliers and outliers [64], and confidence in correspondences using graduated assignment [59], [60], =-=[65]-=-. There are alternatives of CPC. The first of these was point-to-plane ICP. [51] minimizes the shortest distance between a point and the tangent plane of the closest point on another surface. This all... |

353 | A new point matching algorithm for non-rigid registration
- Chui, Rangarajan
- 2003
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Citation Context ...ms are regularization terms (see Section 4.1.4). β is the inverse computational temperature of the system. This method can be sped up by k nearest neighbors [59] and CPC [60]. Non-Rigid Registration: =-=[35]-=- defines a transformation model using thin plate spline, and uses graduated assignment for non-rigid registration and optimization. 5.2.3 Mean Field Annealing Mean field annealing is a deterministic a... |

280 |
Deformation transfer for triangle meshes
- Sumner, Popović
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Citation Context ... 5 Optimization Methods. Rigid Non-Rigid Registration & Registration & Correspondence Correspondence Examples Examples Gradient Descent & related methods [11], [50]–[52], [54], [62], [93] [24], [28], =-=[30]-=-, [34] Newton, [14], [46], [66], [2], [31], [32], Gauss-Newton, L-M [94] [79], [80] method Quasi-Newton [6], [23], [29], [30] Expectation Maximization [27] [9], [27] Branch and Bound & Tree Search [48... |

250 | A spectral technique for correspondence problems using pairwise constraints
- Leordeanu, Hebert
- 2005
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Citation Context ...], [27] Branch and Bound & Tree Search [48] [70] Graduated Assignment [59], [60] [35] Mean Field Annealing [13] Gaussian Field Framework [95] Game Theoretical Framework [96] Spectral Method [2], [5], =-=[97]-=- Genetic Algorithm & Simulated Annealing [15] Particle Filtering [3] Hough Transform [17] [39] RANSAC [39] [71], [98] Belief Propagation [72] Prune and Search Sections 4.1.2, 4.1.3 Geometric Hashing [... |

150 | Salient geometric features for partial shape matching and similarity
- Gal, Cohen-Or
- 2006
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Citation Context ...7] Preserving Properties TransformationLower-Bounding DC [48] Induced Affine Ratio T [4] Constraints Principal Axes T [49] Closest Point Criterion DC [14], [50], [51] Spin Images SC [52] Curvature SC =-=[53]-=-, [54] Features Moments & Spherical Geometry Scale-Space SC SC [54] [17] Integral Descriptors Feature Scale-Space SC SC [46], [48], [55] [48] DCT-DFT Coefficients SC [17] Cluster Signature SC [46] Dif... |

136 | Point-Set Registration: Coherent Point Drift
- Myronenko, Song
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Citation Context ...ce Time Surface Predefined Skeleton [21] [23] Rigid ICP + Thin Plate Splines Bones and Joints [22] [5], [24]–[26] ≪ N Predefined Skeleton [23] Bones and Joints [5], [24]–[26] Displacement Fields [6], =-=[27]-=- Local Rigid 3N[2], [28] Transformation 12N Local Affine [29]–[35] Transformation ≪ N Intrinsic Transformation [8], [36]–[41] Our classification is based on these three components. The focus on constr... |

121 | As-rigid-as-possible surface modeling
- SORKINE, ALEXA
- 2007
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Citation Context ...ry few optimization steps. It is adaptive to the deformation; the DoF depends on the number of clusters. [28] uses local rigid transformations, an iterative as-rigid-as-possible deformation technique =-=[42]-=- and space-time surface constraints to align surfaces from densely temporally sampled sequences. Local Affine Transformation (12N DoF): Local affine transformations are frequently used in non-rigid re... |

114 | Möbius voting for surface correspondence
- Lipman, Funkhouser
- 2009
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Citation Context ... transformations are similar to the domain theory in analytical learning—a global rule, one reason why these techniques can be cast as optimization problems and solved using the Hough transform [17], =-=[39]-=- or RANSAC technique [4], [71] efficiently. This strong domain theory leads to two examples which demonstrate the successful application of typical deductive inference: 1) [40] suggests that fixing on... |

102 | Least squares 3D surface and curve matching
- Gruen, Akca
- 2005
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Citation Context ... point-to-plane ICP; [14] derives a registration method with quadratic convergence. These methods give faster and more stable convergence with accuracy similar to that of standard ICP. Independently, =-=[67]-=- proposed a similar method based on a generalized Gauss-Markov model which uses a statistical framework to model noise. (5) 4.1.2 Features Features are quantities (e.g. principal curvatures) that desc... |

78 | Scale-invariant heat kernel signatures for non-rigid shape recognition
- MM, Kokkinos
- 2010
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Citation Context ...ne isometric mapping. [87] relates and reinterprets HKS with other spectral shape matching techniques through the Gromov-Wasserstein distance. Over the past years, variants of HKS have been proposed. =-=[74]-=- uses Fourier transform to avoid scale differences and defines a scale-invariant version of HKS. [75] extends HKS to volumetric data, using volumetric distance. [76] defines a new first fundamental fo... |

76 | and Szymon Rusinkiewicz. Global non-rigid alignment of 3-d scans - Brown - 2007 |

66 |
Multi-scale features for approximate alignment of point-based surfaces
- LI, GUSKOV
- 2005
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Citation Context ...dely studied. Many kinds of features or landmarks have been proposed, often tailored to the nature of the images, and have inspired the development of surface registration methods (e.g. based on SIFT =-=[17]-=-). Recently, non-parametric image registration techniques have been developed for medical images. These take into account physical properties (e.g. elasticity or viscosity) of tissues, and may also pr... |

62 | A review of geometric transformations for nonrigid body registration
- Holden
- 2008
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Citation Context ...en developed for medical images. These take into account physical properties (e.g. elasticity or viscosity) of tissues, and may also prove useful in surface registration. Readers are referred to [18]–=-=[20]-=- for surveys of such techniques.JOURNAL OF L AT E X CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 3 1.3 Organization Our survey is organized as follows. Section 2 establishes the connection between data f... |

49 |
Robust 3D shape correspondence in the spectral domain
- Jain, Zhang
- 2006
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Citation Context ...edefined Skeleton [23] Bones and Joints [5], [24]–[26] Displacement Fields [6], [27] Local Rigid 3N[2], [28] Transformation 12N Local Affine [29]–[35] Transformation ≪ N Intrinsic Transformation [8], =-=[36]-=-–[41] Our classification is based on these three components. The focus on constraints, in particular, allows us to compare the novelty of various approaches. Since each component interacts with the ot... |

47 | Global optimization for shape fitting
- Lempitsky, Boykov
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Citation Context ... be captured from different viewpoints, each is associated with a different coordinate system. To allow them to be recombined to reconstruct the surfaces that represent the original objects or scenes =-=[1]-=-, these data must be registered. Surface registration is thus an essential component of the 3D acquisition pipeline and is fundamental to computer vision, computer graphics and reverse engineering. Re... |

45 |
M.: Automatic registration for articulated shapes
- CHANG, ZWICKER
- 2008
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Citation Context ...er joints by rigid transformations (e.g. a translation). Bones and Joints: More recent techniques do not use an explicit skeleton. [24] uses predefined bone information to track bone transformations. =-=[25]-=- searches in a finite set of plausible clustered rigid transforms. The small deformations of joints are obtained by blending the transformations of two adjacent bones in the overlap regions [25]: f(pi... |

38 |
Articulated object reconstruction and markerless motion capture from depth video
- Pekelny, Gotsman
- 2008
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Citation Context ... space defined by all possible correspondences. For a sequence of 3D scans, adjacent frames are roughly aligned, and correspondences can be tracked [6], [21], [28], [33], [79]. Other approaches [23], =-=[24]-=-, [29], [30], [43] assume markers or specific segmentation information are provided. 5.6 Observations and Discussion Rigid and non-rigid registration are typically cast as optimization problems. The e... |

27 | A multi-resolution icp with heuristic closest point search for fast and robust 3d registration of range images
- Jost, Hugli
- 2003
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Citation Context ...Scale-Space SC [48] Size & Curvature SC [53] Multi-Scale Slippage SC [57] MSER SC [58] Equalizing Regularization Correspondences DC [59], [60] Maximizing Correspondences DC [13], [61] Localization DC =-=[62]-=- Search Constraint Hierarchical Approaches DC [56], [62] In rigid registration, correspondences assist in further pruning the transformation search space, whilst in the non-rigid case, establishing co... |

19 | Automatic 3d free form shape matching using the graduated assignment algorithm
- Liu
- 2005
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Citation Context ...[56] Rareness SC [48] Saliency Geometry Scale-Space SC [17] Feature Scale-Space SC [48] Size & Curvature SC [53] Multi-Scale Slippage SC [57] MSER SC [58] Equalizing Regularization Correspondences DC =-=[59]-=-, [60] Maximizing Correspondences DC [13], [61] Localization DC [62] Search Constraint Hierarchical Approaches DC [56], [62] In rigid registration, correspondences assist in further pruning the transf... |

11 |
A spectral notion of Gromov-Wasserstein distance and related methods
- Mémoli
- 2011
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Citation Context ...intrinsic (invariant to isometric deformation), multi-scale, informative (contains all information about the intrinsic geometry of a shape) and stable. It is used in [40] to define isometric mapping. =-=[87]-=- relates and reinterprets HKS with other spectral shape matching techniques through the Gromov-Wasserstein distance. Over the past years, variants of HKS have been proposed. [74] uses Fourier transfor... |

10 |
ET AL.: SHREC 2011: Robust feature detection and description benchmark
- BOYER, BRONSTEIN, et al.
- 2011
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Citation Context ...uited to smooth surfaces due to its definition. SHOT signatures perform better than spin images [68]. A comparison of several recent features and saliency measures for nonrigid shapes can be found in =-=[91]-=-. Discussion on priors and space-time registration: Here we discuss the constraints of non-rigid registrations in terms of the strength of prior. Markers and templates are explicit prior knowledge pro... |

9 |
Minimum-distortion isometric shape correspondence using EM algorithm
- Sahillioğlu, Yemez
- 2012
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Citation Context ...[50]–[52], [54], [62], [93] [24], [28], [30], [34] Newton, [14], [46], [66], [2], [31], [32], Gauss-Newton, L-M [94] [79], [80] method Quasi-Newton [6], [23], [29], [30] Expectation Maximization [27] =-=[9]-=-, [27] Branch and Bound & Tree Search [48] [70] Graduated Assignment [59], [60] [35] Mean Field Annealing [13] Gaussian Field Framework [95] Game Theoretical Framework [96] Spectral Method [2], [5], [... |

6 |
et al. 3D analysis of facial morphology
- Hammond, TJ, et al.
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Citation Context ...establishing correspondences across a set of 3D models from heterogeneous data source, scale becomes an important factor. One example includes the registration of sets of faces from different persons =-=[44]-=-. Procrustes analysis [45] is one such important technique. 4 CONSTRAINTS FOR RIGID AND NONRIGID REGISTRATION We next classify various constraints, and roughly ordered them in decreasing strength of p... |

5 | A mean field annealing approach to accurate free form shape matching
- Liu
- 2007
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Citation Context ...s of Surface Registration Ref Rigid NonRigid Focus [10] ̌ ̌ surface registration for medical imaging [11] ̌ systematic breakdown of ICP and its variants [12] ̌ registration and fusion of range images =-=[13]-=- ̌ comparison of several Improved ICPs [14] ̌ comparison of quadratic approximants and ICP [15] ̌ coarse vs fine, pairwise vs multi-view alignments [16] ̌ ̌ techniques for shape correspondence to conn... |

5 | et al, Mutual-Information-Based Registration of Medical Images: A Survey - Pluim |

5 | Constraints for closest point finding
- Liu
- 2008
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Citation Context ...n R,t ∑ ‖qi − (Rpi + t)‖ 2 i This iterative algorithm must be carefully initialized. At each step a new set of parameters (CPC correspondences, rotation R and translation t) are computed and updated. =-=[63]-=- recently provided a formal treatment of CPC showing that it guarantees the established point correspondences cannot be too wrong at each step: it is impossible that some correspondences are of high q... |

4 |
Fofi D, et al. A review of recent range image registration methods with accuracy evaluation. Image Vision Comput 2007; 25: 578–596
- Salvi, Matabosch
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Citation Context ...tions and finally, consider future directions and trends guided by our analysis of the core components and data fitting. 1.1 Comparsion to other surveys Among all the existing surveys (Table 1), [11]–=-=[15]-=- focus on rigid registration only. Our survey tries TABLE 1 Existing Surveys of Surface Registration Ref Rigid NonRigid Focus [10] ̌ ̌ surface registration for medical imaging [11] ̌ systematic breakd... |

4 |
Robust principal axes determination for point-based shapes using least median of squares.” Computer-Aided Design, 41(4), 293–305. Additional imperfection shapes
- Liu, Ramani
- 2009
(Show Context)
Citation Context ...and evaluate the range of convergence. In general, the broader and more stable the convergence funnel, the better the method [94]. Certain methods are designed to obtain coarse alignments (e.g. [17], =-=[49]-=-; see [15]). Non-Rigid Registration: [22], [32] use rigid registration to find an initial estimate. [2] tries multiple initializations if the error of the first is too high. [25] finds the initial tra... |

4 |
et al., “Fast exact and approximate geodesics on meshes
- Surazhsky, Surazhsky, et al.
- 2005
(Show Context)
Citation Context ...distances by unfolding boundary of holes. The geodesic distance is often found byJOURNAL OF L AT E X CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 9 solving the eikonal equation and wavefront propagation =-=[85]-=-. [86] recognizes the connection between heat and distance, and develops an efficient scheme to find geodesic distance, which is less sensitive to noise and holes: d 2 (x, y) = limt→0 −4t log ht(x, y)... |

3 |
et al., “Optimal step nonrigid ICP algorithms for surface registration
- Amberg
(Show Context)
Citation Context ...DoF): Local affine transformations are frequently used in non-rigid registration [29], [31]. Higher DoFs allow more freedom to capture fine surface detail changes (e.g. body fat [43], wrinkles [32]). =-=[34]-=- defines a model: f(pi) = Aipi and uses stiffness to ensure adjacent transformations are similar. [33] uses differential coordinates and can be considered as a local affine transformation with a smoot... |

3 |
et al. SCAPE: Shape Completion and Animation of People
- Anguelov
- 2005
(Show Context)
Citation Context ...e Transformation (12N DoF): Local affine transformations are frequently used in non-rigid registration [29], [31]. Higher DoFs allow more freedom to capture fine surface detail changes (e.g. body fat =-=[43]-=-, wrinkles [32]). [34] defines a model: f(pi) = Aipi and uses stiffness to ensure adjacent transformations are similar. [33] uses differential coordinates and can be considered as a local affine trans... |

3 |
al.: "Robust global registration
- Gelfand, et
- 2005
(Show Context)
Citation Context ...onstraints. T: Transformation; SC / DC: Sparse / Dense Correspondence. Constraints Classifications Type Examples Distance and Angle SC [46], [47] Preserving Properties TransformationLower-Bounding DC =-=[48]-=- Induced Affine Ratio T [4] Constraints Principal Axes T [49] Closest Point Criterion DC [14], [50], [51] Spin Images SC [52] Curvature SC [53], [54] Features Moments & Spherical Geometry Scale-Space ... |

3 | et al., "Spacetime faces: high resolution capture for modeling and animation - Zhang - 2004 |

3 |
et al. Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation
- Fouss
- 2007
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Citation Context ...genvalues and eigenfunctions of ∆. These include the diffusion distance [38] (Ω(λk) = e −2tλk ) which measures the degree of connectivity of two points by paths of length t; the commute-time distance =-=[81]-=- (Ω(λk) = λ −1 k ) which is a scale-invariant version of the diffusion distance; and the biharmonic distance [82] (Ω(λk) = λ −2 k ) which balances the local and global properties of diffusion distance... |

3 |
An intrinsic algorithm for computing geodesic distance fields on triangle meshes with holes. Graphical Models 74
- Quynh, He, et al.
- 2012
(Show Context)
Citation Context ... = y where ˆg provides the inner product to measure length. Geodesic distance is sensitive to noise and holes. [83] proposes fuzzy geodesic distances which trades off between precision and stability. =-=[84]-=- approximates geodesic distances by unfolding boundary of holes. The geodesic distance is often found byJOURNAL OF L AT E X CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 9 solving the eikonal equation and... |

3 |
et al. Persistent Heat Signature for Pose-oblivious Matching of Incomplete Models [C] // Computer Graphics Forum
- Dey, Li, et al.
(Show Context)
Citation Context ...tegral is stable under changes of surface detail. The heat kernel signature (HKS, Section 4.2.4) provides the basis for the definition of salient points and important components for non-rigid shapes. =-=[88]-=- defines ”Persistent Heat Signature” for points using persistent homology. The idea is to track and identify critical points (maxima, minima) when the topology of HKS changes over the surface. [89], [... |

2 |
Ovsjanikov M, et al. Efficient reconstruction of nonrigid shape and motion from real-time 3d scanner data
- Wand, Adams
(Show Context)
Citation Context ... include techniques that target articulation, like [5] that can handle large gaps in 4D sequences, reduce high dimensionality of deformations through automatic construction of consensus skeletons and =-=[6]-=- that can register 4D surfaces and produce an urshape template; [7] that supports facial capture and animation of avatar heads in real-time; and [8], [9] that can handle near- to approximateisometric ... |

2 | et al., “Realtime performance-based facial animation - Weise - 2011 |

2 |
et al., “An algorithmic overview of surface registration techniques for medical imaging
- Audette
- 2000
(Show Context)
Citation Context ...rsion to other surveys Among all the existing surveys (Table 1), [11]–[15] focus on rigid registration only. Our survey tries TABLE 1 Existing Surveys of Surface Registration Ref Rigid NonRigid Focus =-=[10]-=- ̌ ̌ surface registration for medical imaging [11] ̌ systematic breakdown of ICP and its variants [12] ̌ registration and fusion of range images [13] ̌ comparison of several Improved ICPs [14] ̌ compa... |

2 | Kaick et al. “A survey on shape correspondence - van |

2 |
et al., “Articulated body deformation from range scan data
- Allen
- 2002
(Show Context)
Citation Context ...ly) Isometric Deformation TABLE 2 Transformation Models DoF Model Formulation Examples 6 Euclidean Transformation all rigid cases 7-18 Displacement Field + Space Time Surface Predefined Skeleton [21] =-=[23]-=- Rigid ICP + Thin Plate Splines Bones and Joints [22] [5], [24]–[26] ≪ N Predefined Skeleton [23] Bones and Joints [5], [24]–[26] Displacement Fields [6], [27] Local Rigid 3N[2], [28] Transformation 1... |

2 |
et al., Deformation-driven shape correspondence, in
- Zhang, Sheffer, et al.
(Show Context)
Citation Context ...on Type Examples DeformationInduced Constraints 3D Objects SC [69] Optical/Manual SC [23], [33], [34] Template DC, D [6], [23], [28], [34] Isometry Consistency SC, D Self-Deformation Distortion SC, D =-=[70]-=- Spin Images SC [25], [72] Curvature SC [71], [72] Integral Features Descriptors SC [46] Heat Kernel Signature SC [73]–[78] Saliency Extremities Geometric Coherence Search SC DC,D Closest Point [70] S... |

1 |
et al., “Non-rigid registration under isometric deformations
- Huang
- 2008
(Show Context)
Citation Context ...ght non-rigid surface registration into focus. Over the past two decades, many effective rigid registration techniques have been developed. Many of those aforementioned challenges are being addressed =-=[2]-=-. These include [3] which can handle up to 35% noise, and part-in-whole problem, and [4] which can handle up to 40% outliers, and down to 40% overlap as demonstrated in their experiments. Comparativel... |

1 |
et al., “Particle filtering for registration of 2D and 3D point sets with stochastic dynamics
- Sandhu
(Show Context)
Citation Context ... [59], [60] [35] Mean Field Annealing [13] Gaussian Field Framework [95] Game Theoretical Framework [96] Spectral Method [2], [5], [97] Genetic Algorithm & Simulated Annealing [15] Particle Filtering =-=[3]-=- Hough Transform [17] [39] RANSAC [39] [71], [98] Belief Propagation [72] Prune and Search Sections 4.1.2, 4.1.3 Geometric Hashing [53] Embedding [36]–[38], [99] Techniques most frequently used optimi... |

1 |
et al., “4-points congruent sets for robust pairwise surface registration
- Aiger
- 2008
(Show Context)
Citation Context ... rigid registration techniques have been developed. Many of those aforementioned challenges are being addressed [2]. These include [3] which can handle up to 35% noise, and part-in-whole problem, and =-=[4]-=- which can handle up to 40% outliers, and down to 40% overlap as demonstrated in their experiments. Comparatively, non-rigid registration techniques are still in their infancy. Yet many useful techniq... |

1 | et al., “Consensus skeleton for non-rigid space-time registration - Zheng - 2010 |

1 |
et al., “Blended intrinsic maps
- Kim
- 2011
(Show Context)
Citation Context ...h automatic construction of consensus skeletons and [6] that can register 4D surfaces and produce an urshape template; [7] that supports facial capture and animation of avatar heads in real-time; and =-=[8]-=-, [9] that can handle near- to approximateisometric deformation. All these have changed the landscape of digital geometry processing, migrating the focuses to dynamic scenes and motions. The goal of t... |

1 |
et al., “Special issue on registration and fusion of range images
- Rodrigues
- 2002
(Show Context)
Citation Context ... only. Our survey tries TABLE 1 Existing Surveys of Surface Registration Ref Rigid NonRigid Focus [10] ̌ ̌ surface registration for medical imaging [11] ̌ systematic breakdown of ICP and its variants =-=[12]-=- ̌ registration and fusion of range images [13] ̌ comparison of several Improved ICPs [14] ̌ comparison of quadratic approximants and ICP [15] ̌ coarse vs fine, pairwise vs multi-view alignments [16] ... |

1 |
et al., “Geometry and convergence analysis of algorithms for registration of 3D shapes
- Pottmann
- 2006
(Show Context)
Citation Context ...ed an initial estimate. Rigid Registration: [67] interactively selects three common points to define an initial rigid transformation. [46], [52] use reliable correspondences to automate this process. =-=[14]-=-, [54], [59], [60], [62], [64], [94] test their methods on a set of predefined initial transformations within a certain range, and evaluate the range of convergence. In general, the broader and more s... |

1 | Non-rigid image registration: theory and practice - Hill - 2004 |

1 |
et al., “Dynamic geometry registration
- Mitra
(Show Context)
Citation Context ...(Nearly) Isometric Deformation TABLE 2 Transformation Models DoF Model Formulation Examples 6 Euclidean Transformation all rigid cases 7-18 Displacement Field + Space Time Surface Predefined Skeleton =-=[21]-=- [23] Rigid ICP + Thin Plate Splines Bones and Joints [22] [5], [24]–[26] ≪ N Predefined Skeleton [23] Bones and Joints [5], [24]–[26] Displacement Fields [6], [27] Local Rigid 3N[2], [28] Transformat... |

1 | registration of dynamic range scans for articulated model reconstruction - “Global - 2011 |

1 |
et al., “Reconstructing animated meshes from time-varying point clouds
- Süßmuth
- 2008
(Show Context)
Citation Context ...by looking for clusters in transformation space defined by all possible correspondences. For a sequence of 3D scans, adjacent frames are roughly aligned, and correspondences can be tracked [6], [21], =-=[28]-=-, [33], [79]. Other approaches [23], [24], [29], [30], [43] assume markers or specific segmentation information are provided. 5.6 Observations and Discussion Rigid and non-rigid registration are typic... |

1 |
et al., “The space of human body shapes: reconstruction and parameterization from range scans
- Allen
(Show Context)
Citation Context ...n Plate Splines Bones and Joints [22] [5], [24]–[26] ≪ N Predefined Skeleton [23] Bones and Joints [5], [24]–[26] Displacement Fields [6], [27] Local Rigid 3N[2], [28] Transformation 12N Local Affine =-=[29]-=-–[35] Transformation ≪ N Intrinsic Transformation [8], [36]–[41] Our classification is based on these three components. The focus on constraints, in particular, allows us to compare the novelty of var... |

1 | et al., “Global correspondence optimization for nonrigid registration of depth scans - Li - 2008 |

1 |
single-view geometry and motion reconstruction
- “Robust
- 2009
(Show Context)
Citation Context ...n (12N DoF): Local affine transformations are frequently used in non-rigid registration [29], [31]. Higher DoFs allow more freedom to capture fine surface detail changes (e.g. body fat [43], wrinkles =-=[32]-=-). [34] defines a model: f(pi) = Aipi and uses stiffness to ensure adjacent transformations are similar. [33] uses differential coordinates and can be considered as a local affine transformation with ... |

1 |
et al., “Modeling deformable objects from a single depth camera
- Liao
- 2009
(Show Context)
Citation Context ...vents a trivial solution with all ωi = 0. Geometric Coherence: Various methods encourage geometric properties to vary as smoothly as possible, or non-rigid transformation fields to be coherent. [28], =-=[33]-=- use differential coordinates (first order) and [35] uses thin plate splines (TPS) (second order) in nonrigid deformation to provide smoothness. [27] encourages displacement vectors to point in simila... |

1 | et al., “Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching,” PNAS - Bronstein - 2006 |

1 |
Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching
- “A
- 2013
(Show Context)
Citation Context ...works include: [36] seeks a low dimensional embedding that preserves all pairwise geodesic distances, [37] uses generalized multidimensional scaling to embed one mesh in another for partial matching, =-=[38]-=- uses diffusion distance and GromovHausdorff distance to handle topological noise, and [40] shows that a single correspondence can establish correspondences for all points using the heat kernel. [39] ... |

1 |
et al., “One point isometric matching with the heat kernel
- Ovsjanikov
- 2010
(Show Context)
Citation Context ...distances, [37] uses generalized multidimensional scaling to embed one mesh in another for partial matching, [38] uses diffusion distance and GromovHausdorff distance to handle topological noise, and =-=[40]-=- shows that a single correspondence can establish correspondences for all points using the heat kernel. [39] pioneers the use of the Möbius transformation (isometry is a subgroup of the Mobiüs group).... |

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et al., “Intrinsic dense 3d surface tracking
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- 2011
(Show Context)
Citation Context ...ned Skeleton [23] Bones and Joints [5], [24]–[26] Displacement Fields [6], [27] Local Rigid 3N[2], [28] Transformation 12N Local Affine [29]–[35] Transformation ≪ N Intrinsic Transformation [8], [36]–=-=[41]-=- Our classification is based on these three components. The focus on constraints, in particular, allows us to compare the novelty of various approaches. Since each component interacts with the others,... |

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et al., “Global registration of multiple point clouds embedding the generalized procrustes analysis into an ICP framework
- Toldo
- 2010
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Citation Context ...es across a set of 3D models from heterogeneous data source, scale becomes an important factor. One example includes the registration of sets of faces from different persons [44]. Procrustes analysis =-=[45]-=- is one such important technique. 4 CONSTRAINTS FOR RIGID AND NONRIGID REGISTRATION We next classify various constraints, and roughly ordered them in decreasing strength of priors: see Tables 3 (rigid... |

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et al., “Reassembling fractured objects by geometric matching
- Huang
- 2006
(Show Context)
Citation Context ... transformation and correspondences. TABLE 3 Rigid Registration Constraints. T: Transformation; SC / DC: Sparse / Dense Correspondence. Constraints Classifications Type Examples Distance and Angle SC =-=[46]-=-, [47] Preserving Properties TransformationLower-Bounding DC [48] Induced Affine Ratio T [4] Constraints Principal Axes T [49] Closest Point Criterion DC [14], [50], [51] Spin Images SC [52] Curvature... |

1 | et al., “RANSAC-based DARCES: a new approach to fast automatic registration of partially overlapping range images - Chen - 1999 |

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et al., “ICP registration using invariant features
- Sharp
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Citation Context ...initial estimate. Rigid Registration: [67] interactively selects three common points to define an initial rigid transformation. [46], [52] use reliable correspondences to automate this process. [14], =-=[54]-=-, [59], [60], [62], [64], [94] test their methods on a set of predefined initial transformations within a certain range, and evaluate the range of convergence. In general, the broader and more stable ... |

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et al., “Integral invariants for robust geometry processing
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Citation Context ... Criterion DC [14], [50], [51] Spin Images SC [52] Curvature SC [53], [54] Features Moments & Spherical Geometry Scale-Space SC SC [54] [17] Integral Descriptors Feature Scale-Space SC SC [46], [48], =-=[55]-=- [48] DCT-DFT Coefficients SC [17] Cluster Signature SC [46] Differential Properties SC [56] Rareness SC [48] Saliency Geometry Scale-Space SC [17] Feature Scale-Space SC [48] Size & Curvature SC [53]... |

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et al., “Range image registration driven by a hierarchy of surface differential features
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Citation Context ...& Spherical Geometry Scale-Space SC SC [54] [17] Integral Descriptors Feature Scale-Space SC SC [46], [48], [55] [48] DCT-DFT Coefficients SC [17] Cluster Signature SC [46] Differential Properties SC =-=[56]-=- Rareness SC [48] Saliency Geometry Scale-Space SC [17] Feature Scale-Space SC [48] Size & Curvature SC [53] Multi-Scale Slippage SC [57] MSER SC [58] Equalizing Regularization Correspondences DC [59]... |

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et al., “Slippage features
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Citation Context ...s SC [17] Cluster Signature SC [46] Differential Properties SC [56] Rareness SC [48] Saliency Geometry Scale-Space SC [17] Feature Scale-Space SC [48] Size & Curvature SC [53] Multi-Scale Slippage SC =-=[57]-=- MSER SC [58] Equalizing Regularization Correspondences DC [59], [60] Maximizing Correspondences DC [13], [61] Localization DC [62] Search Constraint Hierarchical Approaches DC [56], [62] In rigid reg... |

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et al., “The level set tree on meshes
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Citation Context ...ster Signature SC [46] Differential Properties SC [56] Rareness SC [48] Saliency Geometry Scale-Space SC [17] Feature Scale-Space SC [48] Size & Curvature SC [53] Multi-Scale Slippage SC [57] MSER SC =-=[58]-=- Equalizing Regularization Correspondences DC [59], [60] Maximizing Correspondences DC [13], [61] Localization DC [62] Search Constraint Hierarchical Approaches DC [56], [62] In rigid registration, co... |

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dynamics in the iterative process for accurate range image matching
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- 2009
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Citation Context ...pace SC [17] Feature Scale-Space SC [48] Size & Curvature SC [53] Multi-Scale Slippage SC [57] MSER SC [58] Equalizing Regularization Correspondences DC [59], [60] Maximizing Correspondences DC [13], =-=[61]-=- Localization DC [62] Search Constraint Hierarchical Approaches DC [56], [62] In rigid registration, correspondences assist in further pruning the transformation search space, whilst in the non-rigid ... |

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et al., “Outlier robust ICP for minimizing fractional RMSD
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Citation Context ...Many modifications to ICP have been proposed, to improve speed, range and rate of convergence, and robustness—see the earlier survey in [15]. Recent improvements explicitly model inliers and outliers =-=[64]-=-, and confidence in correspondences using graduated assignment [59], [60], [65]. There are alternatives of CPC. The first of these was point-to-plane ICP. [51] minimizes the shortest distance between ... |

1 | et al., “Registration without - Pottmann - 2004 |

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et al., “Unique signatures of histograms for local surface description
- Tombari
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Citation Context ...ments and spherical harmonics [54], integral descriptors [46], [48], [55], FFT and DCT coefficients of distributions of normals [17], cluster signatures of size and anisotropy [46] and SHOT signature =-=[68]-=-. 4.1.3 Saliency Saliency is a measure of local significance in a surface: salient points/regions are those whose properties are unlike most of their neighbours. They are used for key point/region det... |

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et al., “Reverse engineering of geometric models— an introduction
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Citation Context ...e sparse correspondences. For example, early commercial systems used simple reference objects (e.g. spheres) clamped to a surface before data acquisition, which are then identified by fitting methods =-=[69]-=-. Other techniques identify markers from an accompanying video sequence using e.g. Laplacian convolution filters [23] or SIFT [33]. Some approaches simply assume correspondences are provided [34]. 4.2... |

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et al., “Isometric registration of ambiguous and partial data
- Tevs
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Citation Context ... Gaussian Field Framework [95] Game Theoretical Framework [96] Spectral Method [2], [5], [97] Genetic Algorithm & Simulated Annealing [15] Particle Filtering [3] Hough Transform [17] [39] RANSAC [39] =-=[71]-=-, [98] Belief Propagation [72] Prune and Search Sections 4.1.2, 4.1.3 Geometric Hashing [53] Embedding [36]–[38], [99] Techniques most frequently used optimization techniques in rigid and non-rigid re... |

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et al., “The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces
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Citation Context ...onInduced Constraints 3D Objects SC [69] Optical/Manual SC [23], [33], [34] Template DC, D [6], [23], [28], [34] Isometry Consistency SC, D Self-Deformation Distortion SC, D [70] Spin Images SC [25], =-=[72]-=- Curvature SC [71], [72] Integral Features Descriptors SC [46] Heat Kernel Signature SC [73]–[78] Saliency Extremities Geometric Coherence Search SC DC,D Closest Point [70] Slippage Articulation Const... |

1 | et al., “A concise and provably informative multi-scale signature based on heat diffusion - Sun |

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et al., “Volumetric heat kernel signatures
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Citation Context ..., and develops an efficient scheme to find geodesic distance, which is less sensitive to noise and holes: d 2 (x, y) = limt→0 −4t log ht(x, y) where ht(x, y) = ∑ e −tλk Φk(x)Φk(y) is the heat kernel. =-=[75]-=- extends the diffusion distance on 2D manifold to 3D volume. It targets volume-preserving deformation and is found useful in medical imaging. Different Riemannian metrics can be induced by appropriate... |

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diffusion geometry for the analysis of deformable 3d shapes
- “Affine-invariant
(Show Context)
Citation Context ...ce on 2D manifold to 3D volume. It targets volume-preserving deformation and is found useful in medical imaging. Different Riemannian metrics can be induced by appropriately selecting the arc length. =-=[76]-=-, for example, develops an affine-invariant version of diffusion distance by constructing a new Riemannian metric tensor. It is useful for equi-affine-invariant deformation. Use of isometry: There are... |

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et al., “The wave kernel signature: A quantum mechanical approach to shape analysis
- Aubry
- 2011
(Show Context)
Citation Context ...ion of HKS. [75] extends HKS to volumetric data, using volumetric distance. [76] defines a new first fundamental form and uses a finite-element technique to define an affine-invariant version of HKS. =-=[77]-=- proposed the Wave Heat Kernel Signature (WKS) which uses a quantum mechanical approach to capture multi-scale details. WKS is shown to be more descriptive than HKS. There is an emerging approach [78]... |

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Spectral descriptors for deformable shapes,” Tel Aviv University
- Bronstein
- 2011
(Show Context)
Citation Context ...23], [28], [34] Isometry Consistency SC, D Self-Deformation Distortion SC, D [70] Spin Images SC [25], [72] Curvature SC [71], [72] Integral Features Descriptors SC [46] Heat Kernel Signature SC [73]–=-=[78]-=- Saliency Extremities Geometric Coherence Search SC DC,D Closest Point [70] Slippage Articulation Constraints SC DC,D [24] Criteria [57], [71] Orthonormality DC,D [32] Handling Holes DC,D [31] Regular... |

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et al., “Reconstruction of deforming geometry from time-varying point clouds
- Wand
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Citation Context ...providing strong structural information including priors for shape, constraints on arbitrary deformation, and connectivity. These greatly help to handle topological noise and missing data. [6], [28], =-=[79]-=- constructs a template, an urshape, by accumulating and filling in missing data from other scans in the same sequence. They have been used extensively in non-rigid registration to constrain dense corr... |

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et al., “Biharmonic distance
- Lipman
- 2010
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Citation Context ...e degree of connectivity of two points by paths of length t; the commute-time distance [81] (Ω(λk) = λ −1 k ) which is a scale-invariant version of the diffusion distance; and the biharmonic distance =-=[82]-=- (Ω(λk) = λ −2 k ) which balances the local and global properties of diffusion distance. The biharmonic distance is more shapeaware and insensitive to topology. The geodesic distance can be defined vi... |

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et al., “Fuzzy geodesics and consistent sparse correspondences for deformable shapes
- Sun
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(Show Context)
Citation Context ...efined via the length ∫ 1 0 ‖γ′ (r)‖dr, γ(0) = x of curve γ on M: d(x, y) = minγ and γ(1) = y where ˆg provides the inner product to measure length. Geodesic distance is sensitive to noise and holes. =-=[83]-=- proposes fuzzy geodesic distances which trades off between precision and stability. [84] approximates geodesic distances by unfolding boundary of holes. The geodesic distance is often found byJOURNA... |

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et al., “Geodesics in heat
- Crane
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Citation Context ...ces by unfolding boundary of holes. The geodesic distance is often found byJOURNAL OF L AT E X CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 9 solving the eikonal equation and wavefront propagation [85]. =-=[86]-=- recognizes the connection between heat and distance, and develops an efficient scheme to find geodesic distance, which is less sensitive to noise and holes: d 2 (x, y) = limt→0 −4t log ht(x, y) where... |

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et al., “Diffusion-geometric maximally stable component detection in deformable shapes
- Litman
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Citation Context ...s. [88] defines ”Persistent Heat Signature” for points using persistent homology. The idea is to track and identify critical points (maxima, minima) when the topology of HKS changes over the surface. =-=[89]-=-, [90] apply the concept of maximally stable extremal regions (MSER) from computer vision to detect stable regions/components in non-rigid shapes. 4.2.6 Regularization In Section 3.6, we pointed out t... |

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volumetric features in deformable shapes
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Citation Context ...] defines ”Persistent Heat Signature” for points using persistent homology. The idea is to track and identify critical points (maxima, minima) when the topology of HKS changes over the surface. [89], =-=[90]-=- apply the concept of maximally stable extremal regions (MSER) from computer vision to detect stable regions/components in non-rigid shapes. 4.2.6 Regularization In Section 3.6, we pointed out the imp... |

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et al., “Global temporal registration of multiple nonrigid surface sequences
- Huang
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Citation Context ... or all frames at a time, and generate more accurate results. There are methods that focus on global registration in terms of the alignment order of (multiple) sequences to reduce accumulation errors =-=[92]-=-. 5 OPTIMIZATION METHODS Rigid and non-rigid registration techniques are typically cast as non-linear optimization (see Table 5). Many techniques optimize both transformations and correspondences whil... |

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et al., “Geometrically stable sampling for the ICP algorithm
- Gelfand
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Citation Context ...ormulations TABLE 5 Optimization Methods. Rigid Non-Rigid Registration & Registration & Correspondence Correspondence Examples Examples Gradient Descent & related methods [11], [50]–[52], [54], [62], =-=[93]-=- [24], [28], [30], [34] Newton, [14], [46], [66], [2], [31], [32], Gauss-Newton, L-M [94] [79], [80] method Quasi-Newton [6], [23], [29], [30] Expectation Maximization [27] [9], [27] Branch and Bound ... |

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et al., “Registration of point cloud data from a geometric optimization perspective
- Mitra
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Citation Context ...orrespondence Correspondence Examples Examples Gradient Descent & related methods [11], [50]–[52], [54], [62], [93] [24], [28], [30], [34] Newton, [14], [46], [66], [2], [31], [32], Gauss-Newton, L-M =-=[94]-=- [79], [80] method Quasi-Newton [6], [23], [29], [30] Expectation Maximization [27] [9], [27] Branch and Bound & Tree Search [48] [70] Graduated Assignment [59], [60] [35] Mean Field Annealing [13] Ga... |

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et al., “A new method for the registration of three-dimensional point-sets: The Gaussian fields framework
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Citation Context ...i-Newton [6], [23], [29], [30] Expectation Maximization [27] [9], [27] Branch and Bound & Tree Search [48] [70] Graduated Assignment [59], [60] [35] Mean Field Annealing [13] Gaussian Field Framework =-=[95]-=- Game Theoretical Framework [96] Spectral Method [2], [5], [97] Genetic Algorithm & Simulated Annealing [15] Particle Filtering [3] Hough Transform [17] [39] RANSAC [39] [71], [98] Belief Propagation ... |

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et al., “A non-cooperative game for 3D object recognition in cluttered scenes
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Citation Context ...xpectation Maximization [27] [9], [27] Branch and Bound & Tree Search [48] [70] Graduated Assignment [59], [60] [35] Mean Field Annealing [13] Gaussian Field Framework [95] Game Theoretical Framework =-=[96]-=- Spectral Method [2], [5], [97] Genetic Algorithm & Simulated Annealing [15] Particle Filtering [3] Hough Transform [17] [39] RANSAC [39] [71], [98] Belief Propagation [72] Prune and Search Sections 4... |

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et al., “Intrinsic shape matching by planned landmark sampling
- Tevs
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(Show Context)
Citation Context ...ian Field Framework [95] Game Theoretical Framework [96] Spectral Method [2], [5], [97] Genetic Algorithm & Simulated Annealing [15] Particle Filtering [3] Hough Transform [17] [39] RANSAC [39] [71], =-=[98]-=- Belief Propagation [72] Prune and Search Sections 4.1.2, 4.1.3 Geometric Hashing [53] Embedding [36]–[38], [99] Techniques most frequently used optimization techniques in rigid and non-rigid registra... |

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et al., “Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration
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Citation Context ...lated Annealing [15] Particle Filtering [3] Hough Transform [17] [39] RANSAC [39] [71], [98] Belief Propagation [72] Prune and Search Sections 4.1.2, 4.1.3 Geometric Hashing [53] Embedding [36]–[38], =-=[99]-=- Techniques most frequently used optimization techniques in rigid and non-rigid registration. Rigid Registration: The optimal transformation a at each iteration is updated by (a) taking derivatives of... |

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et al., “A comparison of four algorithms for estimating 3-D rigid transformations
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Citation Context .... In rigid transformation estimation, a closed-form least-squares solution (preferable for efficiency and robustness) exists if three or more distinct non-collinear pairs of correspondences are given =-=[100]-=-, which can be solved by SVD, quaternions, orthonormal matrices or dual quaternions. Non-Rigid Registration: Most methods based on CPC formulate an energy functional with data and regularization terms... |

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et al., “Grouping with asymmetric affinities: A game-theoretic perspective
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Citation Context ...e. 5.2.5 Game Theoretical Framework Finding a large set of correspondences that express a high level of mutual compatibility can be formulated as an inlier selection process of a non-cooperative game =-=[101]-=-. The inlier selection is modelled as two players competing with one another. Rigid Correspondences: [96] uses game theory to recognize rigid objects in a cluttered scene. They use the consistency of ... |