## Fully Automatic Registration Of Multiple 3D Data Sets (2001)

### Cached

### Download Links

- [www.ri.cmu.edu]
- [www.cs.hunter.cuny.edu]
- [www.hunter.cuny.edu]
- [www.ri.cmu.edu]
- [classes.soe.ucsc.edu]
- [www.cvl.iis.u-tokyo.ac.jp]
- DBLP

### Other Repositories/Bibliography

Citations: | 75 - 4 self |

### BibTeX

@MISC{Huber01fullyautomatic,

author = {Daniel Huber and Martial Hebert},

title = {Fully Automatic Registration Of Multiple 3D Data Sets},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper presents a method for automatically registering multiple three dimensional (3D) data sets. Previous approaches required manual specification of initial pose estimates or relied on external pose measurement systems. In contrast, our method does not assume any knowledge of initial poses or even which data sets overlap. Our automatic registration algorithm begins by converting the input data into surface meshes, which are pair-wise registered using a surface matching engine. The resulting matches are tested for surface consistency, but some incorrect matches may be locally undetectable. A global optimization process searches a graph constructed from these potentially faulty pair-wise matches for a connected sub-graph containing only correct matches, employing a global consistency measure to detect incorrect, but locally consistent matches. From this sub-graph, the final poses of all views can be computed directly. We apply our algorithm to the problem of 3D digital reconstruction of real world objects and show results for a collection of automatically digitized objects.

### Citations

9122 | Cache-oblivious algorithms
- Frigo, Leiserson, et al.
- 1999
(Show Context)
Citation Context ...over model graphs for fixed poses. For the discrete optimization, we sequentially construct a spanning tree from the edges in GLR using a modified version of Kruskal’s minimum spanning tree algorithm =-=[41]-=-. Using a spanning tree allows us to directly compute absolute pose estimates for initializing the continuous optimization step. For a fixed graph structure, the continuous optimization is just the mu... |

2384 |
A Method for Registration of 3-D Shapes
- Besl, McKay
- 1992
(Show Context)
Citation Context ...the iterative closest point (ICP) algorithm, which repeatedly updates the relative pose by minimizing the sum of squared distances between closest points on the two surfaces (point-to-point matching) =-=[13]-=-. Chen and Medioni proposed a similar method in which the distance between points and tangent planes is minimized instead (point-to-plane matching) [14]. Rusinkiewicz’ survey of ICP variants provides ... |

1092 |
Computer Graphics: Principles and Practice
- Foley, Dam, et al.
- 1990
(Show Context)
Citation Context ...st test whether q is significantly closer because even for correctly registered surfaces, p and q will not have precisely the same range. We can efficiently implement FSV detection using two zbuffers =-=[38]-=- to construct synthetic range images (Fig. 6). To compute FSVs for surfaces Si and Sj with respect to Ci; the surfaces are projected into separate z-buffers and converted into range images ðRi and RjÞ... |

1025 | Surface simplification using quadric error metrics
- GARLAND, HECKBERT
- 1997
(Show Context)
Citation Context ... the range image) are removed by thresholding the angle between the viewing direction and the surface normal. For computational efficiency, the meshes are simplified using Garland’s quadric algorithm =-=[40]-=-. The simplified meshes are used only for pair-wise surface matching; all other operations use the full resolution meshes. The pair-wise surface matching algorithm registers two surfaces based on thei... |

838 | A volumetric method for building complex models from range images
- Curless, Levoy
- 1996
(Show Context)
Citation Context ...s exhausted, resulting in a set of partial models. Fig. 8 shows the model graph G at several stages. Once the views are registered, they are merged into a single surface using Curless’ VRIP algorithm =-=[42]-=-. The final model, corresponding to the graph in Fig. 8f, is shown in Fig. 10. In addition to the full algorithm described above (full hereafter), we tested two simpler versions of our algorithm to an... |

615 |
modeling by registration of multiple range images
- Chen, Medioni
- 1992
(Show Context)
Citation Context ...s on the two surfaces (point-to-point matching) [13]. Chen and Medioni proposed a similar method in which the distance between points and tangent planes is minimized instead (point-to-plane matching) =-=[14]-=-. Rusinkiewicz’ survey of ICP variants provides an elegant taxonomy and unifying framework for comparing the numerous extensions to the basic algorithm [15]. In our system, we use pair-wise registrati... |

528 | Iterative point matching for registration of free-form curves and surfaces
- Zhang
- 1994
(Show Context)
Citation Context ... improved by applying a pair-wise registration refinement algorithm. We have implemented two algorithms for this – one based on the ICP algorithm but extended to handle partially overlapping surfaces =-=[21]-=-, and a second method that minimizes distances between points and tangent planes in a manner similar to that described by Chen and Medioni [22]. Finally, we perform a local surface consistency test by... |

490 |
Zippered Polygon Meshes from Range Images
- Turk, Levoy
- 1994
(Show Context)
Citation Context ...cene. For smaller objects, absolute poses can be obtained by mounting the sensor on a robot arm [26] or by keeping the sensor fixed and moving the object on a calibrated platform, such as a turntable =-=[27]-=-. For larger scenes, such as the statues scanned in the Digital Michelangelo project, accurate measurement of camera pose becomes considerably more complex, requiring a custom-made gantry system [28].... |

488 | M.: Efficient variants of the icp algorithm
- RUSINKIEWICZ, LEVOY
(Show Context)
Citation Context ...minimized instead (point-to-plane matching) [14]. Rusinkiewicz’ survey of ICP variants provides an elegant taxonomy and unifying framework for comparing the numerous extensions to the basic algorithm =-=[15]-=-. In our system, we use pair-wise registration in the local registration phase to improve pair-wise matches. We have experimented with point-to-point and point-to-plane matching and found that point-t... |

464 | Globally consistent range scan alignment for environment mapping
- Lu, Milios
- 1997
(Show Context)
Citation Context ...ilios derive uncertainty measures (covariance matrices) for the relative poses and solve for the absolute poses that minimize the Mahalanobis distance between the computed and measured relative poses =-=[20]-=-. Stoddart and Hilton use the analogy of a mechanical system, in which corresponding points are attached by springs, to derive a set of force-based incremental motion equations that are equivalent to ... |

427 | The digital michelangelo project: 3D scanning of large statues
- Levoy
- 2000
(Show Context)
Citation Context ... [27]. For larger scenes, such as the statues scanned in the Digital Michelangelo project, accurate measurement of camera pose becomes considerably more complex, requiring a custom-made gantry system =-=[28]-=-. With manual registration, the user may specify corresponding feature points in pairs of range images, from which relative poses can be estimated [16]. In some systems, corresponding feature points a... |

411 | Using spin images for efficient object recognition in cluttered 3d scenes
- Johnson, Hebert
- 1999
(Show Context)
Citation Context ...ion phase, which involves all of the views (Fig. 2). In the local registration phase, the N input views ðV i; i [ 1…NÞ are converted to surface meshes ðS i; i [ 1…NÞ; and a surface matching algorithm =-=[1]-=- is applied to all view pairs. The resulting matches are verified for surface consistency, but some incorrect matches may be indistinguishable from correct matches at this local level. As a result, th... |

190 | Multiview registration for large data sets
- PULLI
- 1999
(Show Context)
Citation Context ... et al. repeatedly perform pair-wise registration on pairs of overlapping views using a modified version of Chen and Medioni’s algorithm [18]. Pulli uses a similar approach based on the ICP algorithm =-=[19]-=-. Another idea is to view the relative poses as constraints on the absolute poses. Lu and Milios derive uncertainty measures (covariance matrices) for the relative poses and solve for the absolute pos... |

164 | A survey of free-form object representation and recognition techniques. Computer Vision and Image Understanding 2001
- Campbell, Flynn
(Show Context)
Citation Context ...ork. 2. Related work We begin with a review of the relevant registration algorithms according to the taxonomy in Fig. 1. A survey by Campbell and Flynn provides additional details on these algorithms =-=[2]-=-. Pair-wise surface matching algorithms register two surfaces without requiring any initial estimate of the relative pose, searching globally over the space of relative pose parameters. Such algorithm... |

148 |
3DPO: a three dimensional part orientation system
- Bolles, Horaud
- 1986
(Show Context)
Citation Context ...ce. Here, we focus on FSVs, but the potential of OSVs is discussed briefly in Section 8. Visibility consistency has been used previously in other 3D vision contexts, including hypothesis verification =-=[34]-=-, surface registration [22], range shadow detection [35], and multiview integration [36,37]. We can detect FSVs with respect to sensor position Ci by projecting a ray from the center of projection of ... |

143 |
Structural Indexing: Efficient 3-D Object Recognition
- Stein, Medioni
- 1992
(Show Context)
Citation Context ...o use point signatures, which encode local surface properties in a data structure that facilitates efficient correspondence search and comparison. Proposed encodings include spin-images [1], splashes =-=[3]-=-, point signatures [4], harmonic shape images [5], spherical attribute images [6], and the tripod-operator [7]. An alternative approach is to explicitly detect extended features, such as curves of max... |

137 |
Towards a general multi-view registration technique
- Bergevin, Soucy, et al.
- 1996
(Show Context)
Citation Context ...ively, the absolute poses can be updated sequentially. Bergevin et al. repeatedly perform pair-wise registration on pairs of overlapping views using a modified version of Chen and Medioni’s algorithm =-=[18]-=-. Pulli uses a similar approach based on the ICP algorithm [19]. Another idea is to view the relative poses as constraints on the absolute poses. Lu and Milios derive uncertainty measures (covariance ... |

126 | Spin-Images: A Representation for 3-D Surface Matching
- Johnson
- 1997
(Show Context)
Citation Context ...h an interactive method [19]. In more advanced approaches, a person indicates only which views to register (i.e. specifies the overlaps), and performs surface matching, manually verifying the results =-=[9,30]-=-. If the motion between successive scans is small, a pair-wise registration algorithm (e.g. ICP) can be used instead, as was done with the Great Buddha digitization project [31] and with Rusinkiewicz’... |

123 |
Point signatures: a new representation for 3d object recognition
- Chua, Jarvis
- 1997
(Show Context)
Citation Context ..., which encode local surface properties in a data structure that facilitates efficient correspondence search and comparison. Proposed encodings include spin-images [1], splashes [3], point signatures =-=[4]-=-, harmonic shape images [5], spherical attribute images [6], and the tripod-operator [7]. An alternative approach is to explicitly detect extended features, such as curves of maximal curvature [8], in... |

102 | Simultaneous registration of multiple range views for use in reverse engineering
- Eggert, Fitzgibbon, et al.
- 1996
(Show Context)
Citation Context ...ental motion equations that are equivalent to gradient descent [21]. Eggert et al. also use a mechanical system analogy, but they include an inertia term and also update the correspondences over time =-=[22]-=-. Goldberger uses a model-based approach based on the EM algorithm [23]. At each iteration, every view is registered to the current model and then a new maximum likelihood model is created from the up... |

98 |
A General Surface Approach to the Integration of a Set of Range Views
- Soucy, Laurendeau
- 1995
(Show Context)
Citation Context ... Visibility consistency has been used previously in other 3D vision contexts, including hypothesis verification [34], surface registration [22], range shadow detection [35], and multiview integration =-=[36,37]-=-. We can detect FSVs with respect to sensor position Ci by projecting a ray from the center of projection of Ci through a point p on Si: If the ray passes through Sj at a point q which is significantl... |

80 | Ransac-based darces: A new approach to fast automatic registration of partially overlapping range images
- Chen, Hung, et al.
- 1999
(Show Context)
Citation Context ...ithm to more than two views are n-view registration refinement algorithms [2][3]. Surface matching, a process often used in 3D recognition systems, is an unconstrained pairwise registration algorithm =-=[4]-=-[5]. Our automatic registration algorithm occupies the fourth corner of this taxonomy: unconstrained n-view registration. Our solution to the unconstrained n-view registration problem consists of two ... |

67 |
M.: Harmonic maps and their applications in surface matching
- ZHANG, HEBERT
- 1999
(Show Context)
Citation Context ...e properties in a data structure that facilitates efficient correspondence search and comparison. Proposed encodings include spin-images [1], splashes [3], point signatures [4], harmonic shape images =-=[5]-=-, spherical attribute images [6], and the tripod-operator [7]. An alternative approach is to explicitly detect extended features, such as curves of maximal curvature [8], intersections of planar regio... |

62 |
Ikeuchi K Building 3-D Models from Unregistered Range Images
- Higuchi, Hebert
- 1993
(Show Context)
Citation Context ... that facilitates efficient correspondence search and comparison. Proposed encodings include spin-images [1], splashes [3], point signatures [4], harmonic shape images [5], spherical attribute images =-=[6]-=-, and the tripod-operator [7]. An alternative approach is to explicitly detect extended features, such as curves of maximal curvature [8], intersections of planar regions [9], or bitangent-curves [10]... |

62 | Registration of Multiple Point Sets
- Stoddart, Hilton
- 1996
(Show Context)
Citation Context ...lton use the analogy of a mechanical system, in which corresponding points are attached by springs, to derive a set of force-based incremental motion equations that are equivalent to gradient descent =-=[21]-=-. Eggert et al. also use a mechanical system analogy, but they include an inertia term and also update the correspondences over time [22]. Goldberger uses a model-based approach based on the EM algori... |

56 |
Avenue: Automated site modeling in urban environments
- Allen, Stamos, et al.
- 2001
(Show Context)
Citation Context ...pherical attribute images [6], and the tripod-operator [7]. An alternative approach is to explicitly detect extended features, such as curves of maximal curvature [8], intersections of planar regions =-=[9]-=-, or bitangent-curves [10], and match them between model and scene. In our system, we use a modified version of Johnson’s spin-image surface matching algorithm to perform initial pair-wise matching in... |

43 | Registration two Overlapping Range Images
- Roth
- 1999
(Show Context)
Citation Context ...e 3D data can be aligned directly through an interactive method [3]. In more advanced approaches, a person indicates only which views to register, and performs unconstrained pair-wise registration [5]=-=[13]-=-. With this approach, the user still must manually verify the registration results. 3. THE MODEL GRAPH A model graph is an undirected graph G that encodes the topological relationship between views (f... |

41 | Automatic modeling and localization for object recognition
- Wheeler
- 1996
(Show Context)
Citation Context ...dification. With calibrated data acquisition systems, the type of hardware used depends on the size of scene. For smaller objects, absolute poses can be obtained by mounting the sensor on a robot arm =-=[26]-=- or by keeping the sensor fixed and moving the object on a calibrated platform, such as a turntable [27]. For larger scenes, such as the statues scanned in the Digital Michelangelo project, accurate m... |

40 |
Geometrical cloning of 3d objects via simultaneous registration of multiple range images
- Neugebauer
- 1997
(Show Context)
Citation Context ...known iterated closest point algorithm (ICP) is a pair-wise registration refinement algorithm [1]. Extensions of the ICP algorithm to more than two views are n-view registration refinement algorithms =-=[2]-=-[3]. Surface matching, a process often used in 3D recognition systems, is an unconstrained pairwise registration algorithm [4][5]. Our automatic registration algorithm occupies the fourth corner of th... |

39 | Reconstruction of Real World Objects via Simultaneous Registration and Robust Combination of Multiple Range Images
- Neugebauer
- 1997
(Show Context)
Citation Context ...ing to slower convergence in many cases. Therefore, we use the point-to-plane matching method. In practice, we use Neugebauer’s multi-view registration algorithm for pairwise registration (see below) =-=[16]-=-. In the two view case, his algorithm essentially reduces to Chen and Medioni’s [14]. Multi-view registration algorithms minimize registration error over an entire network of overlapping views, optimi... |

39 | Robust Simultaneous Registration of Multiple Range Images
- Nishino, Ikeuchi
- 2002
(Show Context)
Citation Context ...erifying the results [9,30]. If the motion between successive scans is small, a pair-wise registration algorithm (e.g. ICP) can be used instead, as was done with the Great Buddha digitization project =-=[31]-=- and with Rusinkiewicz’ real-time modeling system [32]. In the Pieta project, the environment was augmented with markers, which served as feature points to aid in manual registration [33]. Our algorit... |

36 |
Automated 3D reconstruction of interiors with multiple scan-view . http://www.scs.leeds.ac.uk/resolv/pub.htm (accessed 10/02/2001
- Sequeira, Ng, et al.
- 1999
(Show Context)
Citation Context ...with a relative positioning system 61 2 3 4 5 T1,4 6 1 2 3 4 5 Fig. 2. Example model graphs. A complete model (left) and two partial models (right). such as wheel encoders or inertial sensors [10][11]=-=[12]-=-. A common manual registration method is to specify corresponding feature points in pairs of range images, from which relative poses can be estimated [2]. In some systems, corresponding feature points... |

32 | A solution for the registration of multiple 3d point sets using unit quaternions - Benjemaa, Schmitt - 1998 |

28 |
Invariant-based registration of surface patches
- Wyngaerd, Gool, et al.
(Show Context)
Citation Context ... [6], and the tripod-operator [7]. An alternative approach is to explicitly detect extended features, such as curves of maximal curvature [8], intersections of planar regions [9], or bitangent-curves =-=[10]-=-, and match them between model and scene. In our system, we use a modified version of Johnson’s spin-image surface matching algorithm to perform initial pair-wise matching in the local registration ph... |

26 | A system for indoor 3-d mapping and virtual environments
- El-Hakim, Boulanger, et al.
- 1997
(Show Context)
Citation Context ...stimated [16]. In some systems, corresponding feature points are automatically detected and then manually verified for D.F. Huber, M. Hebert / Image and Vision Computing 21 (2003) 637–650 correctness =-=[29]-=-. Alternatively, the 3D data can be aligned directly through an interactive method [19]. In more advanced approaches, a person indicates only which views to register (i.e. specifies the overlaps), and... |

15 | Automatic 3D modeling using range images obtained from unknown viewpoints
- Huber
- 2001
(Show Context)
Citation Context ...s point-to-plane matching approach [16]. Multi-view surface matching algorithms fall into the final category of our taxonomy. To the best of our knowledge, our algorithm is the first in this category =-=[24]-=-. However, since we use multi-view surface matching to automate the process of 3D digitization, it is reasonable to ask how 3D digitization is normally accomplished and to what degree is the process a... |

12 | Large data sets and confusing scenes in 3-d surface matching and recognition
- Carmichael, Huber, et al.
- 1999
(Show Context)
Citation Context ...d match them between model and scene. In our system, we use a modified version of Johnson’s spin-image surface matching algorithm to perform initial pair-wise matching in the local registration phase =-=[1,11,12]-=-. The algorithm is fast, matching two views in 1.5 s, does not require any explicit feature detection, and is robust to holes in the surfaces, which frequently occur when using range image data. Pair-... |

11 | Arctic test flights of the cmu autonomous helicopter
- Miller, Amidi, et al.
- 1999
(Show Context)
Citation Context ...the scanner on a robot equipped with an absolute positioning sensor. For example, Miller used an autonomous helicopter with a differential global positioning system (DGPS) to construct terrain models =-=[7]-=-. For smaller objects, absolute poses can be obtained by mounting the sensor on a robot arm [8] or by keeping the sensor fixed and moving the object on a calibrated platform [9]. Relative poses can be... |

9 |
Strategies for registering range images from unknown camera positions
- Bernardini, Rushmeier
- 2000
(Show Context)
Citation Context ...tion project [31] and with Rusinkiewicz’ real-time modeling system [32]. In the Pieta project, the environment was augmented with markers, which served as feature points to aid in manual registration =-=[33]-=-. Our algorithm offers several advantages over existing approaches. First, it does not require any specialized data acquisition system, which simplifies the hardware and reduces cost. Second, the algo... |

8 |
and Evangelos Milios, “Globally consistent range scan alignment for environment mapping
- Lu
- 1997
(Show Context)
Citation Context ...nly with a relative positioning system 61 2 3 4 5 T1,4 6 1 2 3 4 5 Fig. 2. Example model graphs. A complete model (left) and two partial models (right). such as wheel encoders or inertial sensors [10]=-=[11]-=-[12]. A common manual registration method is to specify corresponding feature points in pairs of range images, from which relative poses can be estimated [2]. In some systems, corresponding feature po... |

7 | Tripod operators for recognizing objects in range images; rapid rejection of library objects
- Pipitone, Adams
- 1992
(Show Context)
Citation Context ...orrespondence search and comparison. Proposed encodings include spin-images [1], splashes [3], point signatures [4], harmonic shape images [5], spherical attribute images [6], and the tripod-operator =-=[7]-=-. An alternative approach is to explicitly detect extended features, such as curves of maximal curvature [8], intersections of planar regions [9], or bitangent-curves [10], and match them between mode... |

7 |
Real-time Acquisition and Rendering of Large 3D Models
- Rusinkiewicz
- 2001
(Show Context)
Citation Context ...cessive scans is small, a pair-wise registration algorithm (e.g. ICP) can be used instead, as was done with the Great Buddha digitization project [31] and with Rusinkiewicz’ real-time modeling system =-=[32]-=-. In the Pieta project, the environment was augmented with markers, which served as feature points to aid in manual registration [33]. Our algorithm offers several advantages over existing approaches.... |

6 |
Toward a general 3-d matching engine: Multiple models, complex scenes, and efficient data filtering
- Johnson, Carmichael, et al.
- 1998
(Show Context)
Citation Context ...d match them between model and scene. In our system, we use a modified version of Johnson’s spin-image surface matching algorithm to perform initial pair-wise matching in the local registration phase =-=[1,11,12]-=-. The algorithm is fast, matching two views in 1.5 s, does not require any explicit feature detection, and is robust to holes in the surfaces, which frequently occur when using range image data. Pair-... |

6 |
Integration of multiple range maps through consistency processing
- Robert, Minaud
- 1998
(Show Context)
Citation Context ...Visibility consistency has been used previously in other 3D vision contexts, including hypothesis verification [14], surface registration [15], range shadow detection [16], and multi-view integration =-=[17]-=-[18]. We can detect FSV’s with respect to sensor position Ci by projecting a ray from the center of projection of Ci through a point p on Si. If the ray passes through Sj at a point q which is signifi... |

5 | Interactive exploration of acquired 3d data
- Nyland, McAllister, et al.
- 1999
(Show Context)
Citation Context ... discussed briefly in Section 8. Visibility consistency has been used previously in other 3D vision contexts, including hypothesis verification [34], surface registration [22], range shadow detection =-=[35]-=-, and multiview integration [36,37]. We can detect FSVs with respect to sensor position Ci by projecting a ray from the center of projection of Ci through a point p on Si: If the ray passes through Sj... |

4 |
Registration of multiple point sets using the em algorithm
- Goldberger
- 1999
(Show Context)
Citation Context ...gert et al. also use a mechanical system analogy, but they include an inertia term and also update the correspondences over time [22]. Goldberger uses a model-based approach based on the EM algorithm =-=[23]-=-. At each iteration, every view is registered to the current model and then a new maximum likelihood model is created from the updated views. Our system uses multi-view registration in the global regi... |

2 |
Computer Grpahics Principles and Practice
- Foley, Dam, et al.
- 1987
(Show Context)
Citation Context ...t test whether q is significantly closer because even for correctly registered surfaces, p and q will not have precisely the same range. We can efficiently implement FSV detection using two z-buffers =-=[19]-=-. To compute FSV’s for surfaces Si and Sj with respect to Ci, both surfaces are projected into separate z-buffers (Zi and Zj) using the coordinate system and parameters of Ci (e.g., focal length, view... |

1 |
Integrating information form multiple views
- Ferrie, Levine
- 1987
(Show Context)
Citation Context ...res [4], harmonic shape images [5], spherical attribute images [6], and the tripod-operator [7]. An alternative approach is to explicitly detect extended features, such as curves of maximal curvature =-=[8]-=-, intersections of planar regions [9], or bitangent-curves [10], and match them between model and scene. In our system, we use a modified version of Johnson’s spin-image surface matching algorithm to ... |

1 |
Gool (Eds.), Integration of multiple range maps through consistency processing
- Robert, Minaud, et al.
- 1998
(Show Context)
Citation Context ... Visibility consistency has been used previously in other 3D vision contexts, including hypothesis verification [34], surface registration [22], range shadow detection [35], and multiview integration =-=[36,37]-=-. We can detect FSVs with respect to sensor position Ci by projecting a ray from the center of projection of Ci through a point p on Si: If the ray passes through Sj at a point q which is significantl... |

1 |
Image and Vision Computing 21 (2003) 637–650 Daniel Huber received the BS degree in electrical engineering from the University of Texas in 1992. He received the MS degree in computer science from Stanford University in 1996. In 2002, he received the PhD d
- Preparata, Shamos, et al.
(Show Context)
Citation Context ...teract. For example, interval trees can be used to compute the intersection of the viewing volume bounding boxes for all view pairs in time OðN log N þ sÞ; where s is the number of intersecting pairs =-=[43]-=-, and only those that intersect need to be tested for consistency. Finally, multi-view registration involves solving a linear system with 6ðN 2 1Þ unknowns (the absolute pose parameters), an OðN 3 Þ o... |