12.3.4.1.2 Register 3-D Surfaces, Mesh Models

Pilgrim, L.,
Robust Estimation Applied to Surface Matching,
PandRS(51), No. 5, October 1996, pp. 243-257. 9611
BibRef

Meek, D.S., Walton, D.J.,
Comparison of Smooth Polynomial Functional Surfaces for Use in Alignment,
IVC(15), No. 7, July 1997, pp. 529-534.
WWW Version. 9708
BibRef

Ristic, M., Brujic, D.,
Efficient Registration of Nurbs Geometry,
IVC(15), No. 12, December 1997, pp. 925-935.
WWW Version. 9802
BibRef
Earlier: A2, A1:
Analysis of Free Form Surface Registration,
ICIP96(II: 393-396).
IEEE DOI Link BibRef

Johnson, A.E.[Andrew Edie], Hebert, M.[Martial],
Surface Matching for Object Recognition in Complex 3-Dimensional Scenes,
IVC(16), No. 9-10, July 1998, pp. 635-651.
WWW Version. 9808
BibRef

Johnson, A.E.[Andrew Edie], Hebert, M.[Martial],
Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes,
PAMI(21), No. 5, May 1999, pp. 433-449.
IEEE Abstract.
IEEE DOI Link BibRef 9905
Earlier:
Efficient Multiple Model Recognition in Cluttered 3-d Scenes,
CVPR98(671-677).
IEEE Abstract. The spin image is a representation for a surface mesh representation. BibRef

Johnson, A.E.[Andrew Edie], Hebert, M.[Martial],
Recognizing Objects by Matching Oriented Points,
CVPR97(684-689).
IEEE Abstract.
IEEE DOI Link 9704
BibRef
And: DARPA97(1207-1218). BibRef
And: CMU-RI-TR-96-04, May 1996. No feature extraction or segmentation needed. Geometric hashing and structural indexing combined for free form objects using 3-D data. BibRef

Marques, J.S.[Jorge S.],
A fuzzy algorithm for curve and surface alignment,
PRL(19), No. 9, 31 July 1998, pp. 797-803. BibRef 9807

Fischer, D.[Daniel], Kohlhepp, P.[Peter], Bulling, F.[Frank],
An evolutionary algorithm for the registration of 3-d surface representations,
PR(32), No. 1, January 1999, pp. 53-69.
WWW Version. See also Intrinsic line features and contour metric for locating 3-D objects in sparse, segmented range images. BibRef 9901

Fischer, D.[Daniel], Kohlhepp, P.[Peter],
Towards Reliable Fusion of Segmented Surface Descriptions,
CVPR00(II: 405-412).
IEEE Abstract.
IEEE DOI Link 0005
BibRef

Kohlhepp, P.[Peter],
Reconstruction and recognition of boundary representations from range images in SOMBRERO,
ICIP94(I: 496-500).
IEEE DOI Link 9411
BibRef

Gabrani, M.[Maria], Tretiak, O.J.[Oleh J.],
Surface-based matching using elastic transformations,
PR(32), No. 1, January 1999, pp. 87-97.
WWW Version. BibRef 9901

Ding, L., Goshtasby, A.A., Satter, M.,
Volume image registration by template matching,
IVC(19), No. 12, October 2001, pp. 821-832.
WWW Version. 0110
BibRef

Zhu, Y.M.[Yang-Ming],
Volume image registration by cross-entropy optimization,
MedImg(21), No. 2, February 2002, pp. 174-180.
IEEE Top Reference. 0204
BibRef

Yamany, S.M.[Sameh M.], Farag, A.A.[Aly A.],
Surfacing Signatures: An Orientation Independent Free-Form Surface Representation Scheme for the Purpose of Objects Registration and Matching,
PAMI(24), No. 8, August 2002, pp. 1105-1120.
IEEE Abstract. 0208
BibRef
Earlier:
3D Objects Coding and Recognition Using Surface Signatures,
ICPR00(Vol IV: 571-574).
IEEE DOI Link 0009
BibRef
Earlier:
Free-Form Surface Registration using Surface Signatures,
ICCV99(1098-1104).
IEEE DOI Link Capture curvature at certain points. Signatures from that. BibRef

Yamany, S.M.[Sameh M.], Farag, A.A.[Aly A.],
Adaptive object identification and recognition using neural networks and surface signatures,
AVSBS03(137-142).
IEEE Abstract. 0310
BibRef

Yamany, S.,
Coding of 3d Objects Using Surface Signatures,
ICIP00(Vol III: 628-631).
IEEE Abstract. 0008
BibRef

Yamany, S.M., Ahmed, M.N., Hemayed, E.E., Farag, A.A.,
Novel surface registration using the grid closest point (GCP) transform,
ICIP98(III: 809-813).
IEEE DOI Link 9810
BibRef

Yamany, S.M.[Sameh M.], Farag, A.A.[Aly A.], El-Bialy, A.M.[Ahmed M.],
Free-Form Object Recognition and Registration Using Surface Signatures,
ICIP99(II:457-461).
IEEE Abstract. BibRef 9900

Park, I.K.[In Kyu], Lee, K.M.[Kyoung Mu], Lee, S.U.[Sang Uk],
Efficient Measurement of Shape Dissimilarity Between 3D Models Using Z-Buffer and Surface Roving Method,
JASP(2002), No. 10, October 2002, pp. 1127-1134.
HTML Version. 0211
BibRef

Chang, J.Y.[Ju Yong], Lee, K.M.[Kyoung Mu], Lee, S.U.[Sang Uk],
Multiview normal field integration using level set methods,
MultiView07(1-8).
IEEE DOI Link 0706
BibRef

Krsek, P.[Pavel], Pajdla, T.[Tomás], Hlavá, V.[Václav],
Differential Invariants as the Base of Triangulated Surface Registration,
CVIU(87), No. 1-3, July 2002, pp. 27-38.
WWW Version. 0301
BibRef

Bujnak, M.[Martin], Kukelova, Z.[Zuzana], Pajdla, T.[Tomas],
New Efficient Solution to the Absolute Pose Problem for Camera with Unknown Focal Length and Radial Distortion,
ACCV10(I: 11-24).
Springer DOI Link 1011
BibRef

Kukelova, Z.[Zuzana], Bujnak, M.[Martin], Pajdla, T.[Tomas],
Polynomial Eigenvalue Solutions to the 5-pt and 6-pt Relative Pose Problems,
BMVC08(xx-yy).
PDF Version. 0809
BibRef

Kukelova, Z.[Zuzana], Bujnak, M.[Martin], Pajdla, T.[Tomas],
Closed-Form Solutions to Minimal Absolute Pose Problems with Known Vertical Direction,
ACCV10(II: 216-229).
Springer DOI Link 1011
BibRef

Hemmendorff, M., Andersson, M.T., Kronander, T., Knutsson, H.,
Phase-based multidimensional volume registration,
MedImg(21), No. 12, December 2002, pp. 1536-1543.
IEEE Top Reference. 0301
BibRef

Chow, C.K.[Chi Kin], Tsui, H.T.[Hung Tat], Lee, T.[Tong],
Surface registration using a dynamic genetic algorithm,
PR(37), No. 1, January 2004, pp. 105-117.
WWW Version. 0311
BibRef

Planitz, B.M., Maeder, A.J., Williams, J.A.,
The correspondence framework for 3D surface matching algorithms,
CVIU(97), No. 3, March 2005, pp. 347-383.
WWW Version. 0412
For analysis of matching algorithms. BibRef

Thurley, M.J.[Matthew J.], Ng, K.C.[Kim C.],
Identifying, visualizing, and comparing regions in irregularly spaced 3D surface data,
CVIU(98), No. 2, May 2005, pp. 239-270.
WWW Version. 0501
BibRef

Liu, Y.,
Eliminating False Matches for the Projective Registration of Free-Form Surfaces With Small Translational Motions,
SMC-B(35), No. 3, June 2005, pp. 607-624.
IEEE DOI Link 0508
BibRef

Specht, A.R.[Andres Restrepo], Sappa, A.D.[Angel D.], Devy, M.[Michel],
Edge registration versus triangular mesh registration, a comparative study,
SP:IC(20), No. 9-10, October-November 2005, pp. 853-868.
WWW Version. 0510
BibRef

Lomonosov, E.[Evgeny], Chetverikov, D.[Dmitry], Ekárt, A.[Anikó],
Pre-registration of arbitrarily oriented 3D surfaces using a genetic algorithm,
PRL(27), No. 11, August 2006, pp. 1201-1208.
WWW Version. 3D registration; Point sets; Data alignment; Genetic algorithms 0606
See also Photo-consistency based registration of an uncalibrated image pair to a 3D surface model using genetic algorithm. BibRef

Ben Hamza, A.[Abdessamad], Krim, H.,
Geodesic Matching of Triangulated Surfaces,
IP(15), No. 8, August 2006, pp. 2249-2258.
IEEE DOI Link 0606
BibRef
Earlier:
Probabilistic Shape Descriptor for Triangulated Surfaces,
ICIP05(I: 1041-1044).
IEEE DOI Link 0512
BibRef
Earlier:
Topological modeling of illuminated surfaces using REEB graph,
ICIP03(I: 769-772).
IEEE Abstract. 0312
BibRef
Earlier:
A topological variational model for image singularities,
ICIP02(I: 369-372).
IEEE Abstract. 0210
Topological features of the surfaces. BibRef

Tarmissi, K.[Khaled], Ben Hamza, A.[Abdessamad],
Geometric Mesh Denoising via Multivariate Kernel Diffusion,
MIRAGE09(23-33).
Springer DOI Link 0905
BibRef

Akca, D.[Devrim],
Matching of 3D surfaces and their intensities,
PandRS(62), No. 2, June 2007, pp. 112-121.
WWW Version. 0709
surface matching; least squares matching; point clouds; registration; laser scanning; intensity matching; attribute information BibRef

Shammaa, M.H.[M. Haitham], Suzuki, H.[Hiromasa], Michikawa, T.[Takashi],
Registration of CAD mesh models with CT volumetric model of assembly of machine parts,
VC(23), No. 12, December 2007, pp. 965-974.
Springer DOI Link 0712
BibRef

Munsell, B.C.[Brent C.], Dalal, P.[Pahal], Wang, S.[Song],
Evaluating Shape Correspondence for Statistical Shape Analysis: A Benchmark Study,
PAMI(30), No. 11, November 2008, pp. 2023-2039.
IEEE DOI Link 0809
Survey, Shape Matching. Create a set of synthetic shapes and apply matching. Gives 3 measures from Davies ( See also Learning Shape: Optimal Models for Analysing Natural Variability. ). Evaluate 5 techniques: Richardson and Wang (SDI) ( See also Nonrigid Shape Correspondence Using Landmark Sliding, Insertion and Deletion. ). Thodberg (T-MDL) ( See also Minimum Description Length Shape and Appearance Models. ) Karlsson and Ericsson (E-MDL) and (E-MDL+ curvature) and Euclidean Distance. ( See also Measures for Benchmarking of Automatic Correspondence Algorithms. ) BibRef

Dalal, P.[Pahal], Ju, L.[Lili], McLaughlin, M.[Michael], Zhou, X.R.[Xiang-Rong], Fujita, H.[Hiroshi], Wang, S.[Song],
3D Open-surface Shape Correspondence for Statistical Shape Modeling: Identifying Topologically Consistent Landmarks,
ICCV09(1857-1864).
IEEE DOI Link
PDF Version. 0909
BibRef

Dalal, P.[Pahal], Munsell, B.C.[Brent C.], Wang, S.[Song], Tang, J.[Jijun], Oliver, K.[Kenton], Ninomiya, H.[Hiroaki], Zhou, X.R.[Xiang-Rong], Fujita, H.[Hiroshi],
A Fast 3D Correspondence Method for Statistical Shape Modeling,
CVPR07(1-8).
IEEE DOI Link 0706
BibRef

Temlyakov, A.[Andrew], Munsell, B.C.[Brent C.], Waggoner, J.W.[Jarrell W.], Wang, S.[Song],
Two perceptually motivated strategies for shape classification,
CVPR10(2289-2296).
IEEE DOI Link 1006
BibRef

Munsell, B.C.[Brent C.], Temlyakov, A.[Andrew], Wang, S.[Song],
Fast multiple shape correspondence by pre-organizing shape instances,
CVPR09(840-847).
IEEE DOI Link 0906
BibRef

Lo, T.W.R.[Tsz-Wai Rachel], Siebert, J.P.[J. Paul],
Local feature extraction and matching on range images: 2.5D SIFT,
CVIU(113), No. 12, Decmeber 2009, pp. 1235-1250,.
Elsevier DOI Link
WWW Version. 0911
Range images; Feature extraction; Point-based matching; SIFT Matching 3D points from extractions. BibRef

Horaud, R.[Radu], Forbes, F.[Florence], Yguel, M.[Manuel], Dewaele, G.[Guillaume], Zhang, J.[Jian],
Rigid and Articulated Point Registration with Expectation Conditional Maximization,
PAMI(33), No. 3, March 2011, pp. 587-602.
IEEE DOI Link 1102
Deal with outliers. Use anisotropic covariances instead of isotropic. See also Hand Motion from 3D Point Trajectories and a Smooth Surface Model. See also Human Motion Tracking by Registering an Articulated Surface to 3D Points and Normals. BibRef

Zaharescu, A.[Andrei], Boyer, E.[Edmond], Varanasi, K.[Kiran], Horaud, R.[Radu],
Surface feature detection and description with applications to mesh matching,
CVPR09(373-380).
IEEE DOI Link 0906
BibRef

Chang, M.C.[Ming-Ching], Kimia, B.B.[Benjamin B.],
Measuring 3D shape similarity by graph-based matching of the medial scaffolds,
CVIU(115), No. 5, May 2011, pp. 707-720.
Elsevier DOI Link
WWW Version. 1103
BibRef
Earlier: Chang, M.C.[Ming-Ching], Kimia, B.B.[Benjamin B.],
Measuring 3D shape similarity by matching the medial scaffolds,
3DIM09(1473-1480).
IEEE DOI Link 0910
BibRef
And:
Regularizing 3D medial axis using medial scaffold transforms,
CVPR08(1-8).
IEEE DOI Link 0806
Medial axis; Medial scaffold; Transition; 3D shape similarity; Hypergraph matching; 3D shape matching; 3D shape retrieval BibRef

Chang, M.C.[Ming-Ching], Leymarie, F.F., Kimia, B.B.,
3D shape registration using regularized medial scaffolds,
3DPVT04(987-994).
IEEE Abstract. 0412
BibRef

Ion, A.[Adrian], Artner, N.M.[Nicole M.], Peyre, G.[Gabriel], Kropatsch, W.G.[Walter G.], Cohen, L.D.[Laurent D.],
Matching 2D and 3D articulated shapes using the eccentricity transform,
CVIU(115), No. 6, June 2011, pp. 817-834.
Elsevier DOI Link
WWW Version. 1104
Eccentricity transform; Shape matching; Articulation; Geodesic distance See also Multi-scale 2D tracking of articulated objects using hierarchical spring systems. BibRef

Ion, A.[Adrian], Haxhimusa, Y.[Yll], Kropatsch, W.G.[Walter G.],
An Improved Coordinate System for Point Correspondences of 2D Articulated Shapes,
DGCI09(92-103).
Springer DOI Link 0909
BibRef

Ion, A.[Adrian], Artner, N.M.[Nicole M.], Peyre, G.[Gabriel], Lopez Marmol, S.B.[Salvador B.], Kropatsch, W.G.[Walter G.], Cohen, L.D.[Laurent D.],
3D shape matching by geodesic eccentricity,
S3D08(1-8).
IEEE DOI Link 0806
BibRef

Bulatov, D.[Dimitri], Wernerus, P.[Peter], Heipke, C.[Christian],
Multi-view dense matching supported by triangular meshes,
PandRS(66), No. 6, November 2011, pp. 907-918.
Elsevier DOI Link
WWW Version. 1112
Depth map; Matching; Multi-view; Semi-global; Triangle mesh BibRef

Abdelmunim, H.[Hossam], Farag, A.A.[Aly A.],
Elastic Shape Registration Using an Incremental Free Form Deformation Approach with the ICP Algorithm,
ICIP11(729-732).
IEEE DOI Link 1201
BibRef
And: CRV11(212-218).
IEEE DOI Link 1105
BibRef

Dyshkant, N.[Natalia],
Measures for Surface Comparison on Unstructured Grids with Different Density,
DGCI11(501-512).
Springer DOI Link 1104
Surface comparison using mesh. BibRef

Tung, T.[Tony], Matsuyama, T.[Takashi],
Dynamic surface matching by geodesic mapping for 3D animation transfer,
CVPR10(1402-1409).
IEEE DOI Link 1006
BibRef

Yu, T.[Ting], Lang, J.[Jochen],
Window-Based Range Flow with an Isometry Constraint,
CRV10(331-338).
IEEE DOI Link 1005
Feature points to anchor surface match. BibRef

Trummer, M.[Michael], Suesse, H.[Herbert], Denzler, J.[Joachim],
Coarse registration of 3D surface triangulations based on moment invariants with applications to object alignment and identification,
ICCV09(1273-1279).
IEEE DOI Link 0909
BibRef

Wuhrer, S.[Stefanie], Shu, C.[Chang], Bose, P.[Prosenjit],
Posture invariant correspondence of triangular meshes in shape space,
3DIM09(1574-1581).
IEEE DOI Link 0910
See also Posture invariant gender classification for 3D human models. BibRef

Wuhrer, S.[Stefanie], Azouz, Z.B.[Zouhour Ben], Shu, C.[Chang],
Posture invariant surface description and feature extraction,
CVPR10(374-381).
IEEE DOI Link 1006
See also Posture invariant gender classification for 3D human models. BibRef

Wuhrer, S.[Stefanie], Shu, C.[Chang], Boisvert, J.[Jonathan], Godin, G.[Guy], Xi, P.C.[Peng-Cheng],
Bending invariant meshes and application to groupwise correspondences,
NORDIA09(382-389).
IEEE DOI Link 0910
BibRef

Schneider, D.C.[David C.], Eisert, P.[Peter],
Fast nonrigid mesh registration with a data-driven deformation prior,
NORDIA09(304-311).
IEEE DOI Link 0910
BibRef

Wetzel, A.W., Nieder, G.L., Durka-Pelok, G., Gest, T.R., Pomerantz, S.M., Nave, D., Czanner, S., Wagner, L., Shirey, E., Deerfield, D.W.,
Photo-realistic representation of anatomical structures for medical education by fusion of volumetric and surface image data,
AIPR03(131-138).
IEEE DOI Link 0310
BibRef

Tang, L.[Lisa], Hamarneh, G.[Ghassan], Abugharbieh, R.[Rafeef],
Reliability-Driven, Spatially-Adaptive Regularization for Deformable Registration,
WBIR10(173-185).
Springer DOI Link 1007
BibRef

Tang, L.[Lisa], Hamarneh, G.[Ghassan],
SMRFI: Shape matching via registration of vector-valued feature images,
CVPR08(1-8).
IEEE DOI Link 0806
BibRef

Wareham, R.[Rich], Lasenby, J.[Joan],
Mesh Vertex Pose and Position Interpolation Using Geometric Algebra,
AMDO08(xx-yy).
Springer DOI Link 0807
BibRef

Choi, Y.K.[Yi-King], Li, X.Q.[Xue-Qing], Rong, F.G.[Feng-Guang], Wang, W.P.[Wen-Ping], Cameron, S.[Stephen],
Determining Directional Contact Range of Two Convex Polyhedra,
GMP08(xx-yy).
Springer DOI Link 0804
BibRef

Liu, Y.[Yang], Wang, W.P.[Wen-Ping],
A Revisit to Least Squares Orthogonal Distance Fitting of Parametric Curves and Surfaces,
GMP08(xx-yy).
Springer DOI Link 0804
BibRef

Wu, H.Y.[Huai-Yu], Pan, C.H.[Chun-Hong], Yang, Q.[Qing], Ma, S.D.[Song-De],
Consistent Correspondence between Arbitrary Manifold Surfaces,
ICCV07(1-8).
IEEE DOI Link 0710
BibRef

Jung, D.U.[Da Un], Seo, Y.H.[Yung Ho], Choi, J.S.[Jong-Soo],
3D Footwear Model Matching System using Two Cameras,
3DTV07(1-4).
IEEE DOI Link 0705
BibRef

Fancourt, C.[Craig],
Registration and Matching of Perspective Surface Normal Maps,
ICIP07(VI: 552-555).
IEEE DOI Link 0709
BibRef

Akca, D., Gruen, A.,
Generalized Least Squares Multiple 3D Surface Matching,
Laser07(1).
PDF Version. 0709
BibRef

Jänichen, S.[Silke], Perner, P.[Petra],
Aligning Concave and Convex Shapes,
SSPR06(243-251).
Springer DOI Link 0608
BibRef

Abd El Munim, H., Farag, A.A.[Aly A.],
A Variational Approach for Shapes Registration Using Vector Maps,
ICIP06(337-340).
IEEE DOI Link 0610
BibRef

Urfalioglu, O.[Onay], Mikulastik, P.A.[Patrick A.], Stegmann, I.[Ivo],
Scale Invariant Robust Registration of 3D-Point Data and a Triangle Mesh by Global Optimization,
ACIVS06(1059-1070).
Springer DOI Link 0609
BibRef

Rugis, J.[John], Klette, R.[Reinhard],
Surface Registration Markers from Range Scan Data,
IWCIA06(430-444).
Springer DOI Link 0606
BibRef

Novatnack, J.[John], Nishino, K.[Ko],
Scale-Dependent/Invariant Local 3D Shape Descriptors for Fully Automatic Registration of Multiple Sets of Range Images,
ECCV08(III: 440-453).
Springer DOI Link 0810
See also Simultaneous Determination of Registration and Deformation Parameters among 3D Range Images. BibRef

Keller, Y.[Yosi], Averbuch, A.[Amir], Shkolnisky, Y.[Yoel],
Algebraically Accurate Volume Registration Using Euler's Theorem and the 3-D Pseudo-Polar FFT,
CVPR05(II: 795-800).
IEEE DOI Link 0507
BibRef
And: A1, A3, A2:
Accurate Multi-Dimensional Alignment,
ICIP05(III: 1052-1055).
IEEE DOI Link 0512
See also angular difference function and its application to image registration, The. BibRef

de Piero, F.W.,
Deterministic Surface Registration at 10Hz Based on Landmark Graphs With Prediction,
BMVC03(xx-yy).
HTML Version. 0409
BibRef
Earlier:
Fast landmark-based registration via deterministic and efficient processing, some preliminary results,
3DPVT02(544-548).
IEEE DOI Link 0206
BibRef

Ikemoto, L., Gelfand, N., Levoy, M.,
A hierarchical method for aligning warped meshes,
3DIM03(434-441).
IEEE Abstract. 0311
BibRef

Dion, Jr., D.[Denis], Laurendeau, D.[Denis], Borgeat, L.[Louis],
3D Triangular Mesh Matching Through a Sequence of Registered 2d and 3d Images,
ICPR00(Vol I: 977-980).
IEEE DOI Link 0009
BibRef

Wingbermühle, J.[Jochen],
Robust Registration of Coarse Binary Volume Models,
ICPR00(Vol I: 999-1002).
IEEE DOI Link 0009
BibRef

Lee, E.J., Hyun, K.H., Min, G., Kwon, K.R., Jeong, I.G.,
Cooperative Relaxation Algorithm of Range Images Using Surface Curvatures,
MVA98(xx-yy). BibRef 9800

Jost, T., Schuetz, C.[Christian], Hugli, H.[Heinz],
Multi-Feature Matching Algorithm for Free-Form 3D Surface Registration,
ICPR98(Vol II: 982-984).
IEEE DOI Link 9808
BibRef

Weik, S.,
Registration of 3D Partial Surfaces Using Luminance and Depth Information,
3DIM97(4 - View Registration) 9702
BibRef

Stoddart, A.J., and Brunnström, K.,
Free-Form Surface Matching using Mean Field Theory,
BMVC96(Matching Surfaces). 9608
BibRef
And: A2, A1:
Genetic Algorithms for Free-Form Surface Matching,
ICPR96(IV: 689-693).
IEEE DOI Link 9608
University of Surrey (S&T Datakonsulter AB, S) BibRef

Ostuni, J.L., Hsu, L., Frank, J.A.,
COCGV: a method for multi-modality 3D volume registration,
ICIP98(II: 25-28).
IEEE DOI Link 9810
BibRef

Shiohara, M., Gotoh, T., Nakagawa, Y., Yoshida, M.,
Surface correspondence based on three-dimensional structure inference in animation images,
ICPR90(I: 194-197).
IEEE DOI Link 9006
BibRef

Chapter on Registration, Matching and Recognition Using Points, Lines, Regions, Areas, Surfaces continues in
3-D Surface Registration, Range Data Registration for Mosaics and Models .