User-Guided Inverse 3D Modeling

Author(s): Andrews, James | Advisor(s): Sequin, Carlo H | Abstract: This thesis introduces and explores the idea of ``user-guided inverse 3D modeling'' -- an interactive approach to shape construction and redesign that extracts well-structured, parameterized, procedural descriptions from unstructured, hierarchically flat input data, such as point clouds, boundary representation meshes, or even multiple pictorial views of a given inspirational prototype. This approach combines traditional ``forward'' 3D modeling tools with a system of user-guided extraction modules and optimization routines. With a few cursor strokes users can express their preferences regarding the type of modeling primitives to be used in a particular area of the given prototype to be approximated, and they can also select the degree of parameterization associated with each modeling routine. The results are then pliable, structured descriptions that are well suited to implement the particular design modifications intended by the user.We present research on the components that make up an inverse 3D modeling system. Our research focuses have been (1) fitting of modeling primitives to data; (2) fitting higher-level structure (CSG expressions, symmetry, and hierarchy) to data; (3) minimal user interactions that guide these fitting processes; and finally (4) shape editing using the fitted structure. We also explore what is necessary to ultimately arrive at a clean, exportable result. A key research question guiding the design of our system has been how bringing the user into the loop affects the problem: i.e., where can the user's inputs simplify, accelerate, or otherwise improve the fitting process? What simple inputs can the user provide to unambiguously extract a desired primitive fit? And how can we let the user immediately begin using their fitted primitives to edit the shape? Answering these questions leads us to many new research findings, including: (1) We identify simple, lightweight inputs that allow the system to extract primitives with a great deal of user control, and we present detailed analysis of how these inputs can be ambiguous and what additional inputs may be needed to exactly capture the user's desired primitive fit. (2) We show multiple improvements to the state of the art in fast, effective fitting methods for sweeps and quadric surfaces. These improvements include identifying and fixing a major problem with previously-standard methods for kinematic surface fitting that led to grossly wrong results for data with small noise, and a new insight into the nature of direct, algebraic fitting that leads us to more accurate type-specific quadric fitting. (3) We show how the user can guide a boundary-to-CSG reverse-engineering process: Specifically, we identify cases where the best result of such a process depends on the user's intent, and we show how simple user interactions can let users specify their intents. (4) In addition to the diverse problems faced by individual structure-fitting and shape editing modules, the combination of these modules also presents new research opportunities; we identify new interactions between these diverse modules, including transformations between primitive types and hierarchies that can be imposed across modules.

[1]  Robert Bergevin,et al.  Generalized cylinders extraction in a range image , 1997, Proceedings. International Conference on Recent Advances in 3-D Digital Imaging and Modeling (Cat. No.97TB100134).

[2]  YANQING CHEN,et al.  Algorithm 8 xx : CHOLMOD , supernodal sparse Cholesky factorization and update / downdate ∗ , 2006 .

[3]  Tamy Boubekeur,et al.  GeoBrush: Interactive Mesh Geometry Cloning , 2011, Comput. Graph. Forum.

[4]  Ulrich Pinkall,et al.  Computing Discrete Minimal Surfaces and Their Conjugates , 1993, Exp. Math..

[5]  Matthew Harker,et al.  Direct type-specific conic fitting and eigenvalue bias correction , 2008, Image Vis. Comput..

[6]  Mark Pauly,et al.  Shape‐Up: Shaping Discrete Geometry with Projections , 2012, Comput. Graph. Forum.

[7]  John C. Hart,et al.  Ray tracing deterministic 3-D fractals , 1989, SIGGRAPH.

[8]  Marc Alexa,et al.  Sketching contours , 2008, Comput. Graph..

[9]  Ligang Liu,et al.  iCutter: a direct cut‐out tool for 3D shapes , 2011, Comput. Animat. Virtual Worlds.

[10]  Naoya Ohta,et al.  Comparing optimal three-dimensional reconstruction for finite motion and optical flow , 2003, J. Electronic Imaging.

[11]  Enhua Wu,et al.  Fast Computing Adaptively Sampled Distance Field on GPU , 2011, PG.

[12]  T. M. Murali,et al.  Consistent solid and boundary representations from arbitrary polygonal data , 1997, SI3D.

[13]  Ralph R. Martin,et al.  Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation , 1998, ECCV.

[14]  H. Pottmann,et al.  Approximation by Profile Surfaces , 2000 .

[15]  Levent Burak Kara,et al.  Pen-based styling design of 3D geometry using concept sketches and template models , 2006, SPM '06.

[16]  Gabriel Taubin,et al.  Cutting and Stitching: Converting Sets of Polygons to Manifold Surfaces , 2001, IEEE Trans. Vis. Comput. Graph..

[17]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[18]  Mario Hirz,et al.  Car side window kinematics , 2011, Comput. Aided Des..

[19]  Ligang Liu,et al.  A comparative evaluation of foreground/background sketch-based mesh segmentation algorithms , 2011, Comput. Graph..

[20]  Hans-Peter Seidel,et al.  Interactive multi-resolution modeling on arbitrary meshes , 1998, SIGGRAPH.

[21]  Carlo H. Séquin Virtual Prototyping of Scherk-Collins Saddle Rings , 1997 .

[22]  Ralph R. Martin,et al.  Fast mesh segmentation using random walks , 2008, SPM '08.

[23]  Dong-Ming Yan,et al.  Quadric Surface Extraction by Variational Shape Approximation , 2006, GMP.

[24]  H. Seidel,et al.  A connection between partial symmetry and inverse procedural modeling , 2010, ACM Trans. Graph..

[25]  J. Dormana,et al.  Surface design using hand motion with smoothing , 2022 .

[26]  Andrew W. Fitzgibbon,et al.  Direct Least Square Fitting of Ellipses , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Marc Alexa,et al.  FiberMesh: designing freeform surfaces with 3D curves , 2007, ACM Trans. Graph..

[28]  Vaughan R. Pratt,et al.  Direct least-squares fitting of algebraic surfaces , 1987, SIGGRAPH.

[29]  Francis Schmitt,et al.  Silhouette and stereo fusion for 3D object modeling , 2003, Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings..

[30]  C. Séquin,et al.  Energy Minimizers for Curvature-Based Surface Functionals , 2007 .

[31]  C. Séquin,et al.  Girl's Surface , 2013 .

[32]  Denis Zorin,et al.  Interactive modeling of topologically complex geometric detail , 2004, ACM Trans. Graph..

[33]  Leif Kobbelt,et al.  An intuitive framework for real-time freeform modeling , 2004, ACM Trans. Graph..

[34]  James F. O'Brien,et al.  Interpolating and approximating implicit surfaces from polygon soup , 2004, SIGGRAPH Courses.

[35]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Thomas F. Stahovich,et al.  Proceedings of the 4th Eurographics workshop on Sketch-based interfaces and modeling , 2007 .

[37]  Hassan Ugail,et al.  Techniques for interactive design using the PDE method , 1999, TOGS.

[38]  Ed Anderson,et al.  LAPACK Users' Guide , 1995 .

[39]  Richard Szeliski,et al.  Interactive 3D architectural modeling from unordered photo collections , 2008, ACM Trans. Graph..

[40]  V. Shapiro,et al.  Efficient CSG Representations of Two-Dimensional Solids , 1991 .

[41]  Marc Levoy,et al.  Fitting smooth surfaces to dense polygon meshes , 1996, SIGGRAPH.

[42]  Jun Li,et al.  Relief extraction and editing , 2011, Comput. Aided Des..

[43]  Leonidas J. Guibas,et al.  Shape segmentation using local slippage analysis , 2004, SGP '04.

[44]  Dong-Ming Yan,et al.  Fitting Sharp Features with Loop Subdivision Surfaces , 2008, Comput. Graph. Forum.

[45]  Peter Meer,et al.  Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint , 2000, International Journal of Computer Vision.

[46]  Alec R. Rivers,et al.  3D modeling with silhouettes , 2010, ACM Trans. Graph..

[47]  Marco Attene,et al.  ReMESH: An Interactive Environment to Edit and Repair Triangle Meshes , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[48]  John F. Hughes,et al.  SmoothSketch: 3D free-form shapes from complex sketches , 2006, SIGGRAPH '06.

[49]  Richard Szeliski,et al.  Rapid octree construction from image sequences , 1993 .

[50]  Yotam I. Gingold,et al.  Shading-based surface editing , 2008, ACM Trans. Graph..

[51]  Kaj Madsen,et al.  Methods for Non-Linear Least Squares Problems (2nd ed.) , 2004 .

[52]  Olga Sorkine-Hornung,et al.  On Linear Variational Surface Deformation Methods , 2008, IEEE Transactions on Visualization and Computer Graphics.

[53]  Wei-Chung Lin,et al.  CSG-based object recognition using range images , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[54]  ZhaoHanli,et al.  Parallel and efficient Boolean on polygonal solids , 2011 .

[55]  Szymon Rusinkiewicz,et al.  Modeling by example , 2004, ACM Trans. Graph..

[56]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[57]  Bert Jüttler,et al.  Computation of rotation minimizing frames , 2008, TOGS.

[58]  PAUL D. SAMPSON,et al.  Fitting conic sections to "very scattered" data: An iterative refinement of the bookstein algorithm , 1982, Comput. Graph. Image Process..

[59]  Ralph R. Martin,et al.  Algorithms for reverse engineering boundary representation models , 2001, Comput. Aided Des..

[60]  Mark Meyer,et al.  Discrete Differential-Geometry Operators for Triangulated 2-Manifolds , 2002, VisMath.

[61]  Jitendra Malik,et al.  Modeling and Rendering Architecture from Photographs: A hybrid geometry- and image-based approach , 1996, SIGGRAPH.

[62]  Benjamin B. Kimia,et al.  3D curve sketch: Flexible curve-based stereo reconstruction and calibration , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[63]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[64]  Marc Alexa,et al.  As-rigid-as-possible surface modeling , 2007, Symposium on Geometry Processing.

[65]  Vadim Shapiro,et al.  Separation for boundary to CSG conversion , 1993, TOGS.

[66]  Vadim Shapiro,et al.  Consistent updates in dual representation systems , 1999, SMA '99.

[67]  Youyi Zheng,et al.  Mesh Decomposition with Cross‐Boundary Brushes , 2010, Comput. Graph. Forum.

[68]  Ligang Liu,et al.  Easy Mesh Cutting , 2006, Comput. Graph. Forum.

[69]  Harry Shum,et al.  Lazy snapping , 2004, ACM Trans. Graph..

[70]  Jiing-Yih Lai,et al.  Sweep-surface reconstruction from three-dimensional measured data , 1998, Comput. Aided Des..

[71]  D. A. Dunavant High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

[72]  Gabriel Taubin,et al.  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[73]  Olga Sorkine-Hornung,et al.  Robust inside-outside segmentation using generalized winding numbers , 2013, ACM Trans. Graph..

[74]  Daniel Cohen-Or,et al.  GlobFit: consistently fitting primitives by discovering global relations , 2011, ACM Trans. Graph..

[75]  Szymon Rusinkiewicz,et al.  Eurographics Symposium on Geometry Processing (2005) Atomic Volumes for Mesh Completion , 2022 .

[76]  Hans-Peter Seidel,et al.  3D-modeling by ortho-image generation from image sequences , 2008, ACM Trans. Graph..

[77]  N. Chernov,et al.  L EAST SQUARES FITTING OF QUADRATIC CURVES AND SURFACES , 2010 .

[78]  Jean Ponce,et al.  Carved Visual Hulls for Image-Based Modeling , 2006, International Journal of Computer Vision.

[79]  Kaj Madsen,et al.  Methods for Non-Linear Least Squares Problems , 1999 .

[80]  Ronald N. Perry,et al.  Adaptively sampled distance fields: a general representation of shape for computer graphics , 2000, SIGGRAPH.

[81]  Tamás Várady,et al.  Automatic Extraction of Surface Structures in Digital Shape Reconstruction , 2006, GMP.

[82]  Ronald N. Perry,et al.  Designing with distance fields , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[83]  Alexandre Boulch,et al.  Fast and Robust Normal Estimation for Point Clouds with Sharp Features , 2012, Comput. Graph. Forum.

[84]  Takeo Igarashi,et al.  Structured annotations for 2D-to-3D modeling , 2009, ACM Trans. Graph..

[85]  Lubin Fan,et al.  Paint Mesh Cutting , 2011, Comput. Graph. Forum.

[86]  Karl Pearson F.R.S. LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[87]  Matthias Eck,et al.  Automatic reconstruction of B-spline surfaces of arbitrary topological type , 1996, SIGGRAPH.

[88]  Andrew W. Fitzgibbon,et al.  A Buyer's Guide to Conic Fitting , 1995, BMVC.

[89]  Thomas A. Funkhouser,et al.  A benchmark for 3D mesh segmentation , 2009, ACM Trans. Graph..

[90]  Brian Wyvill,et al.  Generalized sweep templates for implicit modeling , 2005, GRAPHITE.

[91]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[92]  Leonidas J. Guibas,et al.  Discovering structural regularity in 3D geometry , 2008, ACM Trans. Graph..

[93]  Valérie Burdin,et al.  Type-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Saddle-Shaped Articular Surfaces , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[94]  Chunxia Xiao,et al.  Hierarchical aggregation for efficient shape extraction , 2009, The Visual Computer.

[95]  Steve Marschner,et al.  Filling holes in complex surfaces using volumetric diffusion , 2002, Proceedings. First International Symposium on 3D Data Processing Visualization and Transmission.

[96]  Takeshi Masuda,et al.  Filling the signed distance field by fitting local quadrics , 2004, Proceedings. 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004..

[97]  William A. Barrett,et al.  Interactive part selection for mesh and point models using hierarchical graph-cut partitioning , 2009, Graphics Interface.

[98]  Bernd Hamann,et al.  The asymptotic decider: resolving the ambiguity in marching cubes , 1991, Proceeding Visualization '91.

[99]  John G. Griffiths,et al.  Least squares ellipsoid specific fitting , 2004, Geometric Modeling and Processing, 2004. Proceedings.

[100]  Jürgen Döllner,et al.  OpenCSG: A Library for Image-Based CSG Rendering , 2005, USENIX Annual Technical Conference, FREENIX Track.

[101]  David Corrigan,et al.  Video Matting Using Motion Extended GrabCut , 2008 .

[102]  Mircea Nicolescu,et al.  Visual Hull Construction Using Adaptive Sampling , 2005, 2005 Seventh IEEE Workshops on Applications of Computer Vision (WACV/MOTION'05) - Volume 1.

[103]  Prasanna Rangarajan,et al.  Hyper Least Squares and Its Applications , 2010, 2010 20th International Conference on Pattern Recognition.

[104]  E. Grinspun,et al.  Discrete elastic rods , 2008, SIGGRAPH 2008.

[105]  Hans-Christian Hege,et al.  Visualization and Mathematics III , 2011 .

[106]  James Arvo,et al.  Creating generative models from range images , 1999, SIGGRAPH.

[107]  Sylvain Petitjean,et al.  A survey of methods for recovering quadrics in triangle meshes , 2002, CSUR.

[108]  Niloy J. Mitra,et al.  Symmetry in 3D Geometry: Extraction and Applications , 2013, Comput. Graph. Forum.

[109]  Ligang Liu,et al.  Sketch-based mesh cutting: A comparative study , 2012, Graph. Model..

[110]  R. Bishop There is More than One Way to Frame a Curve , 1975 .

[111]  K. Tang,et al.  Algorithmic aspects of alternating sum of volumes. Part 1: Data structure and difference operation , 1991, Comput. Aided Des..

[112]  Myung-Soo Kim,et al.  Sweep‐based Freeform Deformations , 2006, Comput. Graph. Forum.

[113]  A. Laurentini,et al.  The Visual Hull Concept for Silhouette-Based Image Understanding , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[114]  Charlie C. L. Wang,et al.  Parallel and efficient Boolean on polygonal solids , 2011, The Visual Computer.

[115]  Ralph R. Martin,et al.  Detecting design intent in approximate CAD models using symmetry , 2010, Comput. Aided Des..

[116]  Tao Ju,et al.  Robust repair of polygonal models , 2004, ACM Trans. Graph..

[117]  Michael S. Floater,et al.  Mean value coordinates , 2003, Comput. Aided Geom. Des..

[118]  Daniel Cohen-Or,et al.  Curve skeleton extraction from incomplete point cloud , 2009, ACM Trans. Graph..

[119]  Pierre Alliez,et al.  Computational geometry algorithms library , 2008, SIGGRAPH '08.

[120]  Tony DeRose,et al.  Piecewise smooth surface reconstruction , 1994, SIGGRAPH.

[121]  Andrew W. Fitzgibbon,et al.  High-level model acquisition from range images , 1997, Comput. Aided Des..

[122]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[123]  Ralph R. Martin,et al.  Reverse engineering of geometric models - an introduction , 1997, Comput. Aided Des..

[124]  A. Al-Sharadqah,et al.  Error analysis for circle fitting algorithms , 2009, 0907.0421.

[125]  Jean Ponce,et al.  Accurate, Dense, and Robust Multiview Stereopsis , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[126]  Yizhou Yu,et al.  Photogrammetric reconstruction of free-form objects with curvilinear structures , 2005, The Visual Computer.

[127]  Wojciech Matusik,et al.  Articulated mesh animation from multi-view silhouettes , 2008, ACM Trans. Graph..

[128]  Ioannis Fudos,et al.  A Feature-Based Approach to Re-engineering CAD Models from Cross Sections , 2010 .

[129]  Marcel Campen,et al.  Exact and Robust (Self‐)Intersections for Polygonal Meshes , 2010, Comput. Graph. Forum.

[130]  Michael M. Kazhdan,et al.  Unconstrained isosurface extraction on arbitrary octrees , 2007, Symposium on Geometry Processing.

[131]  Andrew Blake,et al.  "GrabCut" , 2004, ACM Trans. Graph..

[132]  Helmut Pottmann,et al.  Rotational and helical surface approximation for reverse engineering , 1998, Computing.

[133]  Mark Meyer,et al.  Harmonic coordinates for character articulation , 2007, ACM Trans. Graph..

[134]  Johannes Wallner,et al.  3D shape recognition and reconstruction based on line element geometry , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[135]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[136]  Andrew W. Fitzgibbon,et al.  Fast and Controllable 3D Modelling From Silhouettes , 2005, Eurographics.

[137]  Kenichi Kanatani,et al.  Further improving geometric fitting , 2005, Fifth International Conference on 3-D Digital Imaging and Modeling (3DIM'05).

[138]  Greg Turk,et al.  Simplification and Repair of Polygonal Models Using Volumetric Techniques , 2003, IEEE Trans. Vis. Comput. Graph..

[139]  N. Chernov,et al.  On the Convergence of Fitting Algorithms in Computer Vision , 2007, Journal of Mathematical Imaging and Vision.

[140]  Alla Sheffer,et al.  Modeling from contour drawings , 2009, SBIM '09.

[141]  Li Zhang,et al.  Single view modeling of free-form scenes , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[142]  Marco Attene,et al.  Polygon mesh repairing: An application perspective , 2013, CSUR.

[143]  Helmut Pottmann,et al.  Constrained 3D shape reconstruction using a combination of surface fitting and registration , 2006, Comput. Aided Des..

[144]  Youyi Zheng,et al.  Dot Scissor: A Single-Click Interface for Mesh Segmentation , 2012, IEEE Transactions on Visualization and Computer Graphics.

[145]  Christian Rössl,et al.  Laplacian surface editing , 2004, SGP '04.

[146]  Leif Kobbelt,et al.  Structure Preserving CAD Model Repair , 2005, Comput. Graph. Forum.

[147]  Anton van den Hengel,et al.  Image based modelling with VideoTrace , 2008, COMG.

[148]  Vadim Shapiro,et al.  Construction and optimization of CSG representations , 1991, Comput. Aided Des..

[149]  Thomas Randrup Approximation by Cylinder Surfaces , 1997 .

[150]  Marc Alexa,et al.  SilSketch: automated sketch-based editing of surface meshes , 2007, SBIM '07.