(600.658)

The goal of this course is to survey the state-of-the-art methods for reconstructing surfaces in 3D from input 3D point sets, with a particular focus on methods using computational geometry, local function fitting, and global function fitting. Weekly readings will be assigned, and students will be expected to prepare and present to the rest of the class.

This course will be broken up into three separate areas. First, we will consider surface reconstruction techniques that leverage tools from the domain of computational geometry in order to compute a triangulation of the input point set. Next, we will consider local implicit methods, focusing on providing locally-weighted estimations of the surface. Finally, we will consider the class of global implicit function fitting techniques, which generate an output by solving a global linear system to fit an implicit function to the input data.

Students will be regularly assigned papers to read in the area of surface reconstruction, and two students each week will present papers to the seminar. In addition,

Finally, towards the end of the summer, the entire class will consolidate the semester's material by jointly writing a term paper summarizing the methods, analyzing their benefits, and identifying directions for future research in the area.

- Meeting Times: Wednesdays @ 2:45-4:50
- Meeting Place: My Office

Date | Subject | Presenter | Reading | Misc | |
---|---|---|---|---|---|

9/11/13 | Introduction / Alpha Shapes | Kazhdan / Kazhdan | (slides) | Edelsbrunner and Mucke, 1994 | Qhull |

9/18/13 | Ball-pivoting / Cocone | Doverspike / Salume | Bernardini et al., 1999 (slides, reviews) | Dey and Goswami, 2003 (slides, reviews) | |

9/25/13 | Spectral Reconstruction / Robust Reconstruction | Prada / Sinha | Kolluri et al., 2004 (slides, reviews) | Hornung and Kobbelt, 2006 (slides, reviews) | |

10/02/13 | Unorganized Points / Volumetric Models | Prada / Fernandez | Hoppe et al., 1992 (slides, reviews) | Curless and Levoy, 1996 (slides, reviews) | |

10/09/13 | Class Cancelled | ||||

10/16/13 | Overivew of MLS / PSS | Kazhdan / Sinha | McLain, 1974 (slides) | Alexa et al., 2001 (slides, reviews) | |

10/23/13 | Robust MLS / MPU | Prada / Salume | Fleishman et al., 2005 (slides, reviews) | Ohtake et al., 2003 (slides, reviews) | |

10/30/13 | APSS / RIMLS | Chuang / Chuang | Guennebaud et al., 2007 (slides, reviews) | Oztireli et al., 2009 (slides, reviews) | |

11/06/13 | RBF / Interpolating polygon soups | Fernandez / Doverspike | Carr et al., 2001 (slides, reviews) | Shen et al., 2004 (slides, reviews) | |

11/13/13 | Poisson Reconstruction / Variational Voronoi | Kazhdan / Sinha | Kazhdan et al., 2006 (slides, reviews) | Alliez et al., 2007 (slides, reviews) | |

11/20/13 | Scattered Data Approximation / SSD | Salume / Fernandez | Ohtake et al., 2004 (slides, reviews) | Calakli and Taubin, 2011 (slides, reviews) | |

12/04/13 |

Adamson and Alexa, Approximating and Intersecting Surfaces from Points. (2003)

Adamson and Alexa, Approximating Bounded, Non-orientable Surfaces from Points. (2004)

Ahmed

Alexa

Alexa

Alliez

Amenta

Amenta and Bern, Surface Reconstruction by Voronoi Filtering. (1999)

Amenta and Kolluri, Accurate and Efficient Union of Balls. (2000)

Amenta

Amenta

Amenta

Amenta and Kil, The Domain of a Point Set Surface. (2004)

Bajaj

Bajaj

Barequet

Bernardini

Bittar

Boissonnat, Geometric Structures for Three-Dimensional Shape Representation. (1984)

Boissonnat

Boissonnat

Boulch

Boyer and Petitjean, Curve and Surface Reconstruction from Regular and Non-Regular Point Sets. (2001)

Calakli and Taubin, SSD: Smooth Signed Distance Surface Reconstruction. (2011)

Carr

Carr

Cazals and Giesen, Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms. (2006)

Chen and Medioni, Description of Complex Objects from Muliple Range Images Using an Inflating Balloon Model. (1995)

Crossno and angel, Spiraling Edge: Fast Surface Reconstruction from Partially Organized Sample Points. (1999)

Curless and Levoy, A Volumetric Method for Building Complex Models from Range Images. (1996)

Davis

Dey and Goswami, Tight Cocone: A Water-tight Surface Reconstructor. (2003)

Dey

Dey and Goswami, Provable Surface Reconstruction from Noisy Samples. (2004)

Dey and Sun, An Adaptive MLS Surface for Reconstruction with Guarantees. (2005)

Dinge

Dinh

Edelsbrunner

Edelsbrunner and Mucke, Three-Dimensional Alpha Shapes. (1994)

Fang and Gossard, Multidimensional Curve Fitting to Unorganized Data Points by Nonlinear Minimization. (1995)

Fleishman and Cohen-Or, Progressive Point Set Surfaces. (2003)

Fleishman

Freedman, Efficient Simplicial Reconstruction of Manifolds from Their Samples. (2002)

Fuchs

Gopi

Gopi and Krishnan, A Fast and Efficient Projection-Based Approach for Surface Reconstruction. (2002)

Guennebaud and Gross, Algebraic Point Set Surfaces. (2007)

Guy and Medioni, Inference of Surfaces, 3D Curves, and Junctions from Sparse, Noisy, 3D Data. (1997)

Hoppe

Hoppe

Hornung and Kobbelt, Hierarchical Volumetric Multi-view Stereo Reconstruction of Manifold Surfaces based on Dual Graph Embedding. (2006)

Hornung and Kobbelt, Robust Reconstruction of Watertight 3D Models from Non-uniformly Sampled Point Clouds Without Normal Information. (2006)

Kazhdan, Reconstruction of Solid Models from Oriented Point Sets. (2005)

Kazhdan

Kazhdan and Hoppe, Screened Poisson Surface Reconstruction. (2013)

Keren and Gotsman, Fitting Curves and Surfaces with Constrained Implicit Polynomials. (1999)

Kolluri

Kolluri, Provably Good Moving Least Squares. (2005)

Krishnamurthy, Fitting Smooth Surfaces to Dense Polygon Meshes. (1996)

Lempitsky and Boykov, Global Optimization for Shape Fitting. (2007)

Levin, The Approximation Power of Moving Least Squares. (1998)

Levin, Mesh-Independent Surface Interpolation. (2003)

Li

Li

Masuda

McLain, Drawing Contours from Arbitrary Data Points. (1974)

Mederos

Mitra and Nguyen, Estimating Surface Normals in Noisy Point Cloud Data. (2003)

Morse

Muecke

Mullen

Muraki, Volumetric Shape Description of Range Data Using "Blobby Model". (1991)

Murali and Funkhouser, Consistent Solid and Boundary Representations from Arbitrary Polygonal Data. (1997)

Nehab

Newcombe

Ohtake

Ohtake

Ohtake

Oztireli

Paris

Podolak and Rusinkiewicz, Atomic Volumes for Mesh Completion. (2005)

Pons

Pop

Rusinkiewicz

Savchencko

Schall and Samozino, Surface from Scattered Points: A Brief Survey of Recent Developments. (2005)

Scheidegger

Sharf

Sharf

Shen

Sibson, A Vector Identity for the Dirichlet Tessellation. (1980)

Sussmuth

Tang and Medioni, Inference of Integrated Surface, Curve, and Junction Descriptions. (1998)

Terzopoulos and Vasilescu, Sampling and Reconstruction with Adaptive Meshes. (1991)

Turk and Levoy, Zippered Polygon Meshes from Range Images. (1994)

Turk and O'Brien, Shape Transformation Using Variational Implicit Functions. (1999)

Turk and O'Brien, Modelling with Implicit Surfaces that Interpolate. (2004)

Vogiatzis

Walder

Wand

Wand

Whitaker, A Level-Set Approach to 3D Reconstruction from Range Data. (1998)

Xie

Yngve and Turk, Robust Creation of Implicit Surfaces from Polygonal Meshes. (2002)

Yoo

Yoon

Zhang

Zhao