Justin Solomon MIT, Spring

Transcription

1 Justin Solomon MIT, Spring

2 <administrative>

3 Instructor: Justin Solomon Office: 32-D460 Office hours: Wednesdays, 1pm-3pm Geometric Data Processing Group:

4 TA: Abhishek Bajpayee Office: Office hours: Thursdays, 3pm-5pm

5 gdp.csail.mit.edu/ 6838_spring_2017.html +

6 1. Four homeworks (40%) Written + coding 2. One project (50%) Instructions already online 3. Biweekly nanoquizzes (10%) Designed to be easy!

7 Coding Python or Matlab preferred Math Fluency in linear algebra and multivariable calculus Not required (won t hurt): Graphics, differential geometry, numerics

8 Supports LaTeX Supports Python Plot.ly for visualization

9 Schedule is too ambitious! Contact Justin with suggestions, must-cover topics, questions, etc. Experiment: Video (unreliable!)

10 I want you to take this course! Assignments intended to be interesting (may be unintentionally easy/hard!) Will be generous with support/grading

11 Degree Undergraduate M.Eng. M.Sc./PhD

12 Background EECS Math Engineering Elsewhere

13 </administrative>

14

15 I. Theoretical toolbox II. Computational toolbox III. Application areas

16 I. Theoretical toolbox II. Computational toolbox III. Application areas

17

18

19 ?

20 Spivak: A Comprehensive Introduction to Differential Geometry

21 Study of smooth manifolds

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23 Curvature and shape properties

24 Distances Crane, Weischedel, Wardetzky. Geodesics in heat. TOG 2013.

25 Vaxman et al. Directional field synthesis, design, and processing. EG STAR Flows and vector fields

26 Vallet and Lévy. Spectral Geometry Processing with Manifold Harmonics. EG 2008 Differential operators

27 Same distance? Only need angles and distances

28 Ant s view Only need angles and distances

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30 Peyré, Cuturi, and Solomon. Gromov-Wasserstein Averaging of Kernel and Distance Matrices. ICML 2016.

31 x y

32 nce_computation_in_the_frequency_domain_using_the_finite_element_method

33 I. Theoretical toolbox II. Computational toolbox III. Application areas

34 Triangle mesh Triangle soup Graph Point cloud Pairwise distance matrix Nearly anything with a notion of proximity/distance/curvature/

35 Collection of flat triangles Approximates a smooth surface

36 Can a triangle mesh have curvature?

37 Combine smooth and discrete

38

39 Discrete vs. Discretized

40 Discrete theory paralleling differential geometry.

41 Structure preservation [struhk-cher pre-zur-vey-shuh n]: Keeping properties from the continuous abstraction exactly true in a discretization.

42 Images from: Grinspun and Secord, The Geometry of Plane Curves (SIGGRAPH 2006)

43 Convergence [kuh n-vur-juh ns]: Increasing approximation quality as a discretization is refined.

44 Can you have it all?

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46

47 Pick and choose which properties you need. But there is a huge toolbox to draw from!

48 Chuang and Kazhdan. Fast Mean-Curvature Flow via Finite-Elements Tracking. CGF 2011.

49 Smith and Schaefer. Bijective parameterization with free boundaries. SIGGRAPH 2015.

50 Bommes, Zimmer, Kobbelt. Mixed-integer quadrangulation. SIGGRAPH 2009.

51 Huang, Guibas. Consistent shape maps via semidefinite programming. SGP Krishnan, Fattal, Szeliski. Efficient preconditioning of Laplacian matrices for computer graphics. SIGGRAPH 2013.

52 Heeren et al. Splines in the space of shells. SGP 2016.

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54 I. Theoretical toolbox II. Computational toolbox III. Application areas

55 Retrieval Transfer Editing Exploiting patterns Graphics

56 Recognition Navigation Reconstruction Segmentation Vision

57 Analysis Segmentation Registration Medical Imaging

58 Scanning Defect detection Manufacturing and Fabrication

59 Design and analysis Architecture

60 Shape collection analysis

61 Á Correspondence

62 Deformation transfer

63 Simulation

64 Scientific visualization

65 Segmentation

66 Su et al. Estimating image depth using shape collections. SIGGRAPH Computer vision

67 Zhu et al. Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions. ICML Machine learning

68 Hou et al. Novel semisupervised high-dimensional correspondences learning method. Opt. Eng Statistics

69 Justin Solomon MIT, Spring