cs 468, spring 2012 - mit...
TRANSCRIPT
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http://www.gogeometry.com
Justin SolomonMIT, Spring 2017
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<administrative>
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Instructor: Justin SolomonEmail: [email protected]: 32-D460Office hours: Wednesdays, 1pm-3pm
Geometric Data Processing Group:http://gdp.csail.mit.edu
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TA: Abhishek BajpayeeEmail: [email protected]: 1-225Office hours: Thursdays, 3pm-5pm
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gdp.csail.mit.edu/
6838_spring_2017.html
+
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1. Four homeworks (40%)Written + coding
2. One project (50%)Instructions already online
3. Biweekly nanoquizzes (10%)Designed to be easy!
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CodingPython or Matlab preferred
MathFluency in linear algebra and multivariable calculus
Not required (won’t hurt):Graphics, differential geometry, numerics
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•Supports LaTeX•Supports Python•Plot.ly for visualization
http://gryd1.csail.mit.edu/
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Schedule is too ambitious!
Contact Justin with suggestions,must-cover topics, questions, etc.
Experiment: Video(unreliable!)
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I want you to take this course!Assignments intended to be interesting
(may be unintentionally easy/hard!)
Will be generous with support/grading
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DegreeUndergraduate
M.Eng.M.Sc./PhD
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BackgroundEECSMath
EngineeringElsewhere
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</administrative>
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I. Theoretical toolbox
II. Computational toolbox
III. Application areas
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I. Theoretical toolbox
II. Computational toolbox
III. Application areas
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http://www.turbosquid.com/3d-models/medically-human-brain-3d-model/437885
?
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Spivak: A Comprehensive Introduction to Differential Geometry
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http://en.wikipedia.org/wiki/Differential_geometry
Study of smooth manifolds
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http://upload.wikimedia.org/wikipedia/commons/b/bc/Double_torus_illustration.png
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http://www.sciencedirect.com/science/article/pii/S0010448510001983
Curvature and shape properties
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Distances
Crane, Weischedel, Wardetzky.Geodesics in heat. TOG 2013.
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Flows and vector fields
Vaxman et al.Directional field synthesis, design, and processing.
EG STAR 2016.
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Differential operators
Vallet and Lévy.Spectral Geometry Processing with Manifold Harmonics. EG 2008
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Only need angles and distanceshttp://upload.wikimedia.org/wikipedia/commons/2/2c/Hobo%E2%80%93Dyer_projection_SW.jpg
Same distance?
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Only need angles and distanceshttp://www.phy.syr.edu/courses/modules/LIGHTCONE/pics/curved.jpg
Ant’s view
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http://en.wikipedia.org/wiki/Double_pendulumhttp://www.ualberta.ca/dept/math/gauss/fcm/BscIdeas/SpcDmnsn/pndlm2.htm
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Peyré, Cuturi, and Solomon.Gromov-Wasserstein Averaging of Kernel and Distance Matrices.
ICML 2016.
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x
y
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https://www.researchgate.net/publication/274071948_Space_charge_and_resistive_wall_impedance_computation_in_the_frequency_domain_using_the_finite_element_methodhttp://blog.forty.to/wp-content/uploads/2013/05/Bars1.jpg
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I. Theoretical toolbox
II. Computational toolbox
III. Application areas
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Triangle mesh Triangle soup
Graph Point cloud
Pairwise distance matrix
Nearly anything with a notion of proximity/distance/curvature/…
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• Collection of flat triangles
• Approximates a smooth surface
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Can a triangle mesh have curvature?
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Combine smooth and discrete
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http://www.geomtop.org/teaching/conformal_2012Summer/title_image.jpg
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Discretevs.
Discretized
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Discrete theory parallelingdifferential geometry.
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Structure preservation[struhk-cher pre-zur-vey-shuh n]:Keeping properties from the continuous abstraction exactly true in a discretization.
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Images from: Grinspun and Secord, “The Geometry of Plane Curves” (SIGGRAPH 2006)
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Convergence[kuh n-vur-juh ns]:Increasing approximation quality as a discretization is refined.
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Can you have it all?
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Pick and choosewhich properties you need.
But there is a huge toolbox to draw from!
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Chuang and Kazhdan.Fast Mean-Curvature Flow via Finite-Elements Tracking.
CGF 2011.
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Smith and Schaefer. Bijective parameterization with free boundaries. SIGGRAPH 2015.
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Bommes, Zimmer, Kobbelt. Mixed-integer quadrangulation. SIGGRAPH 2009.
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Huang, Guibas. Consistent shape maps via semidefinite
programming. SGP 2013.
Krishnan, Fattal, Szeliski. Efficient preconditioning of
Laplacian matrices for computer graphics. SIGGRAPH 2013.
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Heeren et al. Splines in the space of shells. SGP 2016.
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I. Theoretical toolbox
II. Computational toolbox
III. Application areas
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Graphics
http://people.csail.mit.edu/tmertens/papers/textransfer_electronic.pdfhttp://graphics.stanford.edu/~mdfisher/Data/Context.pdf
http://graphics.stanford.edu/~niloy/research/symmetrization/paper_docs/symmetrization_sig_07.pdfhttp://www.mpi-inf.mpg.de/~mbokeloh/project_dockingSites.html
Editing
Retrieval
Exploiting patterns
Transfer
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Vision
http://eijournal.com/newsite/wp-content/uploads/2012/01/VELODYNE-IMAGE.jpghttp://www.stanford.edu/~jinhae/iccv09/
http://people.csail.mit.edu/jsolomon/assets/intrinsic_part_discovery.pdfhttp://www.cs.technion.ac.il/~ron/PAPERS/BroBroKimIJCV05.pdf
Recognition
Segmentation
Navigation
Reconstruction
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Medical Imaging
http://dmfr.birjournals.org/content/33/4/226/F3.large.jpghttp://www-sop.inria.fr/asclepios/software/inriaviz4d/SphericalImTransp.png
http://www.creatis.insa-lyon.fr/site/sites/default/files/segm2.png
Analysis
Registration
Segmentation
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Manufacturing and Fabrication
http://www.conduitprojects.com/php/images/scan.jpghttp://www.emeraldinsight.com/content_images/fig/0330290204005.png
Scanning Defect detection
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Architecture
Design and analysishttp://gmsv.kaust.edu.sa/people/faculty/pottmann/pottmann_pdf/selfsupporting.pdf
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Shape collection analysishttp://graphics.stanford.edu/projects/lgl/papers/nbwyg-oaicsm-11/nbwyg-oaicsm-11.pdf
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Correspondence
Á
http://people.csail.mit.edu/jsolomon/assets/fmaps.pdf
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Deformation transferhttp://www.hao-li.com/publications/papers/siggraph2011RPBFA.pdf
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Simulationhttp://www.cs.columbia.edu/cg/threads/ http://mbergou.com/
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Scientific visualizationhttp://multires.caltech.edu/~keenan/pdf/spinxform.pdf
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Segmentation
http://www.bioinformaticslaboratory.nl/twiki/pub/EBioScience/News/freesurfer-3d.jpghttp://hal.inria.fr/docs/00/40/21/30/IMG/vivodtzev_et_al-Dagstuhl03.jpg
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Computer vision
Su et al. Estimating image depth using shape collections. SIGGRAPH 2014.
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Machine learningZhu et al. Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions. ICML 2003.
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StatisticsHou et al. Novel semisupervised high-dimensional correspondences learning method. Opt. Eng. 2008.
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http://www.gogeometry.com
Justin SolomonMIT, Spring 2017