Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf ·...
Transcript of Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf ·...
![Page 1: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/1.jpg)
Statistical Geometry Processing Winter Semester 2011/2012
Introduction
![Page 2: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/2.jpg)
2
Research Direction
Statistical geometry processing
• Geometric datasets
• Machine learning / statistical data analysis in graphics
Goals
• Discover structure in geometric data
• Long term goal: “Shape understanding”
![Page 3: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/3.jpg)
3
Ambitious Problem
What does shape understanding mean?
![Page 4: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/4.jpg)
4
Practical Relevance
Computer graphics
• Content creation bottleneck
• 3D scanning: data quality
Geometry beyond graphics
• Science and engineering (CT, MR, [f]MRI, ET, Cryo-EM, ...)
[data sets: G. Wolf, J. Bernauer]
![Page 5: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/5.jpg)
[data set: Institute for Cartography, Leibnitz University Hannover]
![Page 6: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/6.jpg)
6
Scientific Challenge
Philosophical question
• What is “structure”?
• Insight about our own reasoning
[data sets: G. Wolf, Dosch]
![Page 7: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/7.jpg)
7
Research Group at MPI / MMCI
Main focus: low-level problems
• Correspondence problems
• Basic low-level building block
Correspondences
• Formal modelling?
• Efficient computation?
• Analyse the structure of corresponding geometry
![Page 8: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/8.jpg)
8
Example Projects
![Page 9: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/9.jpg)
9
Correspondences
Questions
• What parts are essientially the same?
• Dense-point-to-point correspondences
Variants
• Rigid, deformable, semantic
• Global vs. partial
• Self-matching: symmetry detection
[data sets: C. Theobald, C. Stoll, M. Wacker]
![Page 10: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/10.jpg)
10
Animation Reconstruction
[data set: P. Phong, Stanford University]
![Page 11: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/11.jpg)
11
Real-Time 3D Scanners
space-time stereo
courtesy of James Davis University of California
at Santa Cruz
color-coded structured light
courtesy of Phil Fong Stanford University
high-speed structured light
courtesy of Stefan Gumhold TU Dresden
![Page 12: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/12.jpg)
12 12
Time-of-Flight / PMD Devices
PMD Time-of-flight camera
Minolta Laser Scanner (static)
![Page 13: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/13.jpg)
13
Animation Reconstruction
Problems
• Noisy data
• Incomplete data (acquisition holes)
• No correspondences
• Just point clouds
noise
holes
missing correspondences
![Page 14: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/14.jpg)
14
Animation Reconstruction
Remove noise, outliers
Fill-in holes (from all frames)
Dense correspondences
![Page 15: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/15.jpg)
15
Representation
t = 0 t = 1 t = 2
data
urshape S
f
f f
deformation
![Page 16: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/16.jpg)
16
Matching Algorithm
Variational model
• Maximize data fit
• Penalize deformations
• Penalize abrupt motion
• Favour smooth surfaces
Algorithm
• Numerical optimization
• Greedy assembly
![Page 17: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/17.jpg)
17
![Page 18: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/18.jpg)
18
![Page 19: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/19.jpg)
19
Problem: Local Optima
[Data set: Hao Li, ETH Zürich]
data reconstruction
![Page 20: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/20.jpg)
20
Global Deformable Shape Matching
[data set: Stanford 3D Scanning Repository]
![Page 21: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/21.jpg)
21
Contributions
[data sets: TOSCA]
![Page 22: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/22.jpg)
22
Global Animation Reconstruction
[Data set: Hao Li, ETH Zürich]
![Page 23: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/23.jpg)
23
Symmetry Detection
[data set: M. Wacker, HTW Dresden]
![Page 24: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/24.jpg)
24
Symmetry Detection
[data sets: IKG, University Hannover / M. Wacker, HTW Dresden]
![Page 25: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/25.jpg)
25
Symmetry Detection
[DataSet : IKG, University Hannover]
![Page 26: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/26.jpg)
26
Denoising from Symmetry
overlay of
16 parts [data set: IKG, Leibnitz University Hannover]
![Page 27: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/27.jpg)
27
2D Bitmap Images
![Page 28: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/28.jpg)
28
Rigid, Isometic, Relaxed Isometric
rigid isometric relaxed isometric
![Page 29: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/29.jpg)
29
Learning
Window Variants [data set: IKG, Leibnitz University Hannover]
![Page 30: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/30.jpg)
30
Learning
Window Variants
![Page 31: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/31.jpg)
31
Inverse Procedural Modeling [data set: G. Wolf]
![Page 32: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/32.jpg)
32
Overview
Rules from example geometry
• Example model
• Compute rules describing a class of similar models
Input
Output
[data set: G. Wolf]
![Page 33: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/33.jpg)
33
r-Similarity
• Local neighborhoods match exemplar
What are similar models?
input
output
radius r radius r
radius r
[data set: G. Wolf]
![Page 34: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/34.jpg)
34
Simple Example
input output [data set: G. Wolf]
![Page 35: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/35.jpg)
35
Shape Grammar
![Page 36: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/36.jpg)
36
Results
![Page 37: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/37.jpg)
37
Shape Variations
input
output
![Page 38: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/38.jpg)
38
Shape Variations
input
output
[data set: Dosch]
![Page 39: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/39.jpg)
39
1D Grids
input output
[data set: G. Wolf]
![Page 40: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/40.jpg)
40
2D Grids
~ 500K triangles
input output
[data set: Dosch]
![Page 41: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/41.jpg)
41
3D Scanner Data
input
output
[data set: IKG, Leibnitz University Hannover]
![Page 42: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/42.jpg)
42
Results
![Page 43: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/43.jpg)
Topics
![Page 44: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/44.jpg)
44
Topics (tentative)
Mathematical tools
• Basic statistics
Probability theory, machine learning
Dependencies and graphical models
Maximum likelihood, maximum a posteriori, least-squares
Inverse problems and regularization
• Variational methods
• Geometry
Representations, linear models, acquisition
Differential geometry, descriptors
Operators, eigenfunctions
• Numerics
![Page 45: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/45.jpg)
45
Topics (tentative)
Geometry Processing
• Rigid shape matching
Local registration (ICP)
Global registration (feature-based)
• Linear and Riemannian Shape spaces
Surface reconstruction
Shape deformation and non-rigid shape matching
• Intrinsic geometry
Isometry invariant shape matching
General metrics, high-dimensional shape spaces
![Page 46: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/46.jpg)
46
Topics (tentative)
Geometry Processing
• Symmetry
What is symmetry? Some group theory :-)
Detection algorithms & applications
Inverse procedural modeling
• Shape Learning
![Page 47: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/47.jpg)
47
Another View
Methods:
• Variational and statistical estimation
Least-squares, function estimation
Robust estimation, sparse statistics
Regularization, inverse problems
• Differential geometry
• Group theory
Symmetry groups
• Numerics
Solving large linear and non-linear systems
Eigenvalue problems
![Page 48: Statistical Geometry Processingresources.mpi-inf.mpg.de › ... › 02_Introduction-pub.pdf · Computer graphics •Content creation bottleneck •3D scanning: data quality Geometry](https://reader035.fdocuments.us/reader035/viewer/2022063000/5f11702b51dda100190ce1d0/html5/thumbnails/48.jpg)
“It is tempting, if the only tool
you have is a hammer,
to treat everything as if it were a nail.”
Abraham Maslow (1908-1970)