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MAP inference in Discrete Models
Published on Oct 09, 20129433 Views
Many problems in Computer Vision are formulated in form of a random filed of discrete variables. Examples range from low-level vision such as image segmentation, optical flow and stereo reconstruction
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Chapter list
Tutorial on MAP Inference in Discrete Models00:00
Image Labelling Problems00:27
MRFs for Image Labelling - 102:47
MRFs for Image Labelling - 205:57
MRFs for Image Labelling - 306:04
Maximum a Posteriori (MAP) Inference06:23
Example: Image Segmentation - 106:37
Example: Image Segmentation - 207:34
Example: Image Segmentation - 308:56
Example: Image Segmentation - 409:20
Example: Image Segmentation - 510:52
Example: Image Segmentation - 611:56
Example: Image Segmentation - 712:07
The Problem12:27
Function Minimization: The Problems - 119:28
Function Minimization: The Problems - 220:54
Energy Minimization Problems - 120:58
Energy Minimization Problems - 221:37
Energy Minimization Problems - 322:25
Popular Inference Methods ...24:55
The LP Relaxation Approach25:54
Integer Program 26:01
MAP Inference as an IP27:48
LP Relaxation of MAP Inference29:35
Solving the Linear Program - 130:33
Solving the Linear Program - 231:57
Solving the LP relaxation - 132:41
Solving the LP relaxation - 235:10
Solving the LP relaxation - 335:15
Solving the LP relaxation - 435:16
Message Passing - 135:46
Message Passing - 235:52
Dynamic Programming - 137:20
Dynamic Programming - 243:29
Dynamic Programming - 343:50
BP on a tree [Pearl’88]46:04
Inward pass (dynamic programming) - 146:12
Inward pass (dynamic programming) - 246:15
Inward pass (dynamic programming) - 346:17
Inward pass (dynamic programming) - 446:19
Inward pass (dynamic programming) - 546:21
Inward pass (dynamic programming) - 646:23
Inward pass (dynamic programming) - 746:28
Outward pass46:35
BP on a tree: min-marginals46:41
BP in a general graph48:10
Distance transforms [Felzenszwalb & Huttenlocher’04]49:11
TRW Also see Diffusion (Schlesinger, Werner)52:30
Message Passing Techniques (Recap)57:38
Language Tractability : Submodularity and Graph Cuts01:00:16
Submodular Functions: Definition01:00:56
Submodular Functions01:07:29
Minimizing Submodular Functions01:08:21
The st-Mincut Problem - 101:10:23
The st-Mincut Problem - 201:11:05
The st-Mincut Problem - 301:11:09
The st-Mincut Problem - 401:11:57
So how does this work? 01:12:31
St-mincut and Energy Minimization01:14:14
Graph Construction - 101:15:18
Graph Construction - 201:15:38
Graph Construction - 301:16:51
Graph Construction - 401:17:38
Graph Construction - 501:17:45
Graph Construction - 601:18:21
Graph Construction - 701:18:31
Graph Construction - 801:18:32
Graph Construction - 901:19:21
How to compute the st-mincut?01:19:49
Maxflow Algorithms - 101:20:46
Maxflow Algorithms - 201:21:04
Maxflow Algorithms - 301:21:21
Maxflow Algorithms - 401:21:26
Maxflow Algorithms - 501:21:33
Maxflow Algorithms - 601:21:34
Maxflow Algorithms - 701:21:38
Maxflow Algorithms - 801:21:43
Maxflow Algorithms - 901:21:49
Maxflow Algorithms - 1001:21:53
Maxflow Algorithms - 1101:22:22
Maxflow Algorithms - 1201:22:31
Flow and Reparametrization - 101:22:56
Flow and Reparametrization - 201:23:03
Flow and Reparametrization - 301:23:42
Flow and Reparametrization - 401:23:58
Flow and Reparametrization - 501:24:09
Flow and Reparametrization - 601:24:15
Flow and Reparametrization - 701:24:16
Flow and Reparametrization - 801:24:19
Flow and Reparametrization - 901:24:47
Flow and Reparametrization - 1001:24:53
Flow and Reparametrization - 1101:24:58
Flow and Reparametrization - 1201:27:15
History of Maxflow Algorithms01:27:28
Maxflow in Computer Vision01:28:58
Code for Image Segmentation01:30:34
How does the code look like? - 101:30:56
How does the code look like? - 201:31:25
How does the code look like? - 301:32:02
How does the code look like? - 401:32:29
Demo01:32:54
Going beyond binary variables01:34:05
Graph Cuts for Vision Problems - 101:34:09
Graph Cuts for Vision Problems - 201:34:45
Graph Cuts for Multi-Label Problems01:35:39
Multi-label to Pseudo-boolean - 101:36:26
Multi-label to Pseudo-boolean - 201:38:55
Multi-label to Pseudo-boolean - 301:39:51
Results – Stereo01:40:02
Disadvantages of Exact Transformations01:40:29
Exact Solutions for Multi-label Problems01:40:46
Graph Cuts for Multi-Label Problems01:41:52
Move Making Algorithms - 101:41:59
Move Making Algorithms - 201:42:35
Computing the Optimal Move01:43:41
Move Making Algorithms - 301:43:56
Binary Moves01:45:05
Swap Move - 101:46:41
Swap Move - 201:46:47
Swap Move - 301:47:55
Expansion Move - 101:47:56
Expansion Move - 201:48:06
Expansion Move - 301:49:55
Interesting Connections01:49:56
General Binary Moves01:50:35
Moves for Continuous Variable Problems01:50:41
Graph Cuts for Vision Problems01:51:51
Properties - 101:52:06
Properties - 201:53:34
Examples of Higher order Models01:53:35
Lower Envelop Representation for Higher-order Potentials01:53:43
Transforming higher order potentials into hierarchical models - 101:53:44
Transforming higher order potentials into hierarchical models - 201:54:24
Example01:54:49
Higher-order Potentials for Label Consistency01:54:50
Labelling Consistency in Pixel Groups - 101:54:56
Labelling Consistency in Pixel Groups - 201:55:19
Labelling Consistency in Pixel Groups - 301:55:33
Results01:55:36
More Results01:55:37
Transforming higher order potentials - 101:55:38
Transforming higher order potentials - 201:57:40
Transforming higher order potentials - 301:57:54
Transforming higher order potentials - 401:58:09
Transforming higher order potentials - 501:58:10
Transforming higher order potentials - 601:58:16
Transforming higher order potentials - 701:58:17
Upper Envelopes - 101:58:23
Upper Envelopes - 201:58:24
Why Upper Envelopes?01:58:34
Scalability and Efficiency02:00:12
Why?02:00:14
[Kopf et al. (MSR Redmond) SIGGRAPH 2007 ]02:00:27
More Examples02:00:36
Image Segmentation in Videos - 102:00:40
Image Segmentation in Videos - 202:00:42
Dynamic Energy Minimization - 102:00:43
Dynamic Energy Minimization - 202:00:51
Hybrid Algorithms - 102:00:52
Hybrid Algorithms - 202:00:55
Hybrid Algorithms - 302:01:20
Recap02:01:21
What we didn’t cover ...02:01:40
Future Challenges ...02:02:14
Concluding Example02:03:26
A Model for Video Editing02:03:30
A deforming 3D object - 102:03:58
A deforming 3D object - 202:04:02
A deforming 3D object - 302:04:20
Video Generation Model - 102:04:28
Video Generation Model - 202:04:31
Video Generation Model - 302:04:35
Video Generation Model - 402:04:40
Video Generation Model - 502:04:50
Unwrap Mosaics02:04:58
Thanks for listening Questions?02:05:59