Jure Leskovec (Stanford), Daniel Huttenlocher and Jon Kleinberg (Cornell)
1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning ...
-
date post
15-Jan-2016 -
Category
Documents
-
view
218 -
download
0
Transcript of 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning ...
![Page 1: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/1.jpg)
1
Computer Vision Research
Huttenlocher, Zabih– Recognition, stereopsis, restoration, learning
Strong algorithmic focus– Combinatorial optimization – Geometric algorithms
Application areas– Techniques we developed have
• Played important role at Xerox and Microsoft• Resulted in successful startups
– Medical imaging• Zabih joint with Radiology department in NYC
![Page 2: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/2.jpg)
2
Markov Random Fields
Many computer vision problems can be formalized using Markov random fields – Set of sites and neighborhood system
– Estimate label for each site accounting for• Goodness of fit of label to observed data at site
• Consistency of label with neighbors
MRF’s are undirected graphical models– Probabilistic relational models (directed)
Until recently a formalism used in computer vision, but not very practical
![Page 3: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/3.jpg)
3
Example MRF Problems
Stereopsis– For an image pair, estimate
depth at each pixel
• Sites are pixels, neighbors are 4-connected grid, labels are depths
Object recognition– For an image, estimate location
of a multi-part flexible object
• Sites are parts, neighbors are connected parts, labels are locations
![Page 4: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/4.jpg)
4
MRF Algorithms
Underlying graph G=(S,N)– For tree-structure can solve exactly using
variant of Viterbi recurrence• But impractical for large label set
– For two labels, can solve exactly using min-cut
– For three or more labels and grid-graph problem is NP hard
Recent algorithmic progress– For grid graphs, good approximation methods
– For low tree-width graphs, exact methods even for large label sets
![Page 5: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/5.jpg)
5
Alpha Expansion Technique [BVZ99]
Use min-cut to efficiently solve a special two label problem– Labels “stay the same” or “replace with ”
Iterate over possible values of – Each rules out exponentially many labelings
Red expansion
move from x
Input labeling x
![Page 6: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/6.jpg)
6
Graph Cuts for MRF’s on Grid
Best stereo algorithms use alpha expansion technique – Middlebury stereo benchmark
Beyond computer vision: many image compositing, restoration, editing tasks – E.g., SIGGRAPH, Microsoft
Ground Truth Correlation Alpha Expansion
![Page 7: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/7.jpg)
7
Tree-Like MRF’s
Object recognition– Nodes are parts, labels are locations
Small graph, not at all grid-like– Many labels (millions or more)
Viterbi algorithm for trees– Still not practical because O(m2n) for n parts
and m locations per part
– Fast min convolution techniques make finding best labeling O(mn)
More generally for fan-like graphs
![Page 8: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/8.jpg)
8
Fan Structured Models [CFH05]
K-fan, let RS be a set of reference parts– And R’=S-R be the remaining parts
– Complete graph on R and complete bipartite graph on R,R’
Parts local image patches – Probability of (oriented) edge at each pixel
![Page 9: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/9.jpg)
9
Models (Weakly Supervised)
Car (Rear) 1-fan
Motorbike 2-fan
Face 1-fan
• Training examples only labeled as positive/negative
![Page 10: 1 Computer Vision Research Huttenlocher, Zabih –Recognition, stereopsis, restoration, learning Strong algorithmic focus –Combinatorial optimization.](https://reader034.fdocuments.us/reader034/viewer/2022051517/56649d4a5503460f94a26527/html5/thumbnails/10.jpg)
10
Recognition Results
High detection accuracy– Motorbikes 98.6%, Faces 98.2%,
Cars 94.4%, Planes 95.0%
Fast running time– Approx. 2 sec. per image, 2 fans
Exact (global) method for computing highest probability configuration of parts for given image– No approximations or local search techniques
Single overall optimization problem– Does not depend on “feature detection”