1. Multi-labeling Problems
Solving MultiLabel MRFs using Incremental alpha-expansion on GPU
Vibhav Vineet and P. J. Narayanan
Dynamic Graph-Cuts
Multi-labeling Problems
3/1
2/0
7/0
4/0
5/3
3/1
2/3
3/0
7/0
4/0
5/3
3/1
2/-1
3/0
7/0
4/0
5/3
Energy Minimization Method
Reparameter-rization
Updation
Better Initialized Residual Graph of Next MRF Instance
Residual Graph of Previous MRF
Updated Residual Graph
Low level vision problems involve assigning a label from a set to each pixel in the image
Mapped as an energy minimization problem defined over a discrete MRF.
Two Steps of Updation and
Re-parameterization
Easily parallelizable
Flow
Residual Flow
Incremental alpha Expansion on GPU
Basic Algorithm
On GPU
Initialize the Graph
For First Cycle
For Lable 1:
Construct Graph and perform Graph Cut on GPU
Save final excess flow
For Labels l from 2 to L:
Construct graph and update and repratemeterize flow based on and perform Graph Cuts on GPU
For later cycle i and iteration k:
Construct graph and update and reparameterize based on and perform Graph Cuts on GPU G 2 1 G 1 C 1 G l 1
Dynamic Graph Cut Performed on GPU G 1 C 2 G 2 G l 2 G 1 2
Basic Graph Cuts
On GPU
Graph Cuts on GPU
Push-Relabel Algorithm
Push Operation:
Each Vertex pushing flow to its neighbor; easily parallelizable
Relabel Operation:
Adjustment of heights
Performing local relabel G l 1 G
l-1 1 G 1 k G 2 k G l k C k G k i
Iteration within a Cycle G k
i-1
Cycle
Stochastic Cuts
Incremental alpha Expansion
A complete parallel way of solving multi-label MRF
Energy Function Computed on GPU
Graph Construction on GPU
Dynamic Graph Cuts:
Updation and Re-parameterization done on GPU
Graph Cuts performed on GPU
Memory Requirement
Need to store original graph and residual graphs for all the labels for the previous cycle
MRF constitutes both simple and difficult variables
Simple Variables settle quickly
Based on this observation, block wise processing of the pixels
Delaying the processing of the block which is unlikely to exchange any flow with neighbors
Result Section
Image
Size
#ofLabels
Boykov
Dynamic
Incremental
Tsukuba
384 x 288 16
5400
3230
950
Teddy
450 x 375 60
44200
21400
6890
Penguin
122 x 179
256
34390
12310
5120
Panorama
1071 x480 7
30593
15988
6520
Teddy;
stereo
Penguin;
De-noising
Panorama; Photomontage
Tsukuba;
stereo
Experiments conducted on
stereo, denoising, photomontage etc.
Datasets from Middlebury MRF page.
Observed an speed-up of 4-6 times on different datasets
Code available at:
Hardware used: GTX 280 GPU
Comparison Done with Boykov’s method and Dynamic alpha-expansion on CPU
Center for Visual Information Technology
International Institute of Information Technology Hyderabad