a local descriptor for finding corresponding points in vector fields liefei xu and h. quynh dinh...
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A Local Descriptor for Finding Corresponding Points in Vector Fields
Liefei Xu and H. Quynh DinhDept of Computer Science
Stevens Institute of Technology
ICPR 2008Tampa, Florida
Outline
• Examples of Vector Fields• Related Work• Vector Spin Image• Results• Tracking Example• Summary
Vector Fields ExamplesVideo Analysis Weather Monitoring
From Center for Maritime Systems at Stevens Inst. of Tech.
Simulation of water current in the New York Harbor Region.
Computational Fluid Dynamics
Visualization of the flow inside a diesel engine. [Image courtesy of Laramee et al. 04, Chen et al. 07]
Related Work• Vector Field Analysis
– Singularity classification[Helman & Hesselink 90, Scheuermann et al. 98, Tricoche et al. 01, Zhang et al. 06]
– Comparing Vector Fields[Lavin et al. 98, Tovar 98, Theisel &Weinkauf 02, Ebling et al. 03]
• Shape Matching– Global geometric distributions
[Ankerst et al. 99, Osada et al. 02]
– Local geometric distributions [Johnson and Hebert 99, Belongie et al. 02, Frome et al. 04]
Local Descriptor for 3D Shapes– Spin Image
(radial) values
(d
epth
) va
lue
s
spin-images
[Johnson & Hebert 99]
Local Descriptor for Vector Fields
– Vector Spin Image
[Frome et al. 04]
Distribution of and values
values (radius)
va
lues
few
many
Vector Field
vector dot product
test pt
neighbor
Comparing Vector Spin Images
- χ2 statistical distance
different
similar
Vector Spin Image: Boundary Issue
vector field boundary problem Vector field reflected around edges and normalized
different
similar
Solved by Reflection
Vector Spin Image: Radius of Support
vector field512 X 512
r min = 5
r max = 60
r min = 3
r max = 40
r min = 2
r max = 20
different
similar
Larger radius, more discriminating
Vector Spin Image:Resolution
vector field # of bins (r X dot) 10 X 10 5 X 5 5 X 10
different
similar
Dot-product is the key dimension
Identify Features
different
similar
Test on Real Vector Fieldsx
x
Timing
• Computation of vector spin images– 57 microsecs for each point for rmax =60
– 7 microsecs for each point for rmax =20
• Computation of χ2 statistical distance – < 1 second (262144 comparisons)
Application - Tracking
x
10% 50% 100%[Image courtesy of Laramee et al. 04, Chen et al. 07]
Summary
• Statistical Method • Discriminative• Robust• Efficient
A Local Descriptor – Vector Spin Image
