Download - Jianke Zhu From Haibin Ling’s ICCV talk Fast Marching Method and Deformation Invariant Features
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Jianke Zhu
From Haibin Ling’s ICCV talk
Fast Marching Method and Deformation Invariant Features
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Outline
Introduction Fast Marching Method Deformation Invariant Framework Experiments Conclusion and Future Work
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General Deformation
One-to-one, continuous mapping. Intensity values are deformation invariant.
(their positions may change)
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Our Solution
A deformation invariant framework
Embed images as surfaces in 3D
Geodesic distance is made deformation invariant by adjusting an embedding parameter
Build deformation invariant descriptors using geodesic distances
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Related Work Embedding and geodesics
Beltrami framework [Sochen&etal98] Bending invariant [Elad&Kimmel03] Articulation invariant [Ling&Jacobs05]
Histogram-based descriptors Shape context [Belongie&etal02] SIFT [Lowe04] Spin Image [Lazebnik&etal05, Johnson&Hebert99]
Invariant descriptors Scale invariant descriptors [Lindeberg98, Lowe04] Affine invariant [Mikolajczyk&Schmid04, Kadir04,
Petrou&Kadyrov04] MSER [Matas&etal02]
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Outline
Introduction
Deformation Invariant Framework Intuition through 1D images 2D images
Experiments
Conclusion and Future Work
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1D Image Embedding
1D Image I(x)
EMBEDDINGI(x) ( (1-α)x, αI )αI(1-α)x
Aspect weight α : measures the importance of the intensity
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Geodesic Distance
αI
(1-α)x
p qg(p,q)
• Length of the shortest path along surface
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Geodesic Distance and α
I1 I2
Geodesic distance becomes deformation invariant
for α close to 1
embed embed
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Image Embedding & Curve Lengths
]1,0[:),( 2 RyxI
dtIyxl ttt 222222 )1()1(
))('),('),('()( tztytxt
Depends only on intensity I Deformation Invariant
IzyyxxI ',)1(',)1('),(
dtI t
21
Image I
Embedded Surface
Curve on
Length of
Take limit
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Deformation Invariant SamplingGeodesic Sampling
1. Fast marching: get geodesic level curves with sampling interval Δ
2. Sampling along level curves with Δ
p
sparsedense
Δ
ΔΔ
Δ
Δ
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Deformation Invariant Descriptor
p qp q
Geodesic-Intensity Histogram (GIH)
geodesic distance
inte
nsity
geodesic distance
inte
nsity
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Real Example
pq
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Deformation Invariant Framework
Image Embedding ( close to 1)
Deformation Invariant SamplingGeodesic Sampling
Build Deformation Invariant Descriptors(GIH)
),(),( IyxI
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Practical Issues
Lighting changeAffine lighting modelNormalize the intensity
Interest-PointNo special interest-point is requiredExtreme point (LoG, MSER etc.) is more
reliable and effective
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Invariant vs. Descriminative
0
10
1
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Outline
Introduction
Deformation Invariance for Images
Experiments Interest-point matching
Conclusion and Future Work
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Data Sets
Synthetic Deformation & Lighting Change (8 pairs) Real Deformation (3 pairs)
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Interest-Points
* Courtesy of Mikolajczyk, http://www.robots.ox.ac.uk/~vgg/research/affine/
Interest-point Matching
• Harris-affine points [Mikolajczyk&Schmid04] *
• Affine invariant support regions• Not required by GIH• 200 points per image
• Ground-truth labeling• Automatically for synthetic image pairs• Manually for real image pairs
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Descriptors and Performance Evaluation
Descriptors• We compared GIH with following descriptors:
Steerable filter [Freeman&Adelson91], SIFT [Lowe04], moments [VanGool&etal96], complex filter [Schaffalitzky&Zisserman02], spin image [Lazebnik&etal05] *
•
Performance Evaluation• ROC curve: detection rate among top N matches. • Detection rate
matches possible#
matchescorrect #r
* Courtesy of Mikolajczyk, http://www.robots.ox.ac.uk/~vgg/research/affine/
98.0
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Synthetic Image Pairs
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Real Image Pairs
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Outline
Introduction
Deformation Invariance for Images
Experiments
Conclusion and Future Work
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Thank You!