Jianke Zhu
From Haibin Ling’s ICCV talk
Fast Marching Method and Deformation Invariant Features
Outline
Introduction Fast Marching Method Deformation Invariant Framework Experiments Conclusion and Future Work
General Deformation
One-to-one, continuous mapping. Intensity values are deformation invariant.
(their positions may change)
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
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]
Outline
Introduction
Deformation Invariant Framework Intuition through 1D images 2D images
Experiments
Conclusion and Future Work
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
Geodesic Distance
αI
(1-α)x
p qg(p,q)
• Length of the shortest path along surface
Geodesic Distance and α
I1 I2
Geodesic distance becomes deformation invariant
for α close to 1
embed embed
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
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
Deformation Invariant Descriptor
p qp q
Geodesic-Intensity Histogram (GIH)
geodesic distance
inte
nsity
geodesic distance
inte
nsity
Real Example
pq
Deformation Invariant Framework
Image Embedding ( close to 1)
Deformation Invariant SamplingGeodesic Sampling
Build Deformation Invariant Descriptors(GIH)
),(),( IyxI
Practical Issues
Lighting changeAffine lighting modelNormalize the intensity
Interest-PointNo special interest-point is requiredExtreme point (LoG, MSER etc.) is more
reliable and effective
Invariant vs. Descriminative
0
10
1
Outline
Introduction
Deformation Invariance for Images
Experiments Interest-point matching
Conclusion and Future Work
Data Sets
Synthetic Deformation & Lighting Change (8 pairs) Real Deformation (3 pairs)
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
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
Synthetic Image Pairs
Real Image Pairs
Outline
Introduction
Deformation Invariance for Images
Experiments
Conclusion and Future Work
Thank You!