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!