Spherical Hashing - SGVR Labsglab.kaist.ac.kr/Spherical_Hashing/SphericalHashing... · 2013. 11....

SphericalHashing

Jae‐Pil Heo1,Youngwoon Lee1,Junfeng He2,Shih‐FuChang2,andSung‐Eui Yoon1

1KAIST 2ColumbiaUniv.

IEEEConf.onComputerVisionandPatternRecognition(CVPR)2012

Introduction

• Approximatek‐nearestneighborsearchinhighdimensionalspace– widelyusedinvariousapplications– highcomputationcost,memoryrequirement– tree‐basedmethodsdonotgiveanybenefit(curseofdimensionality)

– spatialhashingtechniquesgetmoreattention

ImageRetrieval

Findingvisuallysimilarimages

ImageDescriptorsHighdimensionalpoint(BoW,GIST,ColorHistogram,etc.)

ImageDescriptorsHighdimensionalpoint(BoW,GIST,ColorHistogram,etc.)Imageretrievalisreducedto

nearestneighborsearchinhighdimensionalspace

Challenge

BoW GISTDim 1000+ 300+1image 4KB+ 1.2KB+1B images 3TB+ 1TB+

BinaryCodes

11000

11000

11001

00001

00011

00111

BinaryCodes11000

11000

11001

00001

00011

00111

* Benefits‐ High compression ratio (scalability)‐ FastsimilaritycalculationwithHammingdistance(efficiency)

*Issue‐ Howwelldobinarycodespreservedatapositionsandtheirdistances(accuracy)

BinaryCodewithHyper‐Planes

0

1

BinaryCodewithHyper‐Planes10

10

10

111

011

010

110000

100

GoodandBadHyper‐Planes

Previousworkfocusedonhowtodeterminegoodhyper‐planes

State‐of‐the‐artMethods• Randomhyper‐planesfromaspecificdistribution[Indyk – STOC1998,Raginsky – NIPS2009]

• Spectralgraphpartitioning[Yeiss – NIPS2008]

• Minimizingquantizationerror(ITQ)[Gong– CVPR2011]

• Independentcomponentanalysis(ICA)[He– CVPR2011]

• Supportvectormachine(SVM)[Joly – CVPR2011]

• Allofthemusehyper‐planes!

OurContributions

• SphericalHashing

• Iterativeoptimizationschemetodeterminehyper‐spheres

• SphericalHammingdistance

OurContributions

• SphericalHashing

• Iterativeoptimizationschemetodeterminehyper‐spheres

• SphericalHammingdistance

SphericalHashing

01

PartitioningExample

111

011

010

110000

100 001101

BoundingPowerofHyper‐Sphere

Average of maximum distances within a partition:‐ Hyper‐spheres gives tighter bound!

openclosed

OurContributions

• SphericalHashing

• Iterativeoptimizationschemetodeterminehyper‐spheres

• SphericalHammingdistance

TwoCriteria[Yeiss 2008,He2011]

1. Balancedpartitioning

2.Independence

<

TwoCriteriawithHyper‐Spheres

1.Balance 2.Independence

IterativeOptimization

1.Balance‐ bycontrollingradiusfor

2.Independence‐ bymovingtwohyper‐spheresfor ∩

Repeatstep1,2untilconvergence.

OurContributions

• SphericalHashing

• Iterativeoptimizationschemetodeterminehyper‐spheres

• SphericalHammingdistance

IntuitionofSphericalHD

Boundedby1hyper‐sphere

IntuitionofSphericalHD

Boundedby2hyper‐spheres

IntuitionofSphericalHD

Boundedby2hyper‐spheres

IntuitionofSphericalHD

Boundedby2hyper‐spheres

IntuitionofSphericalHD

Boundedby3hyper‐spheres

MaxDist.andCommon‘1’

111

011110

101

Common‘1’s

:2

MaxDist.andCommon‘1’

111

011

010

110

100 001101

Common‘1’s

:1

MaxDist.andCommon‘1’

Common‘1’s:1 Common‘1’s:2

Average of maximum distances between two partitions:decreases as number of common ‘1’

SphericalHammingDistance(SHD)

SHD: Hamming Distance divided by the number ofcommon ‘1’s.

Result(1M,384dimGIST)

Result(1M,960dimGIST)

Result(75M,384dimGIST)