Spherical Hashing - SGVR Labsglab.kaist.ac.kr/Spherical_Hashing/SphericalHashing... · 2013. 11....
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Spherical Hashing Jae‐Pil Heo 1 , Youngwoon Lee 1 , Junfeng He 2 , Shih‐Fu Chang 2 , and Sung‐Eui Yoon 1 1 KAIST 2 Columbia Univ. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR) 2012
Transcript of 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)
