Hausdorff Distance for Shape Matching

Speaker: Yu XiaozhouSupervisor: Maylor Leung2004. 9. 29.

Outline

n Introduction n Curve Segment Hausdorff Distance

(CHD)n Experiment Resultsn Conclusion and Future Work

Outline

n Introduction n Curve Segment Hausdorff Distance

(CHD)n Experiment Resultsn Conclusion and Future Work

Introduction-Shape Recognition Application

n Chinese character n Fingerprints

n Industrial parts n Logos

n Hausdorff distance (HD)

For two sets of points and

)),(),,(max(),( ABhBAhBAH =where

||||minmax),( baBAhBbAa

−=∈∈

maaA ,...,1= nbbB ,...,1=

n Modified Hausdorff distance (MHD)

∑∈

∈−=

AaBb

bam

BAh ||||min1

),(

Introduction-Related Works

Introduction-Related Works

n Line segment Hausdorff distance (LHD1, Gao and Leung, 2002)

aL

bL

1||l

⊥l

2||l

1. Parallel distance:

Distances between andaL bL

),min(),( 2||1|||| llLLd ba =

2. Perpendicular distance:

⊥⊥ = lLLd ba ),(

Introduction-Related Works

),( ba LLθ

aL

bL

3. Angle distance:

)),((),( baba LLfLLd θθ =

:f A penalty function which is

determined by a training process.

n Modified line segment Hausdorff distance (LHD2,Chen and Leung, 2003)¨ Perpendicular and parallel distances are

remained without changing.¨ Angle distance is redefined as

)),(sin(

||)||||,min(||),(

ba

baba

LL

LLLLd

θθ

×

=

),( ba LLθ

aL

bL

),()2( baLHD LLdθ

Introduction-Related Works

Introduction-Related Works

n LHD* (Yu and Leung, 2003)¨ Angle and parallel distances are remained the

same as LHD2.¨ Perpendicular distance is redefined as

aL

bL1⊥l

2⊥l

)(21

),( 2211 ⊥⊥⊥ ⋅+⋅⋅= lwlwLLd ba

Where

)2,1(,21

=+

=⊥⊥

⊥ ill

lw i

i

HD

LHD1

LHD2

LHD*

Huttenlocher etc. 1993

Gao and Leung 2002

Chen and Leung 2003

Yu and Leung 2003

CHD

Point to point matching

Line to line matching

Curve to curve matching

HD: HausdorffDistance

LHD: Line Segment

HausdorffDistance

Yu and Leung 2003

CHD: Curve

Segment HausdorffDistance

Introduction-Related Works

Outline

n Introductionn Curve Segment Hausdorff Distance

(CHD)n Experiment Resultsn Conclusion and Future Work

n Basic concepts and terminologies

n Images (LEM)

NM - Model image

- Test image

n Curves

…

Nj

Mi

C

C - Curve on

- Curve on NM

n Lines

…N

qjM

pi LL ,, /Nj

Mi CC /

CHD

- Lines

on

CHD

n Distances between twoline segments (LHD*)

n Angle distance

n Perpendicular distance

)(21

),( 2211 ⊥⊥⊥ ⋅+⋅⋅= lwlwLLd ba

n Parallel distance is omitted

)),(sin(

||)||||,min(||),(

ba

baba

LL

LLLLd

θθ

×

=

aL

bL)2,1(,

21

=+

=⊥⊥

⊥ ill

lw i

i

CHDn Proposed distance between a line and a curve

'NjC

MpiL ,

∑∈

⊥⊥ ⋅⋅='

,,,,

,

),('

1)',(Nj

Nqj CL

Nqj

Mpi

NqjN

j

Nj

Mpi LLdL

CCLd

|),(|)',('

,,,

,

∑∈

=Nj

Nqj CL

Nqj

Mpi

Nj

Mpi LLdCLd θθ

CHD

n Proposed distance between two curves

)',(1

),( ,,

,

Nj

Mpi

CL

MpiM

i

Nj

Mi CLdL

CCCd

Mi

Mpi

⊥∈

⊥ ⋅⋅= ∑

∑∈

=Mi

Mpi CL

Nj

Mpi

Nj

Mi CLdCCd

,

)',(),( ,θθ

CHD

n Proposed distance between two images

∑∑ ∈⊥

∈

⊥ ⋅⋅=)(

)(

),(1

),(Mi

Nj

Mi

Nj

CSC

Nj

Mi

Nj

CSC

Nj

Mi CCdC

CNCdI.

∑∈

=)(

),(),(Mi

Nj CSC

Nj

Mi

Mi CCdNCd θθ

:)( MiCS ,,,

1

NJ

NJ n

CC ⋅⋅⋅ Neighboring part for

Mi

J

Jj

Nj CC

N

≤∑= 1

sC Mi '

matching and

CHD

)),(),(

),(1

(1

),(

NMdNCd

NCdCCR

NMd

cMC

Mi

MC

Mi

Mi

MC

Mim

Mi

Mi

Mi

++

⋅⋅⋅=

∑

∑∑

∈

∈⊥

∈

θ

distanceon compensati :),( NMdc

II.

Outline

n Introductionn Curve Segment Hausdorff Distance

(CHD)n Experiment Resultsn Conclusion and Future Work

Experiment Results

n Some examples of logos

Set 3 Set 4

Set 5 Set 6

Set 7 Set 8

Set 1 Set 2

Examples:

Experiment Results

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

Se t 1 Se t 2 Se t 3 Se t 4 Se t 5 Se t 6 Set 7 Se t 8

Test images

Rec

ogni

tion

rate

MHD

LHD

CHD

Outline

n Introductionn Curve Segment Hausdorff Distance

(CHD)n Experiment Resultsn Conclusion and Future Work

Conclusion

n We analyzed the development of the methods in Hausdorff distance family.

n A novel shape matching algorithm (CHD) is proposed.

n The proposed shape recognition system is relatively robust to distortions and noise with encouraging experiment results.

Future Work

n The performance of CHD can be further improved.

n We will extend CHD for 3D object recognition, CHD’s good performance in occlusion and skewing implies the potential of our work in this direction.

Thank you!