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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
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.