computer vision lab contour matching using epipolar geometry (pami, april 2000) 2004. 6. 4 young ki...

Computer Vision Lab

Contour Matching UsingContour Matching UsingEpipolar GeometryEpipolar Geometry

(PAMI, April 2000)(PAMI, April 2000)

2004. 6. 42004. 6. 4Young Ki BaikYoung Ki Baik

Computer Vision Lab

Contour matchingContour matching

Key ideaKey idea Initial matching refinementInitial matching refinement from the matched from the matched

sets of sets of contourscontours..

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Several primitives to matchSeveral primitives to match Points / Straight linesPoints / Straight lines Both points and straight linesBoth points and straight lines Line segmentsLine segments ContourContour

•A set of chained image points.A set of chained image points.

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Previous contour matching methodsPrevious contour matching methods Smoothness constraints of the contourSmoothness constraints of the contour Smoothness constraints on the second derivativSmoothness constraints on the second derivativ

e of velocitye of velocity Or minimization of curvature variationsOr minimization of curvature variations

Contour matching methodsContour matching methods Contour matching using Contour matching using Epipolar geometryEpipolar geometry

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AssumptionAssumption The images are taken with a The images are taken with a moving cameramoving camera and and

the scenethe scene isis static static..

The The intensity valueintensity value of a region does of a region does not changenot change much as the camera moves.much as the camera moves.

If a space contour is observed by two cameras, If a space contour is observed by two cameras, there can be matching between images of the there can be matching between images of the contourcontour in image space with the in image space with the same parametric same parametric valuevalue..

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Epipolar geometryEpipolar geometry

center optical :

plane image :

epipole:e

lineepipolar :

point image:

point 3D:

O

R

l

x

X

nkxFx ikijTjk ,,1 ,0

Fundamental matrix Fundamental matrix FF

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Contour parameterizationContour parameterization

Let Let C(S)C(S) be a space curve parameterized by be a space curve parameterized by

arc length arc length SS..

are projected contours of are projected contours of C(S)C(S).. scsc ji ,

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Epipolar geometry for ContourEpipolar geometry for Contour

1)(,0)(, 10 , scFlscFl iijscjiijscj ii

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Contour matching algorithmContour matching algorithm

Algorithm (Initial matching)Algorithm (Initial matching) Step1:Find contours in each imageStep1:Find contours in each image

• Using a Using a zero-crossing edge detectorzero-crossing edge detector and an and an edge liedge linkernker..

Step2:Find a set of seed matchesStep2:Find a set of seed matches• Using classical correlation-based matching techniqUsing classical correlation-based matching techniq

ue.ue.

Step3:Compute the epipolar geometryStep3:Compute the epipolar geometry• Using 8-point algorithm (Hartley)Using 8-point algorithm (Hartley)

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Algorithm (Contour matching)Algorithm (Contour matching) Step4:For each contour point, do steps 5-7Step4:For each contour point, do steps 5-7

Step5:Find the initial estimationStep5:Find the initial estimation

Step6:Match pointsStep6:Match points• Using the epipolar constraint and correlation. Using the epipolar constraint and correlation.

Step7:Choose the major corresponding contour.Step7:Choose the major corresponding contour.• Discard contours which match to minor corresponDiscard contours which match to minor correspon

ding contours.ding contours.

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Step5: Find the initial estimation ( 1)Step5: Find the initial estimation ( 1) Finding contour point correspondence.Finding contour point correspondence.

•Using epipolar lineUsing epipolar line

ki sc ?kj sc

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Step5: Find the initial estimation ( 2 )Step5: Find the initial estimation ( 2 ) Finding contour point correspondence.Finding contour point correspondence.

kiljkkiijT

ljnl

kj scsccorrscFscsc ,/ minarg,,1

1212 yx nnW

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Step5: Find the initial estimation ( 3 )Step5: Find the initial estimation ( 3 ) Fast Finding contour point correspondence.Fast Finding contour point correspondence.

•q nearest neighbors ( ) of . q nearest neighbors ( ) of . •Let match points be . Let match points be . •Let is . Let is . • is initial estimate location.is initial estimate location.

ki sciqi xx ,,1 iqi xx ~,,~

1 kj tc ~

q

j ijxq1

~/1 kj sc ˆ

Tkj yxtc ~,~ˆ Tscj cbalki

,,,

1

~

~1

ˆ2

2

22y

x

bcaab

acabb

basc kj

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Step6: Match pointStep6: Match point Finding contour point correspondence.Finding contour point correspondence.

•Using the epipolar constraint and correlation. Using the epipolar constraint and correlation.

kiljkkiijT

ljnl

kj scsccorrscFscsc ,/ minarg,,1

factor ion normalizat:

thresholdsuitable:

k

kiijT

lj scFsc

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Step7:Choose the major corresponding contourStep7:Choose the major corresponding contour Major corresponding contourMajor corresponding contour

•All matches not on the major corresponding contour are All matches not on the major corresponding contour are removed.removed.

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Algorithm (Re-computing)Algorithm (Re-computing) Step8:Re-compute the epipolar geometryStep8:Re-compute the epipolar geometry

•Using points in matched contours.Using points in matched contours.

Step9:For each contour point, rematch along the contoStep9:For each contour point, rematch along the contourur• Using epipolar constraintUsing epipolar constraint

kkiijT

ljnl

kj scFscsc /minarg,,1

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Extension to contour matching Extension to contour matching in three viewsin three views

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Contour matching resultContour matching result

Mosaic box image setMosaic box image set

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Contour matching resultContour matching result

Etc. image setEtc. image set

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ConclusionConclusion

Contour matching algorithm uses Geometric Contour matching algorithm uses Geometric constraints has been presented.constraints has been presented.

Fail caseFail case Bad initial matchBad initial match Lack of corner featuresLack of corner features Simple repetition of a patternSimple repetition of a pattern Highly blurred patternsHighly blurred patterns

Computing time : Computing time : 17sec17sec Number of contours : 1084Number of contours : 1084 Number of points : 18831Number of points : 18831 SGI O2 workstation with an R10000 2.6 processorSGI O2 workstation with an R10000 2.6 processor

computer vision lab contour matching using epipolar geometry (pami, april 2000) 2004. 6. 4 young ki...

Documents

contour slide

space contour

matching technique

contour smoothness constraints

major corresponding

epipolar geometry slide

algorithm hartley slide

match points