A CAMERA CALIBRATION TECHNIQUE USING TARGETS OF CIRCULAR FEATURES

UNIVERSIDAD DE MURCIA

LÍNEA DE INVESTIGACIÓN DE PERCEPCIÓN ARTIFICIAL Y

RECONOCIMIENTO DE PATRONES - GRUPO DE COMPUTACIÓN

CIENTÍFICA

A CAMERA CALIBRATION TECHNIQUE USING

TARGETS OF CIRCULAR FEATURES

A CAMERA CALIBRATION TECHNIQUE USING

TARGETS OF CIRCULAR FEATURES

Ginés García MateosDept. de Informática y Sistemas

Universidad de Murcia - España

2

A CAMERA CALIBRATION TECHNIQUE

USING TARGETS OF

CIRCULAR FEATURES

Ginés García Mateos

SIARP’2000LISBOASEPT. 2000

INTRODUCTIONINTRODUCTION

• Camera calibration: estimation of the unknown values in a camera model.– Intrinsic parameters.

– Extrinsic parameters.

• Calibration target: object of known geometry, easy to detect and locate, used in calibration.

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USING TARGETS OF

CIRCULAR FEATURES




• The whole procedure of camera calibration [Heikkilä et al. 97]:– Determinate a camera model.

– Control point location in the images.

– Camera model fitting.

– Image correction for distortion.

– Estimate the errors of the previous stages.

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USING TARGETS OF

CIRCULAR FEATURES




• Much research has been devoted to model fitting.

• Control point location:– Design physical target structure.

– Design an algorithm for target detection and location.

– Goals: accuracy, robustness, efficiency, simplicity.

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USING TARGETS OF

CIRCULAR FEATURES



TARGET DESIGNTARGET DESIGN

• Previous work: square features.

• Typical methods use:– Edge, segment, corner detection.

– Line intersections.

– Contour following.

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USING TARGETS OF

CIRCULAR FEATURES




• Previous work: dot features.

• Point features (less than 5 pixels radius).

• Centroid calculation.

• Used in photogrametry.

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USING TARGETS OF

CIRCULAR FEATURES




• Circular features. Key ideas:– Circles (ellipses) are mapped to ellipses

(using perspective projection).– Ellipses are the most simple shape to

describe, detect and locate.

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USING TARGETS OF

CIRCULAR FEATURES



TARGET DESIGNTARGET DESIGN• Previous work based on centroid.• Problem of perspective bias: ellipse

centroid is not necessarily the projected centroid of the circle.

C

Rw

RIM

P

e

e'

oo

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USING TARGETS OF

CIRCULAR FEATURES



TARGET DETECTION/LOCATIONTARGET DETECTION/LOCATION

• Process for detection and location of the target. Main steps:– Detection and location of ellipses.

– Extraction of invariant points.

– Matching with known points of the target.

• Then model fitting (DLT) is applied.

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USING TARGETS OF

CIRCULAR FEATURES




• Ellipse detection and location:– Image binarization.

• Threshold: median value of partial histogram.

– Connected component grouping.

– Gaussian component description.• For each region: , and number of

points.

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USING TARGETS OF

CIRCULAR FEATURES



ELLIPSE DETECTION/LOCATIONELLIPSE DETECTION/LOCATION

Binarization

Connected compo-nent grouping

Acquired image

Gaussian description

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USING TARGETS OF

CIRCULAR FEATURES



ELLIPTICAL SHAPE TESTELLIPTICAL SHAPE TEST

• Gaussian parameters: , .

22222

21 44 )()( xyyxvvRSRPixels

• Ellipse mayor and minor radius: a, b

• Ellipse area: SR=ab

• Radius from gaussian parameters:2

12 va 222 vb

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USING TARGETS OF

CIRCULAR FEATURES




• Ellipse location is insufficient: invariant points should be extracted.

• Feature points in a target of circles.– Ellipse centroid is not an

invariant feature point.

– Invariant feature points can be obtained using relations between coplanar circles.

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USING TARGETS OF

CIRCULAR FEATURES




• Tangent invariance: supposing perspective projection common tangent property remains invariant.

p'1

E2

E1

R'

p'2

q'1

q'2

C1

C2

p1

R

p2

q1

q2

Perspective projection

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USING TARGETS OF

CIRCULAR FEATURES




• Some conclusions don’t held when radial distortion is considered.

• Dealing with distortion:– Iterative method: parameter

calculation/image correction.

– Independent estimation (and correction) of distortion.

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USING TARGETS OF

CIRCULAR FEATURES



EXPERIMENTAL RESULTSEXPERIMENTAL RESULTS

• Tests are centered on the target detection/location procedure.– Accuracy: feature point location.

– Robustness: defocusing and noise.

– Efficiency: computation time.• Acquisition: low-cost videoconference

camera QuickCam Pro (Logitech).• Computer: off-the-self PC, with K6 at

350Mhz.

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USING TARGETS OF

CIRCULAR FEATURES




• Target used in the experiments.

320x240 pixels

256 gray levels

• Manual measure to determine ground-truth positions.

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USING TARGETS OF

CIRCULAR FEATURES




Location error vs. ellipse size in images

10 15 20 25 30 350

0.2

0.4

0.6

0.8

1.0

1.2

Mean ellipse radius (pixels)

Location error (pixels)

Manual measureaccuracy

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USING TARGETS OF

CIRCULAR FEATURES




• Manual measure is insufficient.

• Accuracy of the method (using ideal images): 0.05 pixels mean, 0.03 pixels standard deviation.

• The target was detected in 97% of the images.

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USING TARGETS OF

CIRCULAR FEATURES




• Robustness to defocusing and noise.

1 2 3 4 5 60

0.2

0.4

0.6

0.8

1.0

1.2

Gaussian smoothing level,

Location error (pixels)

1.4

7

Location error vs gaussian smoothing

Noise percentage (in each pixel)

Location error (pixels) 0

0.2

0.4

0.6

0.8

0% 10% 20% 30% 40%

Location error vs. random noise

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CIRCULAR FEATURES




• Efficiency:– The main process is a connected

component labeling algorithm.

– This requires a single scanning of the image, with a constant cost per pixel.

– The whole process can be made at approx. 10 Hz.

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USING TARGETS OF

CIRCULAR FEATURES



CONCLUSIONSCONCLUSIONS• A technique for camera calibration is

proposed based in the use of circles as target features.

• This contribution is centered in target detection/location.

• Process of detection and location:– Gaussian description of connected

component.

– Feature point calculation and matching.

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USING TARGETS OF

CIRCULAR FEATURES



CONCLUSIONSCONCLUSIONS

• The method is simple and low-level, which implies efficiency and robustness.

• Subpixel accuracy is clearly reached.

• High robustness to noise and defocusing.

• The technique is suited for automated systems.

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USING TARGETS OF

CIRCULAR FEATURES



LASTLAST

• This work has been supported by CICYT project TIC98-0559.

• Línea PARP web page:

http://www.dis.um.es/parp

• Muito obrigado

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A CAMERA CALIBRATION TECHNIQUE USING TARGETS OF CIRCULAR FEATURES