UNIVERSIDAD DE MURCIA LÍNEA DE INVESTIGACIÓN DE PERCEPCIÓN ARTIFICIAL Y RECONOCIMIENTO DE...

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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• 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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• 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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• 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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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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CIRCULAR FEATURES




• Target used in the experiments.

320x240 pixels

256 gray levels

• Manual measure to determine ground-truth positions.

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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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• 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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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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• 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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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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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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LASTLAST

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

• Línea PARP web page:

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

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