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OutlineIntroduction
Triangulation methodsPractical examples
Conclusion
Triangulation MethodsSeminar work
Robotics and Medicine SS 09Institut fur Prozessrechentechnik, Automation und Robotik
I Laplacian and Difference of Gaussian (DoG) ”points ofinterest” detectors
I Salient region detector: www.robots.ox.ac.uk/∼vgg/research/affine/det eval files/kadir04.pdf
I Maximally stable extremal regions (MSER)(http://www.robots.ox.ac.uk/∼vgg/research/affine/det eval files/matas bmvc2002.pdf - specially developed for the stereoproblem analysis)
3D point reconstructionComputation of the Fundamental matrix F
Algorithms for computing F
Having F computed gives us the possibility to estimate the scenepoints. There are some algorithms available:
I Eight point algorithm: F has 8 degrees of freedom, thereforewe need 8 unique point pairs to compute it. Every pair definesequation, which solution contains the nine coefficients of F
I Algebraic minimization algorithm: based on the eight pointalgorithm, but tries to minimize the algebraic error caused bynoisy measurement.
I Gold standard algorithm: dealing with the problem ofGaussian noise. This approach uses statistical methods forsolving the triangulation puzzle, namely computing F byminimizing the Likelihood function. (proposed in the book:”Multiple View Geometry in Computer Vision” - RichardHartley and Andrew Zisserman)
3D point reconstructionComputation of the Fundamental matrix F
Algorithms for computing F
Having F computed gives us the possibility to estimate the scenepoints. There are some algorithms available:
I Eight point algorithm: F has 8 degrees of freedom, thereforewe need 8 unique point pairs to compute it. Every pair definesequation, which solution contains the nine coefficients of F
I Algebraic minimization algorithm: based on the eight pointalgorithm, but tries to minimize the algebraic error caused bynoisy measurement.
I Gold standard algorithm: dealing with the problem ofGaussian noise. This approach uses statistical methods forsolving the triangulation puzzle, namely computing F byminimizing the Likelihood function. (proposed in the book:”Multiple View Geometry in Computer Vision” - RichardHartley and Andrew Zisserman)
3D point reconstructionComputation of the Fundamental matrix F
Algorithms for computing F
Having F computed gives us the possibility to estimate the scenepoints. There are some algorithms available:
I Eight point algorithm: F has 8 degrees of freedom, thereforewe need 8 unique point pairs to compute it. Every pair definesequation, which solution contains the nine coefficients of F
I Algebraic minimization algorithm: based on the eight pointalgorithm, but tries to minimize the algebraic error caused bynoisy measurement.
I Gold standard algorithm: dealing with the problem ofGaussian noise. This approach uses statistical methods forsolving the triangulation puzzle, namely computing F byminimizing the Likelihood function. (proposed in the book:”Multiple View Geometry in Computer Vision” - RichardHartley and Andrew Zisserman)
I Simple construction: laser ray, lens, detector (CCD or PSD)I Advantages: fast, accurate, independent from surface colorI Disadvantages: the surface should be no ideal mirror
I Disadvantage of the stripe projection: too slowI Correspondence problem by static line pattern projectionI Solutions: Binary coding, Grey coding, Phase shifted pattern
projection, Colored pattern (the picture is taken from thebook ”Digitale Bildverarbeitung” - Bernd Jahne)
I Advanced Realtime Tracking GmbH (A.R.T. GmbH)I Multiple camera systems - 3, 4, 5 cameras for better resultsI Example system: smARTtrack - two ARTtrack2 cameras
mounted on a rigid bar, so that no calibration needed.I different configurations depending on focal length, angle
between both cameras, baselineI http://www.ar-tracking.de/smARTtrack.49.0.html
Through the methods of triangulation the robots similar tohumans process the visual information.For triangulation the following prerequisites are needed:
I at least 2 points of view (implemented either with cameras ormixed with light sources)
I object point, placed on a comparably closer distance (not atinfinity)
I statistically stable algorithms for computing the pointcorrespondences, respectively the distance to the world point