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# Triangulation methods mihaylova

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### Triangulation methods mihaylova

1. 1. Outline Introduction Triangulation methods Practical examples Conclusion Triangulation Methods Seminar work Robotics and Medicine SS 09 Institut f¨r Prozessrechentechnik, Automation und Robotik u (IPR) Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci July 13, 2009 Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
2. 2. Outline Introduction Triangulation methods Practical examples Conclusion Introduction The human visual perception system Epipolar geometry Triangulation methods 3D point reconstruction Computation of the Fundamental matrix F Practical examples Active triangulation Conclusion Appliance in the medical robotics Closing words Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
3. 3. Outline Introduction The human visual perception system Triangulation methods Epipolar geometry Practical examples Conclusion Stereovision Why are we able to percept the relative distance to all objects? Why is it so important to measure the distance to and between the objects? How can another point of view help in solving this problem? Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
4. 4. Outline Introduction The human visual perception system Triangulation methods Epipolar geometry Practical examples Conclusion Stereovision principle x1 b f d f Disparity p = b d , where f represents the lens focal length p is proportional to the stereoscopic base b and inversely proportional to d - the distance to the measured object. Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
5. 5. Outline Introduction The human visual perception system Triangulation methods Epipolar geometry Practical examples Conclusion Basics of the epipolar geometry C � epipolar plane c c’ ep e ipo in rl lar e e’ a lin ol A baseline B ip e ep The baseline connects camera centers A and B and intersects the image planes in the epipoles e and e . Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
6. 6. Outline Introduction The human visual perception system Triangulation methods Epipolar geometry Practical examples Conclusion Basics of the epipolar geometry C � epipolar plane c c’ ep e ipo in rl lar e e’ a lin ol A baseline B ip e ep The baseline connects camera centers A and B and intersects the image planes in the epipoles e and e . The epipolar plane π is deﬁned by the camera centers and the 3D object point C . Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
7. 7. Outline Introduction The human visual perception system Triangulation methods Epipolar geometry Practical examples Conclusion Basics of the epipolar geometry C � epipolar plane c c’ ep e ipo in rl lar e e’ a lin ol A baseline B ip e ep The baseline connects camera centers A and B and intersects the image planes in the epipoles e and e . The epipolar plane π is deﬁned by the camera centers and the 3D object point C . The ambiguous projection of C . Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
8. 8. Outline Introduction The human visual perception system Triangulation methods Epipolar geometry Practical examples Conclusion The Fundamental Matrix F and the camera matrices P, P F is a 3 × 3 matrix representing the mapping between a point in the ﬁrst image and epipolar line in the second image. For all pairs of image points c and c the correspondence condition holds: T c Fc = 0 (1) Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
9. 9. Outline Introduction The human visual perception system Triangulation methods Epipolar geometry Practical examples Conclusion The Fundamental Matrix F and the camera matrices P, P F is a 3 × 3 matrix representing the mapping between a point in the ﬁrst image and epipolar line in the second image. For all pairs of image points c and c the correspondence condition holds: T c Fc = 0 (1) The camera matrices P and P satisfy the conditions c = PC and c = P C for every point correspondence Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
10. 10. Outline Introduction The human visual perception system Triangulation methods Epipolar geometry Practical examples Conclusion The Fundamental Matrix F and the camera matrices P, P F is a 3 × 3 matrix representing the mapping between a point in the ﬁrst image and epipolar line in the second image. For all pairs of image points c and c the correspondence condition holds: T c Fc = 0 (1) The camera matrices P and P satisfy the conditions c = PC and c = P C for every point correspondence In the case, when we deal with calibrated cameras, it is cleverer to compute the Essential Matrix E , which is specialization of F : −T F =P EP −1 (2) Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
11. 11. Outline Introduction 3D point reconstruction Triangulation methods Computation of the Fundamental matrix F Practical examples Conclusion General approach Algorithm: Take two images of the scene, separated by a baseline Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
12. 12. Outline Introduction 3D point reconstruction Triangulation methods Computation of the Fundamental matrix F Practical examples Conclusion General approach Algorithm: Take two images of the scene, separated by a baseline Identify the point correspondences in the images Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
13. 13. Outline Introduction 3D point reconstruction Triangulation methods Computation of the Fundamental matrix F Practical examples Conclusion General approach Algorithm: Take two images of the scene, separated by a baseline Identify the point correspondences in the images Apply the triangulation rules: compute F , P and P Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
14. 14. Outline Introduction 3D point reconstruction Triangulation methods Computation of the Fundamental matrix F Practical examples Conclusion General approach Algorithm: Take two images of the scene, separated by a baseline Identify the point correspondences in the images Apply the triangulation rules: compute F , P and P Find these two lines, which intersection deﬁnes the searched world point Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
15. 15. Outline Introduction 3D point reconstruction Triangulation methods Computation of the Fundamental matrix F Practical examples Conclusion Identiﬁcation the point correspondences in the images The most diﬃcult part is ﬁnding the point correspondences automatically! Robust pattern matching algorithm needed! Harris corner detector: simple but scales dependent Successful combination of Harris and Laplacian detectors: www.robots.ox.ac.uk/∼vgg/research/aﬃne/det eval ﬁles/mikolajczyk ijcv2004.pdf Laplacian and Diﬀerence of Gaussian (DoG) ”points of interest” detectors Salient region detector: www.robots.ox.ac.uk/∼vgg/research/ aﬃne/det eval ﬁles/kadir04.pdf Maximally stable extremal regions (MSER) (http://www.robots.ox.ac.uk/∼vgg/research/aﬃne/det eval ﬁles/ matas bmvc2002.pdf - specially developed for the stereo problem analysis) Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
16. 16. Outline Introduction 3D point reconstruction Triangulation methods Computation of the Fundamental matrix F Practical examples Conclusion Algorithms for computing F Having F computed gives us the possibility to estimate the scene points. There are some algorithms available: Eight point algorithm: F has 8 degrees of freedom, therefore we need 8 unique point pairs to compute it. Every pair deﬁnes equation, which solution contains the nine coeﬃcients of F Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
17. 17. Outline Introduction 3D point reconstruction Triangulation methods Computation of the Fundamental matrix F Practical examples Conclusion Algorithms for computing F Having F computed gives us the possibility to estimate the scene points. There are some algorithms available: Eight point algorithm: F has 8 degrees of freedom, therefore we need 8 unique point pairs to compute it. Every pair deﬁnes equation, which solution contains the nine coeﬃcients of F Algebraic minimization algorithm: based on the eight point algorithm, but tries to minimize the algebraic error caused by noisy measurement. Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
18. 18. Outline Introduction 3D point reconstruction Triangulation methods Computation of the Fundamental matrix F Practical examples Conclusion Algorithms for computing F Having F computed gives us the possibility to estimate the scene points. There are some algorithms available: Eight point algorithm: F has 8 degrees of freedom, therefore we need 8 unique point pairs to compute it. Every pair deﬁnes equation, which solution contains the nine coeﬃcients of F Algebraic minimization algorithm: based on the eight point algorithm, but tries to minimize the algebraic error caused by noisy measurement. Gold standard algorithm: dealing with the problem of Gaussian noise. This approach uses statistical methods for solving the triangulation puzzle, namely computing F by minimizing the Likelihood function. (proposed in the book: ”Multiple View Geometry in Computer Vision” - Richard Hartley and Andrew Zisserman) Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
19. 19. Outline Introduction Triangulation methods Active triangulation Practical examples Conclusion Light spot technique Simple construction: laser ray, lens, detector (CCD or PSD) Advantages: fast, accurate, independent from surface color Disadvantages: the surface should be no ideal mirror laser Ө p’ PSD q’ h q p measured object Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
20. 20. Outline Introduction Triangulation methods Active triangulation Practical examples Conclusion Stripe projection The object’s surface manipulates the scan line Resulting displacement in the light stripe ∼ to obj. distance camera laser d measured object h Ө reference surface (a) (b) Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
21. 21. Outline Introduction Triangulation methods Active triangulation Practical examples Conclusion Projection of encoded patterns Disadvantage of the stripe projection: too slow Correspondence problem by static line pattern projection Solutions: Binary coding, Grey coding, Phase shifted pattern projection, Colored pattern (the picture is taken from the book ”Digitale Bildverarbeitung” - Bernd J¨hne) a Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
22. 22. Outline Introduction Appliance in the medical robotics Triangulation methods Closing words Practical examples Conclusion Polaris R , NDI Standard optical tracking system in medicine, produced by Northern Digital Inc. (NDI) Oﬀers passive, active and hybrid tracking. The triangulated points are ﬁxed on the surgical instrument. http://www.ndigital.com/medical/polarisfamily.php Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
23. 23. Outline Introduction Appliance in the medical robotics Triangulation methods Closing words Practical examples Conclusion A.R.T. R Systems Advanced Realtime Tracking GmbH (A.R.T. GmbH) Multiple camera systems - 3, 4, 5 cameras for better results Example system: smARTtrack - two ARTtrack2 cameras mounted on a rigid bar, so that no calibration needed. diﬀerent conﬁgurations depending on focal length, angle between both cameras, baseline http://www.ar-tracking.de/smARTtrack.49.0.html Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
24. 24. Outline Introduction Appliance in the medical robotics Triangulation methods Closing words Practical examples Conclusion Da Vinci R Surgical System a) A high-resolution 3D endoscope coupled with two 3-chip cameras take the surgeon ”inside” the patient b) The console helps by visualizing the camera records and by repositioning the surgical camera inside the patient. www.intuitivesurgical.com/products/davinci surgicalsystem (c) (d) Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
25. 25. Outline Introduction Appliance in the medical robotics Triangulation methods Closing words Practical examples Conclusion Conclusion Through the methods of triangulation the robots similar to humans process the visual information. For triangulation the following prerequisites are needed: at least 2 points of view (implemented either with cameras or mixed with light sources) object point, placed on a comparably closer distance (not at inﬁnity) statistically stable algorithms for computing the point correspondences, respectively the distance to the world point Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods
26. 26. Outline Introduction Appliance in the medical robotics Triangulation methods Closing words Practical examples Conclusion Questions time Thank You for Your attention! Zlatka Mihaylova Supervisor: M.Phys. Matteo Ciucci Triangulation Methods