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A dvanced C omputer V ision Feature-based Alignment

A dvanced C omputer V ision Feature-based Alignment. Lecturer: Lu Yi & Prof. Fuh l ynn. luyi@gmail.com CSIE NTU. Content. Pre-requisites: mainly about camera model Alignment Algorithm RANdom Sample Consensus (RANSAC ) Pose Estimation. Sources.

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A dvanced C omputer V ision Feature-based Alignment

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  1. Advanced Computer VisionFeature-based Alignment Lecturer: Lu Yi & Prof. Fuh lynn.luyi@gmail.com CSIE NTU

  2. Content • Pre-requisites: mainly about camera model • Alignment Algorithm • RANdomSample Consensus (RANSAC) • Pose Estimation

  3. Sources • EGGN 512 – Computer Vision course by Prof. Willliam Hoff • http://inside.mines.edu/~whoff/courses/EENG512/ • Playlist@Youtube: • http://www.youtube.com/playlist?list=PL4B3F8D4A5CAD8DA3 • Digital Visual Effects course by Prof. Yung-Yu Chuang • http://www.csie.ntu.edu.tw/~cyy/courses/vfx/14spring/news/ • Both are highly recommended

  4. Taught Way • Cover the main parts of textbook chapter 6 • Lecture mostly depended on EGGN 512 course videos

  5. Frames of Reference • Image frames are 2D; other are 3D • The “pose” (position and orientation) of a 3D rigid body has 6 degrees of freedom

  6. Pre-requisites • Image Formation • Geometric Transformations (2D-2D, 3D-3D, 3D-2D) • Camera Model (Camera Matrix = Intrinsic + Extrinsic camera matrix) • Allrelated contents arein textbook chapter 2: Image formation

  7. Pre-requisites • Review • Projective Transformation • Camera Matrix • EGGN 512 – Lecture 5-1 3D-2D Transforms • http://www.youtube.com/watch?v=DFNjOUMuecU&index=11&list=PL4B3F8D4A5CAD8DA3 • EGGN 512 – Lecture 5-2 3D-2D Transforms • http://www.youtube.com/watch?v=5gesrLgNuQo&list=PL4B3F8D4A5CAD8DA3

  8. Alignment Algorithm • EGGN 512 – Lecture 14-1 Alignment • http://www.youtube.com/watch?v=UcU4814hvR8&list=PL4B3F8D4A5CAD8DA3 • EGGN 512 – Lecture 14-2 Alignment • http://www.youtube.com/watch?v=XxEKMecNZk0&list=PL4B3F8D4A5CAD8DA3 • EGGN 512 – Lecture 14-3 Alignment • http://www.youtube.com/watch?v=lSXfv4baMwk&list=PL4B3F8D4A5CAD8DA3 • Slides • http://inside.mines.edu/~whoff/courses/EENG512/lectures/15-AlignmentNonlinear.pdf

  9. Alignment Algorithm • Feature-based methods: only use feature points to estimate parameters • Features: SIFT, SURF, Harris .etc.

  10. Determine pairwise alignment • p’=Mp, where M is a transformation matrix, p and p’ are feature matches • It is possible to use more complicated models such as affine or perspective • For example, assume M is a 2x2 matrix • Find M with the least square error

  11. Determine pairwise alignment • Overdeterminedsystem

  12. Normal Equation • Given an overdeterminedsystem • the normal equation is that which minimizes the sum of the square differences between left and right sides • Why?

  13. Normal Equation nxm, n equations, m variables

  14. Normal Equation

  15. → Normal Equation

  16. Normal Equation

  17. Normal Equation

  18. Determine pairwise alignment • p’=Mp, where M is a transformation matrix, p and p’ are feature matches • For translation model, it is easier. • What if the match is false? Avoid impact of outliers. (Ans: RANSAC)

  19. Application: Image Stitching • Stitching = alignment + blending photometric registration geometrical registration

  20. Application: Image Stitching • Panorama – the whole picture • Compact Camera FOV = 50 x 35°

  21. Application: Image Stitching • Panorama – the whole picture • Compact Camera FOV = 50 x 35° • Human FOV = 200 x 135°

  22. Application: Image Stitching • Panorama – the whole picture • Compact Camera FOV = 50 x 35° • Human FOV = 200 x 135° • Panoramic Mosaic = 360 x 180°

  23. Application: Image Stitching • Example: • http://graphics.stanford.edu/courses/cs178/applets/projection.html

  24. Application: Face Alignment • Face alignment is the key preprocessing step for face recognition

  25. Application: Face Alignment • Examples from LFW dataset:

  26. RANSAC Algorithm • RANSAC = RANdom Sample Consensus • An iterative method to estimate parameters of a mathematical model from a set of observed data which contains outliers [Wiki] • Compare to robust statistics • Given N data points xi, assume that majority of them are generated from a model with parameters , try to recover . • Fischler, M. A., & Bolles, R. C. (1981). Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6), 381-395.

  27. How many times? How big? Smaller is better How to define? Depends on the problem. RANSAC Algorithm Run k times: (1) draw n samples randomly (2) fit parameters  with these n samples (3) for each of other N-n points, calculate its distance to the fitted model, count the number of inlier points, c Output  with the largest c

  28. n samples are all inliers a failure failure after k trials RANSAC Algorithm (How to determine K) p: probability of real inliers P: probability of success after k trials for P=0.99

  29. RANSAC Algorithm (Example: line fitting)

  30. RANSAC Algorithm (Example: line fitting) n=2

  31. RANSAC Algorithm (Example: line fitting)

  32. RANSAC Algorithm (Example: line fitting)

  33. RANSAC Algorithm (Example: line fitting) c=3

  34. RANSAC Algorithm (Example: line fitting) c=3

  35. RANSAC Algorithm (Example: line fitting) c=15

  36. RANSAC Algorithm • EGGN 512 – Lecture 27-1 RANSAC • http://www.youtube.com/watch?v=NKxXGsZdDp8&list=PL4B3F8D4A5CAD8DA3&index=54

  37. RANSAC Algorithm (Example: Homography)

  38. RANSAC Algorithm (Example: Homography)

  39. RANSAC Algorithm (Example: Homography)

  40. Pose Estimation • EGGN 512 – Lecture 16-1 Pose Estimation • http://www.youtube.com/watch?v=kq3c6QpcAGc&list=PL4B3F8D4A5CAD8DA3 • EGGN 512 – Lecture 17-1 Pose from Lines • http://www.youtube.com/watch?v=D_4eUoqgWdc&list=PL4B3F8D4A5CAD8DA3

  41. Pose Estimation • EGGN 512 – Lecture 18-1 SVD • http://www.youtube.com/watch?v=C852P1JrHXI&list=PL4B3F8D4A5CAD8DA3 • EGGN 512 – Lecture 18-2 SVD • http://www.youtube.com/watch?v=aIkzK4CdYes&list=PL4B3F8D4A5CAD8DA3

  42. Pose Estimation • EGGN 512 – Lecture 19-1 Linear Pose Estimation • http://www.youtube.com/watch?v=HojSSrxsB4Q&list=PL4B3F8D4A5CAD8DA3 • EGGN 512 – Lecture 19-2 Linear Pose Estimation • http://www.youtube.com/watch?v=ik8dFybnyPY&list=PL4B3F8D4A5CAD8DA3 • EGGN 512 – Lecture 19-3 Linear Pose Estimation • http://www.youtube.com/watch?v=OS5b-3Xfn1M&list=PL4B3F8D4A5CAD8DA3

  43. END

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