1. Feature tracking Class 5 Read Section 4.1 of course notes http://www.cs.unc.edu/~marc/tutorial/node49.html Read Shi and Tomasi’s paper on good features to track http://www.unc.edu/courses/2004fall/comp/290/089/papers/shi-tomasi-good- features-cvpr1994.pdf Read Lowe’s paper on SIFT features http://www.unc.edu/courses/2004fall/comp/290/089/papers/Lowe_ijcv03.pdf

2. Don’t forget: Assignment 1 (due by next Tuesday before class) Find a camera Calibration approach 1 Build/use calibration grid (2 orthogonal planes) Perform calibration using (a) DLT and (b) complete gold standard algorithm (assume error only in images, model radial distortion, ok to click points by hand) Calibration approach 2 Build/use planar calibration pattern Use Bouguet’s matlab calibration toolbox (≈Zhang’s approach) http://www.vision.caltech.edu/bouguetj/calib_doc/ (or implement it yourself for extra points) Compare results of approach 1(a),1(b) and 2 Make short report of findings and be ready to discuss in class

3. Single view metrology Allows to relate height of point to height of camera

4. Single view metrology Allows to transfer point from one plane to another

5. Feature tracking Class 5 Read Section 4.1 of course notes http://www.cs.unc.edu/~marc/tutorial/node49.html Read Shi and Tomasi’s paper on good features to track http://www.unc.edu/courses/2004fall/comp/290/089/papers/shi-tomasi-good- features-cvpr1994.pdf Read Lowe’s paper on SIFT features http://www.unc.edu/courses/2004fall/comp/290/089/papers/Lowe_ijcv03.pdf

6. Feature matching vs. tracking Extract features independently and then match by comparing descriptors Extract features in first images and then try to find same feature back in next view What is a good feature? Image-to-image correspondences are key to passive triangulation-based 3D reconstruction

7. Compare intensities pixel-by-pixel Comparing image regions I(x,y) I´(x,y) Sum of Square Differences Dissimilarity measures

8. Compare intensities pixel-by-pixel Comparing image regions I(x,y) I´(x,y) Zero-mean Normalized Cross Correlation Similarity measures

9. Feature points Required properties: Well-defined (i.e. neigboring points should all be different) Stable across views (i.e. same 3D point should be extracted as feature for neighboring viewpoints)

10. Feature point extraction homogeneous edge corner Find points that differ as much as possible from all neighboring points

11. Feature point extraction Approximate SSD for small displacement Δ Image difference, square difference for pixel SSD for window

12. Feature point extraction homogeneous edge corner Find points for which the following is maximum i.e. maximize smallest eigenvalue of M

13. Harris corner detector Only use local maxima, subpixel accuracy through second order surface fitting Select strongest features over whole image and over each tile (e.g. 1000/image, 2/tile) Use small local window: Maximize „cornerness“:

14. Simple matching for each corner in image 1 find the corner in image 2 that is most similar (using SSD or NCC) and vice-versa Only compare geometrically compatible points Keep mutual best matches What transformations does this work for?

15. Feature matching: example 0.96-0.40-0.16-0.390.19 -0.050.75-0.470.510.72 -0.18-0.390.730.15-0.75 -0.270.490.160.790.21 0.080.50-0.450.280.99 1 5 2 4 3 15 2 4 3 What transformations does this work for? What level of transformation do we need?

16. Wide baseline matching Requirement to cope with larger variations between images Translation, rotation, scaling Foreshortening Non-diffuse reflections Illumination geometric transformations photometric changes

17. Wide-baseline matching example (Tuytelaars and Van Gool BMVC 2000)

18. Lowe’s SIFT features Recover features with position, orientation and scale (Lowe, ICCV99)

19. Position Look for strong responses of DOG filter (Difference-Of-Gaussian) Only consider local maxima

20. Scale Look for strong responses of DOG filter (Difference-Of-Gaussian) over scale space Only consider local maxima in both position and scale Fit quadratic around maxima for subpixel

21. Orientation Create histogram of local gradient directions computed at selected scale Assign canonical orientation at peak of smoothed histogram Each key specifies stable 2D coordinates (x, y, scale, orientation)

22. Minimum contrast and “cornerness”

23. SIFT descriptor Thresholded image gradients are sampled over 16x16 array of locations in scale space Create array of orientation histograms 8 orientations x 4x4 histogram array = 128 dimensions

25. Matas et al.’s maximally stable regions Look for extremal regions http://cmp.felk.cvut.cz/~matas/papers/matas-bmvc02.pdf

26. Mikolaczyk and Schmid LoG Features

27. Feature tracking Identify features and track them over video Small difference between frames potential large difference overall Standard approach: KLT (Kanade-Lukas-Tomasi)

28. Good features to track Use same window in feature selection as for tracking itself Compute motion assuming it is small Affine is also possible, but a bit harder (6x6 in stead of 2x2)

29. Example

31. Synthetic example

32. Good features to keep tracking Perform affine alignment between first and last frame Stop tracking features with too large errors

33. Live demo OpenCV (try it out!) LKdemo

34. Next class: triangulation and reconstruction C1C1 m1m1 L1L1 m2m2 L2L2 M C2C2 Triangulation - calibration - correspondences