Corner Detection & Tracking 2000. 8. 4 Kim, Sung-Ho

1. Corner Detection & Tracking2000. 8. 4 Kim, Sung-Ho Robotics & Computer Vision Lab. KAIST Robotics & computer Vision

2. Referred Papers • [Zheng, et al., 1999] Z. Zheng, H. Wang and E. Khwang Teoh. Analysis of Gray Level Corner detection. Pattern Recognition Letters, 20:149-162,1999. • [Tomasi, et al.,1991] C. Tomasi and T. Kanade. Detection and Tracking of Point Features. Carnegie Mellon University, 1991. Robotics & computer Vision

3. Paper1:Analysis of Gray Level Corner Detection Robotics & computer Vision

4. Contents • Introduction • Categories of Corner Detection • New Corner Detector • Experimental Results • Conclusions Robotics & computer Vision

5. Introduction • Gray level corner • The point of maximal planar curvature in the line of the steepest gray-level slope • Corner detection • To detect and localize the prominent point or can include the determination of inherent attributes Robotics & computer Vision

6. Performance of Robustness • Detection • Ability to detect subtle corners • Localization • Ability to detect true locations • Stability • The position should not move in the multiple images acquired of the same scene • Complexity • Ability to reduce algorithm complexity for automation and faster implementation Robotics & computer Vision

7. Categories of Corner Detection Robotics & computer Vision

8. Template based Corner Detection • Determining the similarity, or correlation between a given template and all sub- windows in a given image • Implementation • Generating 8 masks by rotating the masks in steps of • Computing appropriate correlation measure • Selecting the maximum value • Cannot cover all directions error inevitable Robotics & computer Vision

9. Geometry based Corner Detection • Relies on measuring the differential geometry features of corner points • 3 ways • Edge-related corner detection • Topology corner detection • Auto-correlation corner detection Robotics & computer Vision

10. Edge-related Corner Detection • Corner point • The junction of two or more edge lines • Approach • Edge detection->edge grouping->digital curve representation • Ex. Using chain code(1996) • The use of the differential geometry operators • Kitchen and Rosenfeld corner detector • Wang and Brady corner detector Robotics & computer Vision

11. Kitchen & Rosenfeld Corner Detector(1982) • Cornerness measure • Properties • Sensitive to noise effect • Instable • Operation: (Note):M by M-size of image N by N-size of gradient operator Robotics & computer Vision

12. Wang & Brady Corner Detector(1995) • Based on the measurement of surface curvature • Cornerness measure s:const. measure of surface curvature • Properties • Simple cornerness measure->used in real time corner detector • Operation: Robotics & computer Vision

13. Topology Corner Detection • Corner point • The interior geometric feature point in the image surface • Beaudet(1978) • Cornerness measure: • Sensitive to noise • Operation: • Deriche(1993) • Using the property of the corner: Laplacian is zero at the corner • Very complicated-time consuming Robotics & computer Vision

14. Auto-correlation Corner Detection • Basic concept • Considering average intensity change of small window • corner is obtained when minimum change value is larger than threshold Robotics & computer Vision

15. Harris or Plessy Corner Detector • Harris performed analytic expansion • Cornerness measure ,W:Gaussian function for smoothing, K: constanct var. • Properties • Best behaved w.r.t.detection • Poor localization performance • Operation: (n by n): Gaussian window Robotics & computer Vision

16. The new Corner Detector-Gradient Direction • Derived from Plessey cornerness measure • Cornerness measure K(x,y):convolution of Gaussian op. with cornerness measure • Properties • Slightly inferior to that of the Plessey detector • The performance of localization is better • Operation: simpler than Plessey Robotics & computer Vision

17. Experiments • About noise effect(ave. #of corners) • The gradient-direction detector has fair detection performance, stable • About localization • The gradient-direction detector has better localization performance than Plessey Robotics & computer Vision

18. The Results of Corner Operator to Synthetic Image Robotics & computer Vision

19. The Results of Corner Operator to Synthetic Image • The gradient-direction detector have well detected and positioned all the features Robotics & computer Vision

20. Conclusions • Summary of corner detectors • Kitchen • The performance is not desirable • Beaudet • More sensitive to noise than others • Plessey • The best performance for detection but poor localization • Gradient direction • Comparable to Plessey but better localization Robotics & computer Vision

21. Paper2:Detection and Tracking of Point Features Robotics & computer Vision

22. Contents • Introduction • Feature tracking • Feature selection • Experiments • Conclusions Robotics & computer Vision

23. Introduction • Defining a good feature • Previous paper • Based on an a priori notion of what constitutes an “interesting” window • Feature selection is indep. With tracking. Ex. based on first and second derivatives of the image intensity function • This paper • Feature to be good if it can be tracked well. • Selection criteria are closely related to tracking. Robotics & computer Vision

24. Feature Tracking(1/5) • Notation • I(x,y,t)-image sequence(x,y;space var. t;discrete time) • - displacement at (x,y) • Local image model Robotics & computer Vision

25. Feature Tracking(2/5) • Find d to minimize the residue error • W; a given window • w; weighting function, ex) Gaussian • If d is smaller than the window size then the linearization possible!! Robotics & computer Vision

26. Feature Tracking(3/5) • Solution • Linearization(using Tayor series) • The residue • Differentiating w.r.t. d and setting 0 ; vector eq. Robotics & computer Vision

27. Feature Tracking(4/5) • d assumed constant in W, and since • In simpler form • -> d is the solution Robotics & computer Vision

28. Feature Tracking(5/5) • About G • Can be computed from one frame • If w is 1 , where • About e • Can be computed from the difference between two frames Robotics & computer Vision

29. Feature Selection(1/2) • If two eigen values of G are we accept a window if ; threshold • About eigen values of G • Two small: constant intensity profile • A large & a small: unidirectional pattern • Two large:represent corner Robotics & computer Vision

30. Feature Selection(2/2) • About window size & occlusion • Smaller windows • more sensitive to noise • Less likely to be affected by distortions due to changes of viewpoint • It minimize the occlusion problem. Robotics & computer Vision

31. Experiment(1/2)(using realized feature extractor) • In synthesized image • Same process speed(0.22sec,0.22sec) • KLT detects more subtle corner points Robotics & computer Vision

32. Experiment(2/2) • In real world imge • KLT is more faster(KLT:0.17sec, Harris:0.34sec) • In general, KLT is faster than Harris in complicated image. Robotics & computer Vision

33. Conclusion • A good feature selection criterion proposed in this paper subsumes previous feature selection criteria. • KLT detects corners fairly well and fast. • Work to be done • Test corner tracking using proposed this paper Robotics & computer Vision