Motivations and Generalizations. Ali Torkamani

Transcription

1 Distribution Tracking B Active Contours, Motivations and Generalizations Ali Torkamani

2 Outline Motivation Calculus of Variations Statistical Distance Earl works on Snakes and Active Contour Models Active Contour For Distribution Tracking Generalizations of Active Contour Models References

3 Outline Motivation Calculus of Variations Statistical Distance Earl works on Snakes and Active Contour Models Active Contour For Distribution Tracking Generalizations of Active Contour Models References

4 Motivation Back to boundar detection This time using perceptual grouping. Non-parametric W We re not looking for a contour of a specific shape. Just a good contour.

5 Sometimes edge detectors find the boundar prett well. And Sometimes edge detectors are not that good.

6 Cann: Threshold=0.7 Cann: Threshold=0.3 Cann: Threshold=0.1 Cann: Threshold=0.05 Sobel

7 Cann: Threshold=0.7 Cann: Threshold=0.3 Cann: Threshold=0.1 Cann: Threshold=0.05 Sobel

8 Improving Boundar Detection Integrate information over distance. Use Gestalt cues Smoothness Closure Humans integrate contour information

9 Problem: Finding The Right Path

10 Calculus of variations Motivation Calculus of Variations Statistical Distance Earl works on Snakes and Active Contour Models Active Contour For Distribution Tracking Generalizations of Active Contour Models References

11 Calculus of Variations Functional Analsis Finding the function = that Maimizes : t 2 f,, d t 1

12 Calculus of Variations Calculus of Variations Functional Analsis F d h f h M Finding the function = that Maimizes : d f t 2 d f t 1,, can be an an function of, and, e.g.:,, f,, 4 2 f + + = but is an eplicit function of, like,, f + = sin

13 Eample Eample What s the function of the shortest path between two point s l? plane? Answer: a straight line! find such that Minimizes the arc length: 2 * 1 arg min 2 d t + = 2 1,, 1 f f t + = =

14 Euler Lagrange Equation Euler-Lagrange Equation,, ] [ 2 = d f I t,, ] [ 1 f d f d f I t = 0 f d d f

15 Straight Line Straight Line d t + = 1 arg min 2 * 2 f d f f f t + = = 0 1,, g 2 1 f d = = 0 0 d f d f = = = + = b a d d + = = = + + = + =

16 Calculus of variations Finding the optimal functional: B Green s Theorem:

17 Calculus of variations Euler-Lagrange

18 Statistical ti ti Distance Motivation Calculus of Variations Statistical Distance Earl works on Snakes and Active Contour Models Active Contour For Distribution Tracking Generalizations of Active Contour Models References

19 Statistical Measures Kullback-Leibler Measure Bhattachara Coefficient

20 Earl works on Snakes and active contours Motivation Calculus of Variations Statistical Distance Earl works on Snakes and Active Contour Models Active Contour For Distribution Tracking Generalizations of Active Contour Models References

21 Snakes A ver fleible non-parametric contour model Desired Curve=Optimal Path, n points: p1,,pn,p Cost Function Smoothness, Discrete Curvature: if ou go from pj-1 to pj to pj+1 how much does direction change? Change of direction of gradient from pj to pj+1 n E p,..., p = d pi, pi+ 1*[ αg p j + βf pi, pi 1] n 1 + i=1 dpj,pj+1 is distance between consecutive path points 1 or sqrt2. gpj j measures strength th of gradient f measures smoothness, curvature Finall α and β are parameters [1]

22 Snakes n E p,..., p = d pi, pi+ 1*[ αg p j + βf pi, pi 1] n 1 + i= 1 1 Ii g pi = l = 0 < ρ < 1 2 i l i + ρ ma I i i Dnamic Programming for Detecting, Tracking, and Matching Deformable Contours, b Geiger, Gupta, Costa, and Vlontzos, IEEE Trans. PAMI , 1995.

23 Snakes: More General Approach Posistion of the snake: v s = s, s Energ Functional:

24 Snakes: Cont d Internal Energ: First and Second Order Derivatives: Tangent and Curvature αs and βs: Weights Controlling Importance, Continuit Image Energ:

25 Snakes: Image Energ Line Functional: Image Intensit itself Dependence on w_line Attracted to lighter or darker border Edge Energ Or Marr-Hildreth Edge Detector Based Edge Energ:

26 Snakes: Termination Functional In Order to find Termination of line segments and Corners Smoothing Image b a Gaussian Filter: Computing The Gradient Angle: Curvature in Contours of Smoothed Image:

27 Ati Active Contour For Distribution Ditibti Tracking kig Motivation Calculus of Variations Statistical Distance Earl works on Snakes and Active Contour Models Active Contour For Distribution Tracking Generalizations of Active Contour Models References

28 Ati Active Contour, Ditibti Distribution Tracking kig Photometric Variables Color Teture Intensit Cumulative Densit Funstion inside a region: F z ω = θ ω z Z d θ is the heaviside function, z is the photometric variable, Z is the video frame. ω d

29 Probabilit Densit Function PDF qz: The distribution of interest KL Distance Bhattachara h Measure

30 KL Flow The goal is to minimize Gradient Descent: B substituting:

31 KL Flow: Cont d Finall: Similarl For Bhattachara:

32 Some Results Tracking b KL Flow:

33 Comparison Geodesic Active Region Kimmel

34 Generalizations of Active Contour Models Motivation Earl works on Snakes and Active Contour Models Calculus of Variations Statistical Distance Active Contour For Distribution Tracking Generalizations of Active Contour Models References

35 Other Generalizations Background Mismatch Freedman Geometric Active ContoursYezzi Active Contour with Occlusion Handling Yilmaz Ver Logicall simple occlusion models Highl discriminate color distribution Black and white No dense Scenario Tracking With Shape Priors Freedman Adaptive Miture models and Active Contour Allili

36 M Current Research High ratio of noise Artificiall Simulated uniform noise Real world: Rain das, Camera jitters No recognizable edges Faded Images Slightl Deformed geometric structure Good News: Stable Color Distribution!!!! Highl Dense Surveillance Scenario Too much occlusion Problem of Shadows

37 M Current Research No Shape Prior Man variations in 3-D geometrical shapes of objects No Goal Distribution prior We have no or few knowledge ld about the distribution ib i of objects that we want to track Man similar objects Man objects have the same Distribution and geometr

38 References Michael Kass, Andrew Witkin, DemetriTerzopoulos "Snakes: Active contour models" 1988, INTERNATIONAL JOURNAL OF COMPUTER VISION Vicent Caselles, Ron Kimmel, Guillermo Sapiro "Geodesic Active Contours International Journal of Computer Vision Dnamic Programming for Detecting, Tracking, and Matching Deformable Contours, b Geiger, Gupta, Costa, and Vlontzos, IEEE Trans. PAMI , Song Chun Zhu, Alan Yuille,"Region i Competition: Unifing i Snakes, Region Growing, and Baes/MDL for Multi-band Image Segmentation" 1996 IEEE Transactions on Pattern Analsis and Machine Intelligence Daniel Freedman," Active Contours for Tracking Distributions" 2004 IEEE Trans. Image Processing AlperYilmaz, Xin Li, Mubarak Shah, "Contour-Based Object Tracking with Occlusion Handling in Video Acquired Using Mobile Cameras" IEEE Transactions on Pattern Analsis and Machine Intelligence archive Volume 26, Issue 11 November 2004 table of contents 2004 Tao Zhang, Daniel Freedman, "Improving Performance of Distribution Tracking through Background Mismatch", IEEE Transactions on Pattern Analsis and Machine Intelligence archive Volume 27, Issue 2 Februar 2005 Mohand Saïd Allili, Djemel Ziou "Object tracking in videos using adaptive miture models and active contours" Neurocomputing archive Volume 71, Issue June 2008

39 Thank ou! Question?