CVPR - Dec. 2001 Scene-Consistent Detection ofFeature Points in Video Sequences Ariel Tankus & Yehezkel Yeshurun Tel-Aviv University
Outline: • Relating convexity-based detection of feature points to scene geometry. • Feature points tracking algorithm. • Comparison with two other methods. • Measures for evaluation of tracking algorithms w.r.t 3D scene-consistency.
Task Definition: Robust detection of scene-consistent features in video sequences. Goals: • Object recognition. • Correspondence points for recovering 3D characteristics of the scene. Intrinsic Property: Convexity.
Operator for Feature Detection (motivation) Detect convex or concave image domains. Detect local “circles” where the gradient of the intensity function points outward along the whole circle. Equivalently: The gradient points in all orientations along the “circles”.
Gradient Argument Yarg derive Operator for Extracting Certain Gradient Orientations At the discontinuity ray of the arctan: Yarg. Darg - An isotropic variant of Yarg.
If at , then has a jump discontinuity there. Response of Yarg to theIntensity Surface • Examine Yarg in well behaving image domains. • Intensity is twice continuously differentiable. The basic observation: • We examine all possible intensity configurations. • Four of them lead to infinite Yarg response.
Response of Yarg to theIntensity Surface (cont.) The cases include: Some configurations where is a local extrema of , and some configurations where one side of is flat, but the other is convex or concave. Only specific differential geometry structures of the intensity function causes Yarg.
For certain intensity function configurations, if has a jump discontinuity, then z(x,y) is: elliptic, hyperbolic or parabolic there. Response to Local 3D Scene Structure • Yarg for certain elliptic, hyperbolic or parabolic points on a Lambertian 3D surface illuminated by a point light source at infinity. • Yarg responds to certain geometric features of the 3D scene object.
Tracking Algorithm • Stable points: points where . • These points are the only input to the point tracker.
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Evaluating the Performance of the Algorithm • Two measures for evaluating performance of scene-consistent point tracking algorithms. • Each measure aimed at a different task: • Maximal tracking time. • Correspondence of points in successive frames. • Their common goal: to quantify the consistency of tracks with 3D scene.
Time(correct 3D point is tracked) Completeness of track T = Time(correct 3D point appears in video) Measures for Evaluation of Scene-Consistency • Completeness: • A track is complete if the same 3D scene point is being tracked, up to a certain level of noise, in every frame where it appears. Correct 3D point of track T = 3D point tracked for the longest time under track T
Stability of tracking in frames fi, fi+1 = #tracks following the correct 3D point in both fi, fi+1 #tracks containing points in both fi, fi+1 Measures for Evaluation of Scene-Consistency (cont.) • Stability:
Tracking Comparison • We compare the Darg-based algorithm with two other algorithms: • Junction detection (Lindeberg).with automatic scale selection.Tracking by Kalman filter. • KLT (Kanade-Lucas-Tomasi). Tracker based on affine image change model. Features maximize tracking quality.
Experimental Results • Darg is more stable the Junction detection, and sometimes more than KLT. Sometimes Darg equates with KLT. • Dargcompleteness is at least comparable to that of Junction detection or KLT, and sometimes even better. • Darg has significantly lower no-trackingtime (Darg: 4, KLT: 81, J.D.: 121 frames).
Summary • Convexity-based method for scene-consistent feature points detection in video sequences. • Detection relates to specific features of the intensity surface. • These intensity features relate to geometric features of the 3D object.
Summary (cont.) • A stable point tracking algorithm is described (2D Kalman filter). • Two measures serve in a comparison with two other tracking methods. • Completeness: Maximizes tracking time of a 3D scene point. • Stability: Consistent tracking of 3D points between successive frames.