Globally Optimal Shape-based Tracking in Real-time

1. Globally Optimal Shape-based Tracking in Real-time Thomas Schoenemann and Daniel Cremers Department of Computer Science University of Bonn, Germany Reporter: Hsieh Chia-Hao Date: 2009/12/01

2. Outline • Introduction • Contour Matching • Tracking • Real-time Optimization • Experiments

3. Introduction • Globally Optimal Shape-based Tracking in Real-time • Pixel-accurate

4. Contribution • First shape-based method • Real-time • Global optima • Real-time • Object motion (prior knowledge) • Combinatorial algorithm • Not requiring complete search over the initial correspondence

5. Contour Matching Given Find Length of a curve • Minimizing a ratio energy • Contours are parameterized by arc-length • Optimal solution • Data term • Positive edge detector function • Shape consistency measure • Deviation of tangent angles • Induced length distortion Image I ? ? Penalty function of length distortion From: Globally optimal image segmentation with an elastic shape prior

6. Contour Matching • Monotone matching function • m : [0, l(C)] → [0, l(S)] • Expressing which point on C corresponds to which point on S • Compare tangent angles • Cyclic distance between tangent angle αC(s) at s and corresponding tangent angle αS(s) From: Globally optimal image segmentation with an elastic shape prior

7. Contour Matching • Resulting optimization problem • Reduced to finding cycles in a regular graph • Applying a combinatorial algorithm Pixel set P of the image, K collections of each node From: Globally optimal image segmentation with an elastic shape prior

8. Tracking • Given • Video sequence • Position of an object in the first frame • Determine object location at time t • find its silhouette Ct • Optimal silhouette • Data term • Shape consistency measure • Motion function Penalty function of length distortion Motion function

9. Tracking • The optimal contour Ct in image t Each possible solution is mapped to a cycle in a graph. Edge e represents a line segment Numerator weight n(e) Denominator weight d(e) Minimum Ratio Cycle algorithm

10. Tracking • Minimum Ratio Cycle algorithm • Two problems • Valid cycles • Real-time

11. Real-time Optimization • Achieve by these steps • Assume maximal velocity Dmax = 15 per frame • Parallel implementation of Minimum Ratio Cycle algorithm on GPU • Smart initialization • Find globally optimal valid cycle by applying a recursive splitting algorithm

12. Real-time Optimization • Smart initialization • Minimum Ratio Cycle algorithm • Iterated negative cycle detection • The better the initial bound, the less iterations are needed • So, provide a tight upper bound by shifting contour up to 5 pixels in each direction • Negative cycles • Cycle detection • Moore-Bellman-Ford algorithm (distance calculation)

13. Real-time Optimization • Parallel Implementation Directed acyclic graph From: Globally optimal image segmentation with an elastic shape prior

14. Real-time Optimization • Excluding Incorrect Solutions • If the globally optimal cycle is a multiply aligned one, all nodes in the cycle that belong to frame 0 are collected • In the end, the globally optimal single alignment is found • Worst case is quadratic in the number of pixels, linear run-times in practice

15. Experiments • Challenges of tracking objects in real-world • Camera shutter time • Difficult weather conditions • Real-time • 25 fps • Set K=2, λ = ν = 0.5, Dmax=15 • CUDA framework, Geforce 8800 GTX

16. Experiments • Rainy weather Proposed method

17. Experiments • Sunlight • Shadow

18. Experiments • Comparison to the State-of-the-art • Level Set approaches

19. Experiments • Significant scale change • Deforming silhouettes • Shadows

20. Conclusion • First shape-based real-time tracking algorithm • Guarantees globally optimal solutions • Finding shape template in an image • Reduced to finding cycles in a product graph • Parallelizable • Profits from smart initialization • Reliable tracking results under harsh weather and illumination conditions