Mean Shift Tracking Orhan Bulan Wencheng Wu Edgar

Mean Shift Tracking Orhan Bulan, Wencheng Wu, Edgar Bernal Slide Credit: Yaron Ukrainitz and Bernard Sarel from the Weizmann Institute http: //www. wisdom. weizmann. ac. il/~vision/courses/2004_2/files/mean_shift. ppt

Mean Shift Theory - Summary[6] No need to estimate the PDF Estimate the gradient ONLY Using the profile form of the Kernel: We get : Note that g(x) = k’(x) is • uniform when k is Epanechnikov • normal when k is normal Size of window Sample mean shift vector

Agenda • General Mean Shift Theory • Mean Shift Object Tracking

Mean Shift Tracking

Non-Rigid Object Tracking … …

Mean-Shift Object Tracking General Framework: Target Representation Choose a reference model in the current frame … Current frame Choose a feature space … Represent the model in the chosen feature space

Mean-Shift Object Tracking General Framework: Target Localization Start from the position of the model in the current frame Search in the model’s neighborhood in next frame Find best candidate by maximizing a similarity func. Repeat the same process with the next pair of frames … Model Candidate Current frame …

Mean-Shift Object Tracking[7] Target Representation Choose a reference target model Choose a feature space Quantized Color Space Represent the model by its histogram in the feature space

Mean-Shift Object Tracking PDF Representation Target Model (centered at 0) Similarity Function: Target Candidate (centered at y)

Mean-Shift Object Tracking Finding the PDF of the target model candidate model Target pixel locations 0 y A differentiable, isotropic, convex, monotonically decreasing profile • Periphery pixels are affected by occlusion and background interference The color bin index (1. . m) of pixel x Probability of feature u in model Normalization factor Factor Pixel weight Pixel Weight Probability of feature u in candidate Normalization factor Factor Pixel weight Weight Pixel

Mean-Shift Object Tracking Similarity Function Target model: Target candidate: Similarity function: The Bhattacharyya Coefficient 1 1

Mean-Shift Object Tracking Target Localization Algorithm Start from the position of the model in the current frame Search in the model’s neighborhood in next frame Find best candidate by maximizing a similarity func.

Mean-Shift Object Tracking Approximating the Similarity Function Model location: Candidate location: Linear approx. (around y 0) Independent of y h Density estimate! (as a function of y)

Mean-Shift Object Tracking Maximizing the Similarity Function The mode of h = sought maximum Important Assumption: The target representation provides sufficient discrimination One mode in the searched neighborhood

Mean-Shift Object Tracking Applying Mean-Shift The mode of h = sought maximum Original Find mode of Mean-Shift: using h Extended Find mode of Mean-Shift: h using h

Mean-Shift Object Tracking About Kernels and Profiles A special class of radially symmetric kernels: The profile of kernel K h Extended Find mode of Mean-Shift: h h using h

Mean-Shift Object Tracking Choosing the Kernel A special class of radially symmetric kernels: Epanechnikov Profile Uniform Profile h h

Mean-Shift Object Tracking Results Partial occlusion Distraction Motion blur

Questions?

References • Mean Shift 1. 2. 3. 4. 5. “The estimation of the gradient of a density function, with applications in pattern recognition, ” K. Fukunaga and L. Hostetler, IEEE Trans. on Info. Theory, Vol. 21, 1975. “Mean shift, mode seeking and clustering, ” IEEE Trans. on Pattern Analysis and Machine Intelligence, ” Y. Cheng, Vol. 17(8), 1995. “Mean shift analysis and applications, ” D. Comaniciu and P. Meer, Proc. of the 7 th IEEE Int. Conf. on Computer Vision, 1999. “Mean shift: a robust approach toward feature space analysis, ” D. Comaniciu and P. Meer, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 24(5), 2002. “Distribution-free decomposition of multivariate data, ” D. Comaniciu and P. Meer, Pattern Analysis and Applications, 1999. • Mean Shift Tracking 6. 7. 8. “Real-time tracking of non-rigid objects using mean shift, ” D. Comaniciu, V. Ramesh and P. Meer, CVPR 2000. “Kernel-based object tracking, ” D. Comaniciu, V. Ramesh and P. Meer, IEEE Trans. on Pattern Analysis and Recognition, Vol. 25(5), 2003. “Robust mean shift tracking with corrected background-weighted histogram, ” J. Ning, L. Zhang, D. Zhang and C. Wu, Computer Vision IET, Vol. 6(1) • Density Estimation 9. D. W. Scott, Multivariate Density Estimation, New York, Wiley, 1992. 10. “Introduction to kernel smoothing, ” http: //compdiag. molgen. mpg. de/docs/talk_05_01_04_stefanie. pdf