Visual Tracking using Kernel Projected Measurement and Log-Polar Transformation


K.N. Toosi University of Technology


Visual Servoing is generally contained of control and feature tracking. Study of previous methods shows that no attempt has been made to optimize these two parts together. In kernel based visual servoing method, the main objective is to combine and optimize these two parts together and to make an entire control loop. This main target is accomplished by using Lyapanov theory. A Lyapanov candidate function is formed based on kernel definition such that the Lyapanov stability can be verified. The implementation is done in four degrees of freedom and Fourier transform is used for decomposition of the rotation and scale directions from 2D translation. In the present study, a new method in scale and rotation correction is presented. Log-Polar Transform is used instead of Fourier transform for these two degrees of freedom. Tracking in four degrees of freedom is synthesized to show the visual tracking of an unmarked object. Comparison between Log-Polar transform and Fourier transform shows the advantages of the presented method. KBVS based on Log-Polar transform proposed in this paper, because of its robustness, speed and featureless properties.


A. Castano and S. Hutchinson, Visual compliance: Task directed visual servo control, IEEE Transactions on Robotics and Automation, 10 (1994) 334-342.

S. Hutchinson, G.D. Hager, P.I. Corke, A tutorial on visual servo control, 12 (1996) 651 -670.

W.J. Wilson, C.C. Williams Hulls, G.S. Bell, Relative end-effector control using cartesian position based visual servoing, IEEE Transactions on Robotics and Automation, 12 (1996) 684-696.

F. Chaumette and E. Malis, 2 1/2 D visual servoing: a possible solution to improve image-based and positionbased visual servoings, IEEE International Conference on Robotics and Automation, 1 (2000) 630-635.

F. Chaumette and S. Hutchinson, Visual servo control, part II: Advanced approaches, IEEE Robotics and Automation Magazine, 14 (2007) 109-118.

D. Kragic and H.I. Christensen, Technical report, Computational Vision and Active Perception Laboratory, (2002).

D. Comaniciu, V. Ramesh,. Meerc, IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(5) (2003) 564-575.

M. Dewan and G. Hager, Towards optimal kernel-based tracking, Computer Vision and Pattern Recognition, 1 (2006) 618-625.

Z. Fan, Y. Wu, M. Yang, Multiple collaborative kernel tracking. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition , 2005.

G.D. Hager, M. Dewan, C.V. Stewart, Multiple kernel tracking with ssd, In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1 (2004) 790-797.

J. Swensen, V. Kallem, N. Cowan, Empirical Characterization of Convergence Properties for Kernelbased Visual Servoing, Visual Servoing via Advanced Numerical Methods, Springer–Verlag, (2010) 23-38.

V. Kallem, J.P. Swensen, M. Dewan, G.D. Hager, N.J. Cowan, Kernel-Based Visual Servoing: Featureless Control using Spatial Sampling Functions.

V. Kallem, M. Dewan, J.P. Swensen, G.D Hager, N.J. Cowan, Kernel-based visual servoing, In IEEE/RSJ International . Conference. on Intelligent Robots and System, (2007) 1975-1980.

H. Araujo and J.M. Dias, "An introduction to the logpolar mapping", Second Workshop on Cybernetic Vision, pp. 139 - 144, 2002.

R. Matungka, "Studies on Log-Polar Transform for Image Registration and Improvements Using Adaptive Sampling and Logarithmic Spiral", 2009.

K. Palander and S.S. Brandt, "Epipolar geometry and log-polar transform in wide baseline stereo matching", International Conference on Pattern Recognition, pp. 1 -4, 2008.

R. Matungka, Y.F. Zheng and R.L.Ewing, "Image registration using adaptive polar transform", IEEE Transactions on Image Processing, 18, pp. 2340-2354, 2009.

R. Montoliu, V.J. Traver and F. Pla,"Log-polar mapping in generalized least-squares motion estimation", Proccedings of 2002 IASTED International Conference on Visualization, Imaging, and Image Processing (VIIP’2002), pp. 656-661, 2002.

H. Taghirad, M. Shahbazi, F. Atashzar and S. Rayatdoost, "Singular Free Motion Planning in Visual Servoing of Redundant Manipulators", Submitted to IET Computer Vision.