@conference {13196,
	title = {Efficient mean-shift tracking via a new similarity measure},
	booktitle = {Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on},
	volume = {1},
	year = {2005},
	month = {2005/06//},
	pages = {176 - 183 vol. 1 - 176 - 183 vol. 1},
	abstract = {The mean shift algorithm has achieved considerable success in object tracking due to its simplicity and robustness. It finds local minima of a similarity measure between the color histograms or kernel density estimates of the model and target image. The most typically used similarity measures are the Bhattacharyya coefficient or the Kullback-Leibler divergence. In practice, these approaches face three difficulties. First, the spatial information of the target is lost when the color histogram is employed, which precludes the application of more elaborate motion models. Second, the classical similarity measures are not very discriminative. Third, the sample-based classical similarity measures require a calculation that is quadratic in the number of samples, making real-time performance difficult. To deal with these difficulties we propose a new, simple-to-compute and more discriminative similarity measure in spatial-feature spaces. The new similarity measure allows the mean shift algorithm to track more general motion models in an integrated way. To reduce the complexity of the computation to linear order we employ the recently proposed improved fast Gauss transform. This leads to a very efficient and robust nonparametric spatial-feature tracking algorithm. The algorithm is tested on several image sequences and shown to achieve robust and reliable frame-rate tracking.},
	keywords = {algorithm;, analysis;, Bhattacharyya, coefficient;, Color, colour, density, divergence;, estimates;, extraction;, fast, feature, frame-rate, Gauss, Gaussian, histograms;, image, Kernel, Kullback-Leibler, matching;, Mean-shift, measures;, nonparametric, processes;, sample-based, sequences;, similarity, spaces;, spatial-feature, tracking, tracking;, transform;},
	doi = {10.1109/CVPR.2005.139},
	author = {Yang,Changjiang and Duraiswami, Ramani and Davis, Larry S.}
}
@article {13235,
	title = {Efficient kernel density estimation using the fast gauss transform with applications to color modeling and tracking},
	journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
	volume = {25},
	year = {2003},
	month = {2003/11//},
	pages = {1499 - 1504},
	abstract = {Many vision algorithms depend on the estimation of a probability density function from observations. Kernel density estimation techniques are quite general and powerful methods for this problem, but have a significant disadvantage in that they are computationally intensive. In this paper, we explore the use of kernel density estimation with the fast Gauss transform (FGT) for problems in vision. The FGT allows the summation of a mixture of ill Gaussians at N evaluation points in O(M+N) time, as opposed to O(MN) time for a naive evaluation and can be used to considerably speed up kernel density estimation. We present applications of the technique to problems from image segmentation and tracking and show that the algorithm allows application of advanced statistical techniques to solve practical vision problems in real-time with today{\textquoteright}s computers.},
	keywords = {algorithms;, Color, Computer, density, estimation;, fast, function;, Gauss, image, Kernel, modeling;, segmentation;, tracking;, transform;, transforms;, VISION, vision;},
	isbn = {0162-8828},
	doi = {10.1109/TPAMI.2003.1240123},
	author = {Elgammal,A. and Duraiswami, Ramani and Davis, Larry S.}
}
@conference {13237,
	title = {Improved fast gauss transform and efficient kernel density estimation},
	booktitle = {Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on},
	year = {2003},
	month = {2003/10//},
	pages = {664 -671 vol.1 - 664 -671 vol.1},
	abstract = {Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this algorithm to practical applications. The fast Gauss transform (FGT) has successfully accelerated the kernel density estimation to linear running time for low-dimensional problems. Unfortunately, the cost of a direct extension of the FGT to higher-dimensional problems grows exponentially with dimension, making it impractical for dimensions above 3. We develop an improved fast Gauss transform to efficiently estimate sums of Gaussians in higher dimensions, where a new multivariate expansion scheme and an adaptive space subdivision technique dramatically improve the performance. The improved FGT has been applied to the mean shift algorithm achieving linear computational complexity. Experimental results demonstrate the efficiency and effectiveness of our algorithm.},
	keywords = {adaptive, algorithm;multivariate, complexity;computer, complexity;Gaussian, computational, density, estimation;mean, expansion, Gauss, processes;computational, recognition;quadratic, scheme;pattern, shift, space, subdivision, technique;computer, theory;, transform;kernel, vision;estimation, vision;fast},
	doi = {10.1109/ICCV.2003.1238383},
	author = {Yang,C. and Duraiswami, Ramani and Gumerov, Nail A. and Davis, Larry S.}
}
