@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.}
}
@article {14889,
	title = {Robust and efficient detection of salient convex groups},
	journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
	volume = {18},
	year = {1996},
	month = {1996/01//},
	pages = {23 - 37},
	abstract = {This paper describes an algorithm that robustly locates salient convex collections of line segments in an image. The algorithm is guaranteed to find all convex sets of line segments in which the length of the gaps between segments is smaller than some fixed proportion of the total length of the lines. This enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise. We give an expected case analysis of the algorithm performance. This demonstrates that salient convexity is unlikely to occur at random, and hence is a strong clue that grouped line segments reflect underlying structure in the scene. We also show that our algorithm run time is O(n <sup>2</sup>log(n)+nm), when we wish to find the m most salient groups in an image with n line segments. We support this analysis with experiments on real data, and demonstrate the grouping system as part of a complete recognition system},
	keywords = {complexity;computer, complexity;contours;image, computational, convex, detection;feature, detection;object, extraction;object, groups;computational, organisation;proximity;salient, recognition;, recognition;line, recognition;perceptual, segment, vision;edge},
	isbn = {0162-8828},
	doi = {10.1109/34.476008},
	author = {Jacobs, David W.}
}
