@conference {13122,
	title = {Kernel integral images: A framework for fast non-uniform filtering},
	booktitle = {Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on},
	year = {2008},
	month = {2008/06//},
	pages = {1 - 8},
	abstract = {Integral images are commonly used in computer vision and computer graphics applications. Evaluation of box filters via integral images can be performed in constant time, regardless of the filter size. Although Heckbert (1986) extended the integral image approach for more complex filters, its usage has been very limited, in practice. In this paper, we present an extension to integral images that allows for application of a wide class of non-uniform filters. Our approach is superior to Heckbertpsilas in terms of precision requirements and suitability for parallelization. We explain the theoretical basis of the approach and instantiate two concrete examples: filtering with bilinear interpolation, and filtering with approximated Gaussian weighting. Our experiments show the significant speedups we achieve, and the higher accuracy of our approach compared to Heckbertpsilas.},
	keywords = {approximated, equations;interpolation;, filtering;bilinear, filtering;kernel, Gaussian, graphics;computer, images;approximation, integral, interpolation;computer, nonuniform, processing;integral, theory;filtering, theory;image, vision;fast, weighting},
	doi = {10.1109/CVPR.2008.4587641},
	author = {Hussein,M. and Porikli, F. 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.}
}
