Improved fast gauss transform and efficient kernel density estimation
Yang, C.
Duraiswami, R.
Gumerov, N.A.
Davis, L.
Perceptual Interfaces & Reality Lab., Maryland Univ., College Park, MD, USA;
This paper appears in: Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on
Publication Date: 13-16 Oct. 2003
On page(s): 664-671 vol.1
Location: Nice, France,
ISBN: 0-7695-1950-4
INSPEC Accession Number: 8301649
Digital Object Identifier: 10.1109/ICCV.2003.1238383
Current Version Published: 2008-04-03
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.
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