Improved fast gauss transform and efficient kernel density estimation

Yang, Kan; Duraiswami, Ramani; Gumerov,; Davis, W. Rhett

doi:10.1109/iccv.2003.1238383

Cited by 350 publications

(287 citation statements)

References 23 publications

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“…We can speed up inference by considering approximate log-likelihoods. There exist many fast methods for the evaluation of kernel density estimates, but the popular approaches are either not suited for high-dimensional data [7], do not lead to a speed-up for sequential data [26] or are hard to implement due to their complexity [9]. Here, we want to propose a simple alternative to these complex methods that will be sufficient for our purpose.…”

Section: Real-time Scoringmentioning

confidence: 99%

A Non-parametric Bayesian Network Prior of Human Pose

Lehrmann

Gehler

Nowozin

2013

2013 IEEE International Conference on Computer Vision

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Having a sensible prior of human pose is a vital ingredient for many computer vision applications, including tracking and pose estimation. While the application of global non-parametric approaches and parametric models has led to some success, finding the right balance in terms of flexibility and tractability, as well as estimating model parameters from data has turned out to be challenging. In this work, we introduce a sparse Bayesian network model of human pose that is non-parametric with respect to the estimation of both its graph structure and its local distributions. We describe an efficient sampling scheme for our model and show its tractability for the computation of exact log-likelihoods. We empirically validate our approach on the Human 3.6M dataset and demonstrate superior performance to global models and parametric networks. We further illustrate our model's ability to represent and compose poses not present in the training set (compositionality) and describe a speed-accuracy trade-off that allows realtime scoring of poses.

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Section: Real-time Scoringmentioning

confidence: 99%

A Non-parametric Bayesian Network Prior of Human Pose

Lehrmann

Gehler

Nowozin

2013

2013 IEEE International Conference on Computer Vision

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“…For image segmentation, a comparative test shows that Ada-MS is at least twice as faster as IFGT [20], which to our knowledge is one of the fastest image segmentation method based on mean shift. We then point out that, although derived from the kernel density mode-seeking problem, Ada-MS is also applicable to some other kernel based optimization problems.…”

Section: Introductionmentioning

confidence: 99%

“…Among different kernels, the special case of profile based kernels are mostly studied [5,8]. Mean shift algorithm is widely used in computer vision applications, including tracking [7] and image segmentation [20] Despite the popularity of mean shift, few attempts have been made since Cheng [4] to understand the procedure theoretically. Cheng [4] shows that mean shift is fundamentally a gradient ascent algorithm with an adaptive step size.…”

Section: Introductionmentioning

confidence: 99%

Half Quadratic Analysis for Mean Shift: with Extension to A Sequential Data Mode-Seeking Method

Yuan

2007

2007 IEEE 11th International Conference on Computer Vision

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“…The improved fast Gauss transform [74] deals with this issue by a new efficient estimate of the sum of Gaussians in higher dimensions. In this method n sample points are divided into k clusters, where the maximum distance of a point to a cluster center is minimized.…”

Section: Related Workmentioning

confidence: 99%

“…In the KDE literature, methods that tackle overall computational complexity primarily approach from the perspective of reducing pairwise kernel evaluations; examples include Nystrom approximation [72], Fast Gauss Transform [73,74] and sparse dictionary learning methods [75].…”

Section: Introductionmentioning

confidence: 99%

Manifold learning and unwrapping using density ridges

Shaker¹

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xii 3.6 Unwrapped mnist-0 digits with a selection of images of the actual digits on top. Orientation and thickness of digits smoothly vary across horizontal and vertical directions, respectively. . 34 3.7 Unfolding mnist-0 digits using two benchmark manifold learning methods. Unlike the proposed method, no smooth variation of structure is preserved using these methods. . . . . 35 3.8 Unfolding mnist-2 digits using the proposed method and t-SNE. Similar to Figure 3.7(b) for mnist-0, no smooth variation of structure is preserved using t-SNE, while proposed method shows smooth change of thickness and shape in horizontal and vertical coordinates, respectively. 36 3.9 Unfolding mnist-9 digits using the proposed method, which shows smooth change of thickness Sylvain Bouix, who were also my mentors, for all of their guidance through this process; your discussion, ideas, and feedback have been absolutely invaluable.

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Improved fast gauss transform and efficient kernel density estimation

Abstract: Abstract

Cited by 350 publications

References 23 publications

A Non-parametric Bayesian Network Prior of Human Pose

A Non-parametric Bayesian Network Prior of Human Pose

Half Quadratic Analysis for Mean Shift: with Extension to A Sequential Data Mode-Seeking Method

Manifold learning and unwrapping using density ridges

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