854 research outputs found
On the Convergence and Consistency of the Blurring Mean-Shift Process
The mean-shift algorithm is a popular algorithm in computer vision and image
processing. It can also be cast as a minimum gamma-divergence estimation. In
this paper we focus on the "blurring" mean shift algorithm, which is one
version of the mean-shift process that successively blurs the dataset. The
analysis of the blurring mean-shift is relatively more complicated compared to
the nonblurring version, yet the algorithm convergence and the estimation
consistency have not been well studied in the literature. In this paper we
prove both the convergence and the consistency of the blurring mean-shift. We
also perform simulation studies to compare the efficiency of the blurring and
the nonblurring versions of the mean-shift algorithms. Our results show that
the blurring mean-shift has more efficiency.Comment: arXiv admin note: text overlap with arXiv:1201.197
LASS: a simple assignment model with Laplacian smoothing
We consider the problem of learning soft assignments of items to
categories given two sources of information: an item-category similarity
matrix, which encourages items to be assigned to categories they are similar to
(and to not be assigned to categories they are dissimilar to), and an item-item
similarity matrix, which encourages similar items to have similar assignments.
We propose a simple quadratic programming model that captures this intuition.
We give necessary conditions for its solution to be unique, define an
out-of-sample mapping, and derive a simple, effective training algorithm based
on the alternating direction method of multipliers. The model predicts
reasonable assignments from even a few similarity values, and can be seen as a
generalization of semisupervised learning. It is particularly useful when items
naturally belong to multiple categories, as for example when annotating
documents with keywords or pictures with tags, with partially tagged items, or
when the categories have complex interrelations (e.g. hierarchical) that are
unknown.Comment: 20 pages, 4 figures. A shorter version appears in AAAI 201
Higher-order image statistics for unsupervised, information-theoretic, adaptive, image filtering
technical reportThe restoration of images is an important and widely studied problem in computer vision and image processing. Various image filtering strategies have been effective, but invariably make strong assumptions about the properties of the signal and/or degradation. Therefore, these methods typically lack the generality to be easily applied to new applications or diverse image collections. This paper describes a novel unsupervised, informationtheoretic, adaptive filter (UINTA) that improves the predictability of pixel intensities from their neighborhoods by decreasing the joint entropy between them. Thus UINTA automatically discovers the statistical properties of the signal and can thereby restore a wide spectrum of images and applications. This paper describes the formulation required to minimize the joint entropy measure, presents several important practical considerations in estimating image-region statistics, and then presents results on both real and synthetic data
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