345,524 research outputs found
Systematic approach to nonlinear filtering associated with aggregation operators. Part 2. Frechet MIMO-filters
Median filtering has been widely used in scalar-valued image processing as an edge preserving operation. The basic idea is that the pixel value is replaced by the median of the pixels contained in a window around it. In this work, this idea is extended onto vector-valued images. It is based on the fact that the median is also the value that minimizes the sum of distances between all grey-level pixels in the window. The Frechet median of a discrete set of vector-valued pixels in a metric space with a metric is the point minimizing the sum of metric distances to the all sample pixels. In this paper, we extend the notion of the Frechet median to the general Frechet median, which minimizes the Frechet cost function (FCF) in the form of aggregation function of metric distances, instead of the ordinary sum. Moreover, we propose use an aggregation distance instead of classical metric distance. We use generalized Frechet median for constructing new nonlinear Frechet MIMO-filters for multispectral image processing. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No 17-07-00886, No 17-29-03369 and by Ural State Forest University Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"
Average Distance Queries through Weighted Samples in Graphs and Metric Spaces: High Scalability with Tight Statistical Guarantees
The average distance from a node to all other nodes in a graph, or from a
query point in a metric space to a set of points, is a fundamental quantity in
data analysis. The inverse of the average distance, known as the (classic)
closeness centrality of a node, is a popular importance measure in the study of
social networks. We develop novel structural insights on the sparsifiability of
the distance relation via weighted sampling. Based on that, we present highly
practical algorithms with strong statistical guarantees for fundamental
problems. We show that the average distance (and hence the centrality) for all
nodes in a graph can be estimated using single-source
distance computations. For a set of points in a metric space, we show
that after preprocessing which uses distance computations we can compute
a weighted sample of size such that the average
distance from any query point to can be estimated from the distances
from to . Finally, we show that for a set of points in a metric
space, we can estimate the average pairwise distance using
distance computations. The estimate is based on a weighted sample of
pairs of points, which is computed using distance
computations. Our estimates are unbiased with normalized mean square error
(NRMSE) of at most . Increasing the sample size by a
factor ensures that the probability that the relative error exceeds
is polynomially small.Comment: 21 pages, will appear in the Proceedings of RANDOM 201
- …