77,626 research outputs found
Time-causal and time-recursive spatio-temporal receptive fields
We present an improved model and theory for time-causal and time-recursive
spatio-temporal receptive fields, based on a combination of Gaussian receptive
fields over the spatial domain and first-order integrators or equivalently
truncated exponential filters coupled in cascade over the temporal domain.
Compared to previous spatio-temporal scale-space formulations in terms of
non-enhancement of local extrema or scale invariance, these receptive fields
are based on different scale-space axiomatics over time by ensuring
non-creation of new local extrema or zero-crossings with increasing temporal
scale. Specifically, extensions are presented about (i) parameterizing the
intermediate temporal scale levels, (ii) analysing the resulting temporal
dynamics, (iii) transferring the theory to a discrete implementation, (iv)
computing scale-normalized spatio-temporal derivative expressions for
spatio-temporal feature detection and (v) computational modelling of receptive
fields in the lateral geniculate nucleus (LGN) and the primary visual cortex
(V1) in biological vision.
We show that by distributing the intermediate temporal scale levels according
to a logarithmic distribution, we obtain much faster temporal response
properties (shorter temporal delays) compared to a uniform distribution.
Specifically, these kernels converge very rapidly to a limit kernel possessing
true self-similar scale-invariant properties over temporal scales, thereby
allowing for true scale invariance over variations in the temporal scale,
although the underlying temporal scale-space representation is based on a
discretized temporal scale parameter.
We show how scale-normalized temporal derivatives can be defined for these
time-causal scale-space kernels and how the composed theory can be used for
computing basic types of scale-normalized spatio-temporal derivative
expressions in a computationally efficient manner.Comment: 39 pages, 12 figures, 5 tables in Journal of Mathematical Imaging and
Vision, published online Dec 201
Separable time-causal and time-recursive spatio-temporal receptive fields
We present an improved model and theory for time-causal and time-recursive
spatio-temporal receptive fields, obtained by a combination of Gaussian
receptive fields over the spatial domain and first-order integrators or
equivalently truncated exponential filters coupled in cascade over the temporal
domain. Compared to previous spatio-temporal scale-space formulations in terms
of non-enhancement of local extrema or scale invariance, these receptive fields
are based on different scale-space axiomatics over time by ensuring
non-creation of new local extrema or zero-crossings with increasing temporal
scale. Specifically, extensions are presented about parameterizing the
intermediate temporal scale levels, analysing the resulting temporal dynamics
and transferring the theory to a discrete implementation in terms of recursive
filters over time.Comment: 12 pages, 2 figures, 2 tables. arXiv admin note: substantial text
overlap with arXiv:1404.203
Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
In the framework of large deformation diffeomorphic metric mapping (LDDMM),
we develop a multi-scale theory for the diffeomorphism group based on previous
works. The purpose of the paper is (1) to develop in details a variational
approach for multi-scale analysis of diffeomorphisms, (2) to generalise to
several scales the semidirect product representation and (3) to illustrate the
resulting diffeomorphic decomposition on synthetic and real images. We also
show that the approaches presented in other papers and the mixture of kernels
are equivalent.Comment: 21 pages, revised version without section on evaluatio
The Kardar-Parisi-Zhang equation and universality class
Brownian motion is a continuum scaling limit for a wide class of random
processes, and there has been great success in developing a theory for its
properties (such as distribution functions or regularity) and expanding the
breadth of its universality class. Over the past twenty five years a new
universality class has emerged to describe a host of important physical and
probabilistic models (including one dimensional interface growth processes,
interacting particle systems and polymers in random environments) which display
characteristic, though unusual, scalings and new statistics. This class is
called the Kardar-Parisi-Zhang (KPZ) universality class and underlying it is,
again, a continuum object -- a non-linear stochastic partial differential
equation -- known as the KPZ equation. The purpose of this survey is to explain
the context for, as well as the content of a number of mathematical
breakthroughs which have culminated in the derivation of the exact formula for
the distribution function of the KPZ equation started with {\it narrow wedge}
initial data. In particular we emphasize three topics: (1) The approximation of
the KPZ equation through the weakly asymmetric simple exclusion process; (2)
The derivation of the exact one-point distribution of the solution to the KPZ
equation with narrow wedge initial data; (3) Connections with directed polymers
in random media. As the purpose of this article is to survey and review, we
make precise statements but provide only heuristic arguments with indications
of the technical complexities necessary to make such arguments mathematically
rigorous.Comment: 57 pages, survey article, 7 figures, addition physics ref. added and
typo's correcte
Localization and delocalization of random interfaces
The probabilistic study of effective interface models has been quite active
in recent years, with a particular emphasis on the effect of various external
potentials (wall, pinning potential, ...) leading to
localization/delocalization transitions. I review some of the results that have
been obtained. In particular, I discuss pinning by a local potential, entropic
repulsion and the (pre)wetting transition, both for models with continuous and
discrete heights.Comment: Published at http://dx.doi.org/10.1214/154957806000000050 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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