43,461 research outputs found
Idealized computational models for auditory receptive fields
This paper presents a theory by which idealized models of auditory receptive
fields can be derived in a principled axiomatic manner, from a set of
structural properties to enable invariance of receptive field responses under
natural sound transformations and ensure internal consistency between
spectro-temporal receptive fields at different temporal and spectral scales.
For defining a time-frequency transformation of a purely temporal sound
signal, it is shown that the framework allows for a new way of deriving the
Gabor and Gammatone filters as well as a novel family of generalized Gammatone
filters, with additional degrees of freedom to obtain different trade-offs
between the spectral selectivity and the temporal delay of time-causal temporal
window functions.
When applied to the definition of a second-layer of receptive fields from a
spectrogram, it is shown that the framework leads to two canonical families of
spectro-temporal receptive fields, in terms of spectro-temporal derivatives of
either spectro-temporal Gaussian kernels for non-causal time or the combination
of a time-causal generalized Gammatone filter over the temporal domain and a
Gaussian filter over the logspectral domain. For each filter family, the
spectro-temporal receptive fields can be either separable over the
time-frequency domain or be adapted to local glissando transformations that
represent variations in logarithmic frequencies over time. Within each domain
of either non-causal or time-causal time, these receptive field families are
derived by uniqueness from the assumptions.
It is demonstrated how the presented framework allows for computation of
basic auditory features for audio processing and that it leads to predictions
about auditory receptive fields with good qualitative similarity to biological
receptive fields measured in the inferior colliculus (ICC) and primary auditory
cortex (A1) of mammals.Comment: 55 pages, 22 figures, 3 table
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
Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
To supplement the already known classification of traces on classical
pseudodifferential operators, we present a classification of traces on the
algebras of odd-class pseudodifferential operators of non-positive order acting
on smooth functions on a closed odd-dimensional manifold. By means of the one
to one correspondence between continuous traces on Lie algebras and
determinants on the associated regular Lie groups, we give a classification of
determinants on the group associated to the algebra of odd-class
pseudodifferential operators with fixed non-positive order. At the end we
discuss two possible ways to extend the definition of a determinant outside a
neighborhood of the identity on the Lie group associated to the algebra of
odd-class pseudodifferential operators of order zero
Cohomology of classes of symbols and classi cation of traces on corresponding classes of operators with non positive order
This thesis is devoted to the classification issue of traces on classical pseudo-differential operators with fixed non positive order on closed manifolds of dimension . We describe the space of homogeneous functions on a symplectic cone in terms of Poisson brackets of appropriate homogeneous functions, and we use it to find a representation of a pseudo-differential operator as a sum of commutators. We compute the cohomology groups of certain spaces of classical symbols on the --dimensional Euclidean space with constant coefficients, and we show that any closed linear form on the space of symbols of fixed order can be written either in terms of a leading symbol linear form and the noncommutative residue, or in terms of a leading symbol linear form and the cut-off regularized integral. On the operator level, we infer that any trace on the algebra of classical pseudo-differential operators of order can be written either as a linear combination of a generalized leading symbol trace and the residual trace when , or as a linear combination of a generalized leading symbol trace and any linear map that extends the --trace when . In contrast, for odd class pseudo-differential operators in odd dimensions, any trace can be written as a linear combination of a generalized leading symbol trace and the canonical trace. We derive from these results the classification of determinants on the Fr\'echet Lie group associated to the algebras of classical pseudo-differential operators with non positive integer order
A new perspective on the Propagation-Separation approach: Taking advantage of the propagation condition
The Propagation-Separation approach is an iterative procedure for pointwise
estimation of local constant and local polynomial functions. The estimator is
defined as a weighted mean of the observations with data-driven weights. Within
homogeneous regions it ensures a similar behavior as non-adaptive smoothing
(propagation), while avoiding smoothing among distinct regions (separation). In
order to enable a proof of stability of estimates, the authors of the original
study introduced an additional memory step aggregating the estimators of the
successive iteration steps. Here, we study theoretical properties of the
simplified algorithm, where the memory step is omitted. In particular, we
introduce a new strategy for the choice of the adaptation parameter yielding
propagation and stability for local constant functions with sharp
discontinuities.Comment: 28 pages, 5 figure
Stability
Reproducibility is imperative for any scientific discovery. More often than
not, modern scientific findings rely on statistical analysis of
high-dimensional data. At a minimum, reproducibility manifests itself in
stability of statistical results relative to "reasonable" perturbations to data
and to the model used. Jacknife, bootstrap, and cross-validation are based on
perturbations to data, while robust statistics methods deal with perturbations
to models. In this article, a case is made for the importance of stability in
statistics. Firstly, we motivate the necessity of stability for interpretable
and reliable encoding models from brain fMRI signals. Secondly, we find strong
evidence in the literature to demonstrate the central role of stability in
statistical inference, such as sensitivity analysis and effect detection.
Thirdly, a smoothing parameter selector based on estimation stability (ES),
ES-CV, is proposed for Lasso, in order to bring stability to bear on
cross-validation (CV). ES-CV is then utilized in the encoding models to reduce
the number of predictors by 60% with almost no loss (1.3%) of prediction
performance across over 2,000 voxels. Last, a novel "stability" argument is
seen to drive new results that shed light on the intriguing interactions
between sample to sample variability and heavier tail error distribution (e.g.,
double-exponential) in high-dimensional regression models with predictors
and independent samples. In particular, when
and the error distribution is
double-exponential, the Ordinary Least Squares (OLS) is a better estimator than
the Least Absolute Deviation (LAD) estimator.Comment: Published in at http://dx.doi.org/10.3150/13-BEJSP14 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
On the 3 dimensional structure of edge-on disk galaxies
A simple algorithm is employed to deproject the two dimensional images of a
pilot sample of 12 high-quality images of edge-on disk galaxies and to study
their intrinsic 3 dimensional stellar distribution. We examine the radial
profiles of the stars as a function of height above the plane and report a
general trend within our sample of an increasing radial scalelength with height
outside of the dustlane. This could be explained by the widespread presence of
a thick disk component in these galaxies. In addition, the 3 dimensional view
allows the study of the vertical distribution of the outer disk, beyond the
break region, where we detect a significant increase in scalelength with
vertical distance from the major axis for the truncated disks. This could be
regarded as a weakening of the "truncation" with increasing distance from the
plane. Furthermore, we conclude that the recently revised classification of the
radial surface brightness profiles found for face-on galaxies is indeed
independent of geometry. In particular, we find at least one example of each of
the three main profile classes as defined in complete samples of intermediate
to face-on galaxies: not-truncated, truncated and antitruncated. The position
and surface brightness that mark the break location in the radial light
distribution are found to be consistent with those of face-on galaxies.Comment: LaTeX, 25 pages, 10 figures (some low resolution), MNRAS accepted.
Version with all figures in full resolution (~6MB) available at
http://www.astro.rug.nl/~pohlen/pohlen_3Dedgeon.p
Fast Graph-Based Object Segmentation for RGB-D Images
Object segmentation is an important capability for robotic systems, in
particular for grasping. We present a graph- based approach for the
segmentation of simple objects from RGB-D images. We are interested in
segmenting objects with large variety in appearance, from lack of texture to
strong textures, for the task of robotic grasping. The algorithm does not rely
on image features or machine learning. We propose a modified Canny edge
detector for extracting robust edges by using depth information and two simple
cost functions for combining color and depth cues. The cost functions are used
to build an undirected graph, which is partitioned using the concept of
internal and external differences between graph regions. The partitioning is
fast with O(NlogN) complexity. We also discuss ways to deal with missing depth
information. We test the approach on different publicly available RGB-D object
datasets, such as the Rutgers APC RGB-D dataset and the RGB-D Object Dataset,
and compare the results with other existing methods
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