129,904 research outputs found
Invariance of visual operations at the level of receptive fields
Receptive field profiles registered by cell recordings have shown that
mammalian vision has developed receptive fields tuned to different sizes and
orientations in the image domain as well as to different image velocities in
space-time. This article presents a theoretical model by which families of
idealized receptive field profiles can be derived mathematically from a small
set of basic assumptions that correspond to structural properties of the
environment. The article also presents a theory for how basic invariance
properties to variations in scale, viewing direction and relative motion can be
obtained from the output of such receptive fields, using complementary
selection mechanisms that operate over the output of families of receptive
fields tuned to different parameters. Thereby, the theory shows how basic
invariance properties of a visual system can be obtained already at the level
of receptive fields, and we can explain the different shapes of receptive field
profiles found in biological vision from a requirement that the visual system
should be invariant to the natural types of image transformations that occur in
its environment.Comment: 40 pages, 17 figure
Dynamic texture recognition using time-causal and time-recursive spatio-temporal receptive fields
This work presents a first evaluation of using spatio-temporal receptive
fields from a recently proposed time-causal spatio-temporal scale-space
framework as primitives for video analysis. We propose a new family of video
descriptors based on regional statistics of spatio-temporal receptive field
responses and evaluate this approach on the problem of dynamic texture
recognition. Our approach generalises a previously used method, based on joint
histograms of receptive field responses, from the spatial to the
spatio-temporal domain and from object recognition to dynamic texture
recognition. The time-recursive formulation enables computationally efficient
time-causal recognition. The experimental evaluation demonstrates competitive
performance compared to state-of-the-art. Especially, it is shown that binary
versions of our dynamic texture descriptors achieve improved performance
compared to a large range of similar methods using different primitives either
handcrafted or learned from data. Further, our qualitative and quantitative
investigation into parameter choices and the use of different sets of receptive
fields highlights the robustness and flexibility of our approach. Together,
these results support the descriptive power of this family of time-causal
spatio-temporal receptive fields, validate our approach for dynamic texture
recognition and point towards the possibility of designing a range of video
analysis methods based on these new time-causal spatio-temporal primitives.Comment: 29 pages, 16 figure
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
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
Temporal naturalism
Two people may claim both to be naturalists, but have divergent conceptions
of basic elements of the natural world which lead them to mean different things
when they talk about laws of nature, or states, or the role of mathematics in
physics. These disagreements do not much affect the ordinary practice of
science which is about small subsystems of the universe, described or explained
against a background, idealized to be fixed. But these issues become crucial
when we consider including the whole universe within our system, for then there
is no fixed background to reference observables to. I argue here that the key
issue responsible for divergent versions of naturalism and divergent approaches
to cosmology is the conception of time. One version, which I call temporal
naturalism, holds that time, in the sense of the succession of present moments,
is real, and that laws of nature evolve in that time. This is contrasted with
timeless naturalism, which holds that laws are immutable and the present moment
and its passage are illusions. I argue that temporal naturalism is empirically
more adequate than the alternatives, because it offers testable explanations
for puzzles its rivals cannot address, and is likely a better basis for solving
major puzzles that presently face cosmology and physics.
This essay also addresses the problem of qualia and experience within
naturalism and argues that only temporal naturalism can make a place for qualia
as intrinsic qualities of matter
Multiscale Bayesian State Space Model for Granger Causality Analysis of Brain Signal
Modelling time-varying and frequency-specific relationships between two brain
signals is becoming an essential methodological tool to answer heoretical
questions in experimental neuroscience. In this article, we propose to estimate
a frequency Granger causality statistic that may vary in time in order to
evaluate the functional connections between two brain regions during a task. We
use for that purpose an adaptive Kalman filter type of estimator of a linear
Gaussian vector autoregressive model with coefficients evolving over time. The
estimation procedure is achieved through variational Bayesian approximation and
is extended for multiple trials. This Bayesian State Space (BSS) model provides
a dynamical Granger-causality statistic that is quite natural. We propose to
extend the BSS model to include the \`{a} trous Haar decomposition. This
wavelet-based forecasting method is based on a multiscale resolution
decomposition of the signal using the redundant \`{a} trous wavelet transform
and allows us to capture short- and long-range dependencies between signals.
Equally importantly it allows us to derive the desired dynamical and
frequency-specific Granger-causality statistic. The application of these models
to intracranial local field potential data recorded during a psychological
experimental task shows the complex frequency based cross-talk between amygdala
and medial orbito-frontal cortex.
Keywords: \`{a} trous Haar wavelets; Multiple trials; Neuroscience data;
Nonstationarity; Time-frequency; Variational methods
The published version of this article is
Cekic, S., Grandjean, D., Renaud, O. (2018). Multiscale Bayesian state-space
model for Granger causality analysis of brain signal. Journal of Applied
Statistics. https://doi.org/10.1080/02664763.2018.145581
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