1,474 research outputs found
Scale Space Smoothing, Image Feature Extraction and Bessel Filters
The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian filters. The features extracted by the Bessel filter are therefore scale invariant. Edges, blobs, and junctions are features considered here to show that the extracted features remain unchanged by varying the scale of a Bessel filter. The scale invariance property of Bessel filters for edges is analytically proved here. We conjecture that Bessel filters also enjoy this scale invariance property for other kinds of features. The experimental results presente
Scale Space Smoothing, Image Feature Extraction and Bessel Filters
The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian filters. The features extracted by the Bessel filter are therefore scale invariant. Edges, blobs, and junctions are features considered here to show that the extracted features remain unchanged by varying the scale of a Bessel filter. The scale invariance property of Bessel filters for edges is analytically proved here. We conjecture that Bessel filters also enjoy this scale invariance property for other kinds of features. The experimental results presente
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
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
Higher-Order Properties of Analytic Wavelets
The influence of higher-order wavelet properties on the analytic wavelet
transform behavior is investigated, and wavelet functions offering advantageous
performance are identified. This is accomplished through detailed investigation
of the generalized Morse wavelets, a two-parameter family of exactly analytic
continuous wavelets. The degree of time/frequency localization, the existence
of a mapping between scale and frequency, and the bias involved in estimating
properties of modulated oscillatory signals, are proposed as important
considerations. Wavelet behavior is found to be strongly impacted by the degree
of asymmetry of the wavelet in both the frequency and the time domain, as
quantified by the third central moments. A particular subset of the generalized
Morse wavelets, recognized as deriving from an inhomogeneous Airy function,
emerge as having particularly desirable properties. These "Airy wavelets"
substantially outperform the only approximately analytic Morlet wavelets for
high time localization. Special cases of the generalized Morse wavelets are
examined, revealing a broad range of behaviors which can be matched to the
characteristics of a signal.Comment: 15 pages, 6 Postscript 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
Spatial dissection of a soundfield using spherical harmonic decomposition
A real-world soundfield is often contributed by multiple desired and undesired sound sources. The performance of many acoustic systems such as automatic speech recognition, audio surveillance, and teleconference relies on its ability to extract the desired sound components in such a mixed environment. The existing solutions to the above problem are constrained by various fundamental limitations and require to enforce different priors depending on the acoustic condition such as reverberation and spatial distribution of sound sources. With the growing emphasis and integration of audio applications in diverse technologies such as smart home and virtual reality appliances, it is imperative to advance the source separation technology in order to overcome the limitations of the traditional approaches.
To that end, we exploit the harmonic decomposition model to dissect a mixed soundfield into its underlying desired and undesired components based on source and signal characteristics. By analysing the spatial projection of a soundfield, we achieve multiple outcomes such as (i) soundfield separation with respect to distinct source regions, (ii) source separation in a mixed soundfield using modal coherence model, and (iii) direction of arrival (DOA) estimation of multiple overlapping sound sources through pattern recognition of the modal coherence of a soundfield.
We first employ an array of higher order microphones for soundfield separation in order to reduce hardware requirement and implementation complexity. Subsequently, we develop novel mathematical models for modal coherence of noisy and reverberant soundfields that facilitate convenient ways for estimating DOA and power spectral densities leading to robust source separation algorithms. The modal domain approach to the soundfield/source separation allows us to circumvent several practical limitations of the existing techniques and enhance the performance and robustness of the system. The proposed methods are presented with several practical applications and performance evaluations using simulated and real-life dataset
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