17,611 research outputs found
A geometric model of multi-scale orientation preference maps via Gabor functions
In this paper we present a new model for the generation of orientation
preference maps in the primary visual cortex (V1), considering both orientation
and scale features. First we undertake to model the functional architecture of
V1 by interpreting it as a principal fiber bundle over the 2-dimensional
retinal plane by introducing intrinsic variables orientation and scale. The
intrinsic variables constitute a fiber on each point of the retinal plane and
the set of receptive profiles of simple cells is located on the fiber. Each
receptive profile on the fiber is mathematically interpreted as a rotated Gabor
function derived from an uncertainty principle. The visual stimulus is lifted
in a 4-dimensional space, characterized by coordinate variables, position,
orientation and scale, through a linear filtering of the stimulus with Gabor
functions. Orientation preference maps are then obtained by mapping the
orientation value found from the lifting of a noise stimulus onto the
2-dimensional retinal plane. This corresponds to a Bargmann transform in the
reducible representation of the group. A
comparison will be provided with a previous model based on the Bargman
transform in the irreducible representation of the group,
outlining that the new model is more physiologically motivated. Then we present
simulation results related to the construction of the orientation preference
map by using Gabor filters with different scales and compare those results to
the relevant neurophysiological findings in the literature
Left-invariant evolutions of wavelet transforms on the Similitude Group
Enhancement of multiple-scale elongated structures in noisy image data is
relevant for many biomedical applications but commonly used PDE-based
enhancement techniques often fail at crossings in an image. To get an overview
of how an image is composed of local multiple-scale elongated structures we
construct a multiple scale orientation score, which is a continuous wavelet
transform on the similitude group, SIM(2). Our unitary transform maps the space
of images onto a reproducing kernel space defined on SIM(2), allowing us to
robustly relate Euclidean (and scaling) invariant operators on images to
left-invariant operators on the corresponding continuous wavelet transform.
Rather than often used wavelet (soft-)thresholding techniques, we employ the
group structure in the wavelet domain to arrive at left-invariant evolutions
and flows (diffusion), for contextual crossing preserving enhancement of
multiple scale elongated structures in noisy images. We present experiments
that display benefits of our work compared to recent PDE techniques acting
directly on the images and to our previous work on left-invariant diffusions on
orientation scores defined on Euclidean motion group.Comment: 40 page
Deformable kernels for early vision
Early vision algorithms often have a first stage of linear-filtering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. A technique is presented that allows: 1) computing the best approximation of a given family using linear combinations of a small number of `basis' functions; and 2) describing all finite-dimensional families, i.e., the families of filters for which a finite dimensional representation is possible with no error. The technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations. The relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated. Experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi-scale 2D edge-detection kernels. The implementation issues are also discussed
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
Singularity-free quantum tracking control of molecular rotor orientation
Quantum tracking control aims to identify applied fields to steer the
expectation values of particular observables along desired paths in time. The
associated temporal fields can be identified by inverting the underlying
dynamical equations for the observables. However, fields found in this manner
are often plagued by undesirable singularities. In this paper we consider a
planar molecular rotor, and derive singularity-free tracking expressions for
the fields that steer the expectation of the orientation of the rotor along
desired trajectories in time. Simulations are presented that utilize two
orthogonal control electric fields to drive the orientation of the rotor along
a series of designated tracks
Source extraction and photometry for the far-infrared and sub-millimeter continuum in the presence of complex backgrounds
(Abridged) We present a new method for detecting and measuring compact
sources in conditions of intense, and highly variable, fore/background. While
all most commonly used packages carry out the source detection over the signal
image, our proposed method builds from the measured image a "curvature" image
by double-differentiation in four different directions. In this way point-like
as well as resolved, yet relatively compact, objects are easily revealed while
the slower varying fore/background is greatly diminished. Candidate sources are
then identified by looking for pixels where the curvature exceeds, in absolute
terms, a given threshold; the methodology easily allows us to pinpoint
breakpoints in the source brightness profile and then derive reliable guesses
for the sources extent. Identified peaks are fit with 2D elliptical Gaussians
plus an underlying planar inclined plateau, with mild constraints on size and
orientation. Mutually contaminating sources are fit with multiple Gaussians
simultaneously using flexible constraints. We ran our method on simulated
large-scale fields with 1000 sources of different peak flux overlaid on a
realistic realization of diffuse background. We find detection rates in excess
of 90% for sources with peak fluxes above the 3-sigma signal noise limit; for
about 80% of the sources the recovered peak fluxes are within 30% of their
input values.Comment: Accepted on A&
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