173 research outputs found
An Improved Observation Model for Super-Resolution under Affine Motion
Super-resolution (SR) techniques make use of subpixel shifts between frames
in an image sequence to yield higher-resolution images. We propose an original
observation model devoted to the case of non isometric inter-frame motion as
required, for instance, in the context of airborne imaging sensors. First, we
describe how the main observation models used in the SR literature deal with
motion, and we explain why they are not suited for non isometric motion. Then,
we propose an extension of the observation model by Elad and Feuer adapted to
affine motion. This model is based on a decomposition of affine transforms into
successive shear transforms, each one efficiently implemented by row-by-row or
column-by-column 1-D affine transforms.
We demonstrate on synthetic and real sequences that our observation model
incorporated in a SR reconstruction technique leads to better results in the
case of variable scale motions and it provides equivalent results in the case
of isometric motions
Polymorphic evolution sequence and evolutionary branching
We are interested in the study of models describing the evolution of a
polymorphic population with mutation and selection in the specific scales of
the biological framework of adaptive dynamics. The population size is assumed
to be large and the mutation rate small. We prove that under a good combination
of these two scales, the population process is approximated in the long time
scale of mutations by a Markov pure jump process describing the successive
trait equilibria of the population. This process, which generalizes the
so-called trait substitution sequence, is called polymorphic evolution
sequence. Then we introduce a scaling of the size of mutations and we study the
polymorphic evolution sequence in the limit of small mutations. From this study
in the neighborhood of evolutionary singularities, we obtain a full
mathematical justification of a heuristic criterion for the phenomenon of
evolutionary branching. To this end we finely analyze the asymptotic behavior
of 3-dimensional competitive Lotka-Volterra systems
Super-resolution in map-making based on a physical instrument model and regularized inversion. Application to SPIRE/Herschel
We investigate super-resolution methods for image reconstruction from data
provided by a family of scanning instruments like the Herschel observatory. To
do this, we constructed a model of the instrument that faithfully reflects the
physical reality, accurately taking the acquisition process into account to
explain the data in a reliable manner. The inversion, ie the image
reconstruction process, is based on a linear approach resulting from a
quadratic regularized criterion and numerical optimization tools. The
application concerns the reconstruction of maps for the SPIRE instrument of the
Herschel observatory. The numerical evaluation uses simulated and real data to
compare the standard tool (coaddition) and the proposed method. The inversion
approach is capable to restore spatial frequencies over a bandwidth four times
that possible with coaddition and thus to correctly show details invisible on
standard maps. The approach is also applied to real data with significant
improvement in spatial resolution.Comment: Astronomy & Astrophysic
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
We consider an "elastic" version of the statistical mechanical monomer-dimer
problem on the n-dimensional integer lattice. Our setting includes the
classical "rigid" formulation as a special case and extends it by allowing each
dimer to consist of particles at arbitrarily distant sites of the lattice, with
the energy of interaction between the particles in a dimer depending on their
relative position. We reduce the free energy of the elastic dimer-monomer (EDM)
system per lattice site in the thermodynamic limit to the moment Lyapunov
exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value
and covariance function are the Boltzmann factors associated with the monomer
energy and dimer potential. In particular, the classical monomer-dimer problem
becomes related to the MLE of a moving average GRF. We outline an approach to
recursive computation of the partition function for "Manhattan" EDM systems
where the dimer potential is a weighted l1-distance and the auxiliary GRF is a
Markov random field of Pickard type which behaves in space like autoregressive
processes do in time. For one-dimensional Manhattan EDM systems, we compute the
MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a
compact transfer operator on a Hilbert space which is related to the
annihilation and creation operators of the quantum harmonic oscillator and also
recast it as the eigenvalue problem for a pantograph functional-differential
equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue
of DCDS-
Use of a Priori Information for the Deconvolution of Ultrasonic Signals
The resolution of pulse-echo imaging technique is limited by the band-width of the transducer impulse response (IR). For flaws sizing or thickness measurement simple and accurate methods exist if the echoes do not overlap. These classical methods break if the echoes can not be separated in time domain
The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations
We study a class of processes that are akin to the Wright-Fisher model, with
transition probabilities weighted in terms of the frequency-dependent fitness
of the population types. By considering an approximate weak formulation of the
discrete problem, we are able to derive a corresponding continuous weak
formulation for the probability density. Therefore, we obtain a family of
partial differential equations (PDE) for the evolution of the probability
density, and which will be an approximation of the discrete process in the
joint large population, small time-steps and weak selection limit. If the
fitness functions are sufficiently regular, we can recast the weak formulation
in a more standard formulation, without any boundary conditions, but
supplemented by a number of conservation laws. The equations in this family can
be purely diffusive, purely hyperbolic or of convection-diffusion type, with
frequency dependent convection. The particular outcome will depend on the
assumed scalings. The diffusive equations are of the degenerate type; using a
duality approach, we also obtain a frequency dependent version of the Kimura
equation without any further assumptions. We also show that the convective
approximation is related to the replicator dynamics and provide some estimate
of how accurate is the convective approximation, with respect to the
convective-diffusion approximation. In particular, we show that the mode, but
not the expected value, of the probability distribution is modelled by the
replicator dynamics. Some numerical simulations that illustrate the results are
also presented
3D Fluid Flow Estimation with Integrated Particle Reconstruction
The standard approach to densely reconstruct the motion in a volume of fluid
is to inject high-contrast tracer particles and record their motion with
multiple high-speed cameras. Almost all existing work processes the acquired
multi-view video in two separate steps, utilizing either a pure Eulerian or
pure Lagrangian approach. Eulerian methods perform a voxel-based reconstruction
of particles per time step, followed by 3D motion estimation, with some form of
dense matching between the precomputed voxel grids from different time steps.
In this sequential procedure, the first step cannot use temporal consistency
considerations to support the reconstruction, while the second step has no
access to the original, high-resolution image data. Alternatively, Lagrangian
methods reconstruct an explicit, sparse set of particles and track the
individual particles over time. Physical constraints can only be incorporated
in a post-processing step when interpolating the particle tracks to a dense
motion field. We show, for the first time, how to jointly reconstruct both the
individual tracer particles and a dense 3D fluid motion field from the image
data, using an integrated energy minimization. Our hybrid Lagrangian/Eulerian
model reconstructs individual particles, and at the same time recovers a dense
3D motion field in the entire domain. Making particles explicit greatly reduces
the memory consumption and allows one to use the high-res input images for
matching. Whereas the dense motion field makes it possible to include physical
a-priori constraints and account for the incompressibility and viscosity of the
fluid. The method exhibits greatly (~70%) improved results over our recently
published baseline with two separate steps for 3D reconstruction and motion
estimation. Our results with only two time steps are comparable to those of
sota tracking-based methods that require much longer sequences.Comment: To appear in International Journal of Computer Vision (IJCV
Brainstem Respiratory Oscillators Develop Independently of Neuronal Migration Defects in the Wnt/PCP Mouse Mutant looptail
The proper development and maturation of neuronal circuits require precise migration of component neurons from their birthplace (germinal zone) to their final positions. Little is known about the effects of aberrant neuronal position on the functioning of organized neuronal groups, especially in mammals. Here, we investigated the formation and properties of brainstem respiratory neurons in looptail (Lp) mutant mice in which facial motor neurons closely apposed to some respiratory neurons fail to migrate due to loss of function of the Wnt/Planar Cell Polarity (PCP) protein Vangl2. Using calcium imaging and immunostaining on embryonic hindbrain preparations, we found that respiratory neurons constituting the embryonic parafacial oscillator (e-pF) settled at the ventral surface of the medulla in Vangl2Lp/+ and Vangl2Lp/Lp embryos despite the failure of tangential migration of its normally adjacent facial motor nucleus. Anatomically, the e-pF neurons were displaced medially in Lp/+ embryos and rostro-medially Lp/Lp embryos. Pharmacological treatments showed that the e-pF oscillator exhibited characteristic network properties in both Lp/+ and Lp/Lp embryos. Furthermore, using hindbrain slices, we found that the other respiratory oscillator, the preBötzinger complex, was also anatomically and functionally established in Lp mutants. Importantly, the displaced e-pF oscillator established functional connections with the preBötC oscillator in Lp/+ mutants. Our data highlight the robustness of the developmental processes that assemble the neuronal networks mediating an essential physiological function
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