4,709 research outputs found
Scalable Dense Monocular Surface Reconstruction
This paper reports on a novel template-free monocular non-rigid surface
reconstruction approach. Existing techniques using motion and deformation cues
rely on multiple prior assumptions, are often computationally expensive and do
not perform equally well across the variety of data sets. In contrast, the
proposed Scalable Monocular Surface Reconstruction (SMSR) combines strengths of
several algorithms, i.e., it is scalable with the number of points, can handle
sparse and dense settings as well as different types of motions and
deformations. We estimate camera pose by singular value thresholding and
proximal gradient. Our formulation adopts alternating direction method of
multipliers which converges in linear time for large point track matrices. In
the proposed SMSR, trajectory space constraints are integrated by smoothing of
the measurement matrix. In the extensive experiments, SMSR is demonstrated to
consistently achieve state-of-the-art accuracy on a wide variety of data sets.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October
201
Macroscopic equations governing noisy spiking neuronal populations
At functional scales, cortical behavior results from the complex interplay of
a large number of excitable cells operating in noisy environments. Such systems
resist to mathematical analysis, and computational neurosciences have largely
relied on heuristic partial (and partially justified) macroscopic models, which
successfully reproduced a number of relevant phenomena. The relationship
between these macroscopic models and the spiking noisy dynamics of the
underlying cells has since then been a great endeavor. Based on recent
mean-field reductions for such spiking neurons, we present here {a principled
reduction of large biologically plausible neuronal networks to firing-rate
models, providing a rigorous} relationship between the macroscopic activity of
populations of spiking neurons and popular macroscopic models, under a few
assumptions (mainly linearity of the synapses). {The reduced model we derive
consists of simple, low-dimensional ordinary differential equations with}
parameters and {nonlinearities derived from} the underlying properties of the
cells, and in particular the noise level. {These simple reduced models are
shown to reproduce accurately the dynamics of large networks in numerical
simulations}. Appropriate parameters and functions are made available {online}
for different models of neurons: McKean, Fitzhugh-Nagumo and Hodgkin-Huxley
models
A multiscale method for heterogeneous bulk-surface coupling
In this paper, we construct and analyze a multiscale (finite element) method
for parabolic problems with heterogeneous dynamic boundary conditions. As
origin, we consider a reformulation of the system in order to decouple the
discretization of bulk and surface dynamics. This allows us to combine
multiscale methods on the boundary with standard Lagrangian schemes in the
interior. We prove convergence and quantify explicit rates for low-regularity
solutions, independent of the oscillatory behavior of the heterogeneities. As a
result, coarse discretization parameters, which do not resolve the fine scales,
can be considered. The theoretical findings are justified by a number of
numerical experiments including dynamic boundary conditions with random
diffusion coefficients
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