16,447 research outputs found
Semantic 3D Reconstruction with Finite Element Bases
We propose a novel framework for the discretisation of multi-label problems
on arbitrary, continuous domains. Our work bridges the gap between general FEM
discretisations, and labeling problems that arise in a variety of computer
vision tasks, including for instance those derived from the generalised Potts
model. Starting from the popular formulation of labeling as a convex relaxation
by functional lifting, we show that FEM discretisation is valid for the most
general case, where the regulariser is anisotropic and non-metric. While our
findings are generic and applicable to different vision problems, we
demonstrate their practical implementation in the context of semantic 3D
reconstruction, where such regularisers have proved particularly beneficial.
The proposed FEM approach leads to a smaller memory footprint as well as faster
computation, and it constitutes a very simple way to enable variable, adaptive
resolution within the same model
A Posteriori Error Control for the Binary Mumford-Shah Model
The binary Mumford-Shah model is a widespread tool for image segmentation and
can be considered as a basic model in shape optimization with a broad range of
applications in computer vision, ranging from basic segmentation and labeling
to object reconstruction. This paper presents robust a posteriori error
estimates for a natural error quantity, namely the area of the non properly
segmented region. To this end, a suitable strictly convex and non-constrained
relaxation of the originally non-convex functional is investigated and Repin's
functional approach for a posteriori error estimation is used to control the
numerical error for the relaxed problem in the -norm. In combination with
a suitable cut out argument, a fully practical estimate for the area mismatch
is derived. This estimate is incorporated in an adaptive meshing strategy. Two
different adaptive primal-dual finite element schemes, and the most frequently
used finite difference discretization are investigated and compared. Numerical
experiments show qualitative and quantitative properties of the estimates and
demonstrate their usefulness in practical applications.Comment: 18 pages, 7 figures, 1 tabl
Getting Feasible Variable Estimates From Infeasible Ones: MRF Local Polytope Study
This paper proposes a method for construction of approximate feasible primal
solutions from dual ones for large-scale optimization problems possessing
certain separability properties. Whereas infeasible primal estimates can
typically be produced from (sub-)gradients of the dual function, it is often
not easy to project them to the primal feasible set, since the projection
itself has a complexity comparable to the complexity of the initial problem. We
propose an alternative efficient method to obtain feasibility and show that its
properties influencing the convergence to the optimum are similar to the
properties of the Euclidean projection. We apply our method to the local
polytope relaxation of inference problems for Markov Random Fields and
demonstrate its superiority over existing methods.Comment: 20 page, 4 figure
Faster SDP hierarchy solvers for local rounding algorithms
Convex relaxations based on different hierarchies of linear/semi-definite
programs have been used recently to devise approximation algorithms for various
optimization problems. The approximation guarantee of these algorithms improves
with the number of {\em rounds} in the hierarchy, though the complexity of
solving (or even writing down the solution for) the 'th level program grows
as where is the input size.
In this work, we observe that many of these algorithms are based on {\em
local} rounding procedures that only use a small part of the SDP solution (of
size instead of ). We give an algorithm to
find the requisite portion in time polynomial in its size. The challenge in
achieving this is that the required portion of the solution is not fixed a
priori but depends on other parts of the solution, sometimes in a complicated
iterative manner.
Our solver leads to time algorithms to obtain the same
guarantees in many cases as the earlier time algorithms based on
rounds of the Lasserre hierarchy. In particular, guarantees based on rounds can be realized in polynomial time.
We develop and describe our algorithm in a fairly general abstract framework.
The main technical tool in our work, which might be of independent interest in
convex optimization, is an efficient ellipsoid algorithm based separation
oracle for convex programs that can output a {\em certificate of infeasibility
with restricted support}. This is used in a recursive manner to find a sequence
of consistent points in nested convex bodies that "fools" local rounding
algorithms.Comment: 30 pages, 8 figure
Synchronized Oscillations During Cooperative Feature Linking in a Cortical Model of Visual Perception
A neural network model of synchronized oscillator activity in visual cortex is presented in order to account for recent neurophysiological findings that such synchronization may reflect global properties of the stimulus. In these recent experiments, it was reported that synchronization of oscillatory firing responses to moving bar stimuli occurred not only for nearby neurons, but also occurred between neurons separated by several cortical columns (several mm of cortex) when these neurons shared some receptive field preferences specific to the stimuli. These results were obtained not only for single bar stimuli but also across two disconnected, but colinear, bars moving in the same direction. Our model and computer simulations obtain these synchrony results across both single and double bar stimuli. For the double bar case, synchronous oscillations are induced in the region between the bars, but no oscillations are induced in the regions beyond the stimuli. These results were achieved with cellular units that exhibit limit cycle oscillations for a robust range of input values, but which approach an equilibrium state when undriven. Single and double bar synchronization of these oscillators was achieved by different, but formally related, models of preattentive visual boundary segmentation and attentive visual object recognition, as well as nearest-neighbor and randomly coupled models. In preattentive visual segmentation, synchronous oscillations may reflect the binding of local feature detectors into a globally coherent grouping. In object recognition, synchronous oscillations may occur during an attentive resonant state that triggers new learning. These modelling results support earlier theoretical predictions of synchronous visual cortical oscillations and demonstrate the robustness of the mechanisms capable of generating synchrony.Air Force Office of Scientific Research (90-0175); Army Research Office (DAAL-03-88-K0088); Defense Advanced Research Projects Agency (90-0083); National Aeronautics and Space Administration (NGT-50497
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