32,786 research outputs found
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization
We present a reconstruction method involving maximum-likelihood expectation
maximization (MLEM) to model Poisson noise as applied to fluorescence molecular
tomography (FMT). MLEM is initialized with the output from a sparse
reconstruction-based approach, which performs truncated singular value
decomposition-based preconditioning followed by fast iterative
shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation
for this approach is that sparsity information could be accounted for within
the initialization, while MLEM would accurately model Poisson noise in the FMT
system. Simulation experiments show the proposed method significantly improves
images qualitatively and quantitatively. The method results in over 20 times
faster convergence compared to uniformly initialized MLEM and improves
robustness to noise compared to pure sparse reconstruction. We also
theoretically justify the ability of the proposed approach to reduce noise in
the background region compared to pure sparse reconstruction. Overall, these
results provide strong evidence to model Poisson noise in FMT reconstruction
and for application of the proposed reconstruction framework to FMT imaging
Identifying the lights position in photometric stereo under unknown lighting
Reconstructing the 3D shape of an object from a set of images is a classical
problem in Computer Vision. Photometric stereo is one of the possible
approaches. It stands on the assumption that the object is observed from a
fixed point of view under different lighting conditions. The traditional
approach requires that the position of the light sources is accurately known.
It has been proved that the lights position can be estimated directly from the
data, when at least 6 images of the observed object are available. In this
paper, we give a Matlab implementation of the algorithm for solving the
photometric stereo problem under unknown lighting, and propose a simple
shooting technique to solve the bas-relief ambiguity.Comment: new versio
A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries
We present a new multigrid scheme for solving the Poisson equation with
Dirichlet boundary conditions on a Cartesian grid with irregular domain
boundaries. This scheme was developed in the context of the Adaptive Mesh
Refinement (AMR) schemes based on a graded-octree data structure. The Poisson
equation is solved on a level-by-level basis, using a "one-way interface"
scheme in which boundary conditions are interpolated from the previous coarser
level solution. Such a scheme is particularly well suited for self-gravitating
astrophysical flows requiring an adaptive time stepping strategy. By
constructing a multigrid hierarchy covering the active cells of each AMR level,
we have designed a memory-efficient algorithm that can benefit fully from the
multigrid acceleration. We present a simple method for capturing the boundary
conditions across the multigrid hierarchy, based on a second-order accurate
reconstruction of the boundaries of the multigrid levels. In case of very
complex boundaries, small scale features become smaller than the discretization
cell size of coarse multigrid levels and convergence problems arise. We propose
a simple solution to address these issues. Using our scheme, the convergence
rate usually depends on the grid size for complex grids, but good linear
convergence is maintained. The proposed method was successfully implemented on
distributed memory architectures in the RAMSES code, for which we present and
discuss convergence and accuracy properties as well as timing performances.Comment: 33 pages, 15 figures, accepted for publication in Journal of
Computational Physic
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