10,189 research outputs found
3D particle tracking velocimetry using dynamic discrete tomography
Particle tracking velocimetry in 3D is becoming an increasingly important
imaging tool in the study of fluid dynamics, combustion as well as plasmas. We
introduce a dynamic discrete tomography algorithm for reconstructing particle
trajectories from projections. The algorithm is efficient for data from two
projection directions and exact in the sense that it finds a solution
consistent with the experimental data. Non-uniqueness of solutions can be
detected and solutions can be tracked individually
Bounds for discrete tomography solutions
We consider the reconstruction of a function on a finite subset of
if the line sums in certain directions are prescribed. The real
solutions form a linear manifold, its integer solutions a grid. First we
provide an explicit expression for the projection vector from the origin onto
the linear solution manifold in the case of only row and column sums of a
finite subset of . Next we present a method to estimate the
maximal distance between two binary solutions. Subsequently we deduce an upper
bound for the distance from any given real solution to the nearest integer
solution. This enables us to estimate the stability of solutions. Finally we
generalize the first mentioned result to the torus case and to the continuous
case
Do-It-Yourself Single Camera 3D Pointer Input Device
We present a new algorithm for single camera 3D reconstruction, or 3D input
for human-computer interfaces, based on precise tracking of an elongated
object, such as a pen, having a pattern of colored bands. To configure the
system, the user provides no more than one labelled image of a handmade
pointer, measurements of its colored bands, and the camera's pinhole projection
matrix. Other systems are of much higher cost and complexity, requiring
combinations of multiple cameras, stereocameras, and pointers with sensors and
lights. Instead of relying on information from multiple devices, we examine our
single view more closely, integrating geometric and appearance constraints to
robustly track the pointer in the presence of occlusion and distractor objects.
By probing objects of known geometry with the pointer, we demonstrate
acceptable accuracy of 3D localization.Comment: 8 pages, 6 figures, 2018 15th Conference on Computer and Robot Visio
Asteroid Models from Multiple Data Sources
In the past decade, hundreds of asteroid shape models have been derived using
the lightcurve inversion method. At the same time, a new framework of 3-D shape
modeling based on the combined analysis of widely different data sources such
as optical lightcurves, disk-resolved images, stellar occultation timings,
mid-infrared thermal radiometry, optical interferometry, and radar
delay-Doppler data, has been developed. This multi-data approach allows the
determination of most of the physical and surface properties of asteroids in a
single, coherent inversion, with spectacular results. We review the main
results of asteroid lightcurve inversion and also recent advances in multi-data
modeling. We show that models based on remote sensing data were confirmed by
spacecraft encounters with asteroids, and we discuss how the multiplication of
highly detailed 3-D models will help to refine our general knowledge of the
asteroid population. The physical and surface properties of asteroids, i.e.,
their spin, 3-D shape, density, thermal inertia, surface roughness, are among
the least known of all asteroid properties. Apart for the albedo and diameter,
we have access to the whole picture for only a few hundreds of asteroids. These
quantities are nevertheless very important to understand as they affect the
non-gravitational Yarkovsky effect responsible for meteorite delivery to Earth,
or the bulk composition and internal structure of asteroids.Comment: chapter that will appear in a Space Science Series book Asteroids I
Phase Retrieval via Matrix Completion
This paper develops a novel framework for phase retrieval, a problem which
arises in X-ray crystallography, diffraction imaging, astronomical imaging and
many other applications. Our approach combines multiple structured
illuminations together with ideas from convex programming to recover the phase
from intensity measurements, typically from the modulus of the diffracted wave.
We demonstrate empirically that any complex-valued object can be recovered from
the knowledge of the magnitude of just a few diffracted patterns by solving a
simple convex optimization problem inspired by the recent literature on matrix
completion. More importantly, we also demonstrate that our noise-aware
algorithms are stable in the sense that the reconstruction degrades gracefully
as the signal-to-noise ratio decreases. Finally, we introduce some theory
showing that one can design very simple structured illumination patterns such
that three diffracted figures uniquely determine the phase of the object we
wish to recover
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