7,169 research outputs found
From 3D Point Clouds to Pose-Normalised Depth Maps
We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)
Applying inversion to construct rational spiral curves
A method is proposed to construct spiral curves by inversion of a spiral arc
of parabola. The resulting curve is rational of 4-th order. Proper selection of
the parabolic arc and parameters of inversion allows to match a wide range of
boundary conditions, namely, tangents and curvatures at the endpoints,
including those, assuming inflection.Comment: 18 pages, 11 figure
Gauge Invariant Framework for Shape Analysis of Surfaces
This paper describes a novel framework for computing geodesic paths in shape
spaces of spherical surfaces under an elastic Riemannian metric. The novelty
lies in defining this Riemannian metric directly on the quotient (shape) space,
rather than inheriting it from pre-shape space, and using it to formulate a
path energy that measures only the normal components of velocities along the
path. In other words, this paper defines and solves for geodesics directly on
the shape space and avoids complications resulting from the quotient operation.
This comprehensive framework is invariant to arbitrary parameterizations of
surfaces along paths, a phenomenon termed as gauge invariance. Additionally,
this paper makes a link between different elastic metrics used in the computer
science literature on one hand, and the mathematical literature on the other
hand, and provides a geometrical interpretation of the terms involved. Examples
using real and simulated 3D objects are provided to help illustrate the main
ideas.Comment: 15 pages, 11 Figures, to appear in IEEE Transactions on Pattern
Analysis and Machine Intelligence in a better resolutio
A method for delineation of bone surfaces in photoacoustic computed tomography of the finger
Photoacoustic imaging of interphalangeal peripheral joints is of interest in
the context of using the synovial membrane as a surrogate marker of rheumatoid
arthritis. Previous work has shown that ultrasound produced by absorption of
light at the epidermis reflects on the bone surfaces within the finger. When
the reflected signals are backprojected in the region of interest, artifacts
are produced, confounding interpretation of the images. In this work, we
present an approach where the photoacoustic signals known to originate from the
epidermis, are treated as virtual ultrasound transmitters, and a separate
reconstruction is performed as in ultrasound reflection imaging. This allows us
to identify the bone surfaces. Further, the identification of the joint space
is important as this provides a landmark to localize a region-of-interest in
seeking the inflamed synovial membrane. The ability to delineate bone surfaces
allows us not only to identify the artifacts, but also to identify the
interphalangeal joint space without recourse to new US hardware or a new
measurement. We test the approach on phantoms and on a healthy human finger
Imagining circles: empirical data and a perceptual model for the arc-size illusion
An essential part of visual object recognition is the evaluation of the curvature of both an object's outline as well as the contours on its surface. We studied a striking illusion of visual curvature--the arc-size illusion (ASI)--to gain insight into the visual coding of curvature. In the ASI, short arcs are perceived as flatter (less curved) compared to longer arcs of the same radius. We investigated if and how the ASI depends on (i) the physical size of the stimulus and (ii) on the length of the arc. Our results show that perceived curvature monotonically increases with arc length up to an arc angle of about 60°, thereafter remaining constant and equal to the perceived curvature of a full circle. We investigated if the misjudgment of curvature in the ASI translates into predictable biases for three other perceptual tasks: (i) judging the position of the centre of circular arcs; (ii) judging if two circular arcs fall on the circumference of the same (invisible) circle and (iii) interpolating the position of a point on the circumference of a circle defined by two circular arcs. We found that the biases in all the above tasks were reliably predicted by the same bias mediating the ASI. We present a simple model, based on the central angle subtended by an arc, that captures the data for all tasks. Importantly, we argue that the ASI and related biases are a consequence of the fact that an object's curvature is perceived as constant with viewing distance, in other words is perceptually scale invariant
The geometry of nonlinear least squares with applications to sloppy models and optimization
Parameter estimation by nonlinear least squares minimization is a common
problem with an elegant geometric interpretation: the possible parameter values
of a model induce a manifold in the space of data predictions. The minimization
problem is then to find the point on the manifold closest to the data. We show
that the model manifolds of a large class of models, known as sloppy models,
have many universal features; they are characterized by a geometric series of
widths, extrinsic curvatures, and parameter-effects curvatures. A number of
common difficulties in optimizing least squares problems are due to this common
structure. First, algorithms tend to run into the boundaries of the model
manifold, causing parameters to diverge or become unphysical. We introduce the
model graph as an extension of the model manifold to remedy this problem. We
argue that appropriate priors can remove the boundaries and improve convergence
rates. We show that typical fits will have many evaporated parameters. Second,
bare model parameters are usually ill-suited to describing model behavior; cost
contours in parameter space tend to form hierarchies of plateaus and canyons.
Geometrically, we understand this inconvenient parametrization as an extremely
skewed coordinate basis and show that it induces a large parameter-effects
curvature on the manifold. Using coordinates based on geodesic motion, these
narrow canyons are transformed in many cases into a single quadratic, isotropic
basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting
algorithms as an Euler approximation to geodesic motion in these natural
coordinates on the model manifold and the model graph respectively. By adding a
geodesic acceleration adjustment to these algorithms, we alleviate the
difficulties from parameter-effects curvature, improving both efficiency and
success rates at finding good fits.Comment: 40 pages, 29 Figure
Computing parametrized solutions for plasmonic nanogap structures
The interaction of electromagnetic waves with metallic nanostructures
generates resonant oscillations of the conduction-band electrons at the metal
surface. These resonances can lead to large enhancements of the incident field
and to the confinement of light to small regions, typically several orders of
magnitude smaller than the incident wavelength. The accurate prediction of
these resonances entails several challenges. Small geometric variations in the
plasmonic structure may lead to large variations in the electromagnetic field
responses. Furthermore, the material parameters that characterize the optical
behavior of metals at the nanoscale need to be determined experimentally and
are consequently subject to measurement errors. It then becomes essential that
any predictive tool for the simulation and design of plasmonic structures
accounts for fabrication tolerances and measurement uncertainties.
In this paper, we develop a reduced order modeling framework that is capable
of real-time accurate electromagnetic responses of plasmonic nanogap structures
for a wide range of geometry and material parameters. The main ingredients of
the proposed method are: (i) the hybridizable discontinuous Galerkin method to
numerically solve the equations governing electromagnetic wave propagation in
dielectric and metallic media, (ii) a reference domain formulation of the
time-harmonic Maxwell's equations to account for geometry variations; and (iii)
proper orthogonal decomposition and empirical interpolation techniques to
construct an efficient reduced model. To demonstrate effectiveness of the
models developed, we analyze geometry sensitivities and explore optimal designs
of a 3D periodic annular nanogap structure.Comment: 28 pages, 9 figures, 4 tables, 2 appendice
Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications
Phase mixing of chaotic orbits exponentially distributes these orbits through
their accessible phase space. This phenomenon, commonly called ``chaotic
mixing'', stands in marked contrast to phase mixing of regular orbits which
proceeds as a power law in time. It is operationally irreversible; hence, its
associated e-folding time scale sets a condition on any process envisioned for
emittance compensation. A key question is whether beams can support chaotic
orbits, and if so, under what conditions? We numerically investigate the
parameter space of three-dimensional thermal-equilibrium beams with space
charge, confined by linear external focusing forces, to determine whether the
associated potentials support chaotic orbits. We find that a large subset of
the parameter space does support chaos and, in turn, chaotic mixing. Details
and implications are enumerated.Comment: 39 pages, including 14 figure
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