95,688 research outputs found
Distance-Sensitive Planar Point Location
Let be a connected planar polygonal subdivision with edges
that we want to preprocess for point-location queries, and where we are given
the probability that the query point lies in a polygon of
. We show how to preprocess such that the query time
for a point~ depends on~ and, in addition, on the distance
from to the boundary of~---the further away from the boundary, the
faster the query. More precisely, we show that a point-location query can be
answered in time , where
is the shortest Euclidean distance of the query point~ to the
boundary of . Our structure uses space and
preprocessing time. It is based on a decomposition of the regions of
into convex quadrilaterals and triangles with the following
property: for any point , the quadrilateral or triangle
containing~ has area . For the special case where
is a subdivision of the unit square and
, we present a simpler solution that achieves a
query time of . The latter solution can be extended to
convex subdivisions in three dimensions
Diagnostic-robust statistical analysis for Local Surface Fitting in 3D Point Cloud Data
Objectives: Surface reconstruction and fitting for geometric primitives and three Dimensional (3D) modeling is a fundamental task in the field of photogrammetry and reverse engineering. However it is impractical to get point cloud data without outliers/noise being present. The noise in the data acquisition process induces rough and uneven surfaces, and reduces the precision/accuracy of the acquired model. This paper investigates the problem of local surface reconstruction and best fitting from unorganized outlier contaminated 3D point cloud data. Methods: Least Squares (LS) method, Principal Component Analysis (PCA) and RANSAC are the three most popular techniques for fitting planar surfaces to 2D and 3D data. All three methods are affected by outliers and do not give reliable and robust parameter estimation. In the statistics literature, robust techniques and outlier diagnostics are two complementary approaches but any one alone is not sufficient for outlier detection and robust parameter estimation. We propose a diagnostic-robust statistical algorithm that uses both approaches in combination for fitting planar surfaces in the presence of outliers.Robust distance is used as a multivariate diagnostic technique for outlier detection and robust PCA is used as an outlier resistant technique for plane fitting. The robust distance is the robustification of the well-known Mohalanobis distance by using the recently introduced high breakdown Minimum Covariance Determinant (MCD) location and scatter estimates. The classical PCA measures data variability through the variance and the corresponding directions are the latent vectors which are sensitive to outlying observations. In contrast, the robust PCA which combines the 'projection pursuit' approach with a robust scatter matrix based on the MCD of the covariance matrix, is robust with outlying observations in the dataset. In addition, robust PCA produces graphical displays of orthogonal distance and score distance as the by-products which can detects outliers and aids better robust fitting by using robust PCA for a second time in the final plane fitting stage. In summary, the proposed method removes the outliers first and then fits the local surface in a robust way.Results and conclusions: We present a new diagnostic-robust statistical technique for local surface fitting in 3D point cloud data. Finally, the benefits of the new diagnostic-robust algorithm are demonstrated through an artificial dataset and several terrestrial mobile mapping laser scanning point cloud datasets. Comparative results show that the classical LS and PCA methods are very sensitive to outliers and failed to reliably fit planes. The RANSAC algorithm is not completely free from the effect of outliers and requires more processing time for large datasets. The proposed method smooths away noise and is significantly better and efficient than the other three methods for local planar surface fitting even in the presence of roughness. This method is applicable for 3D straight line fitting as well and has great potential for local normal estimation and different types of surface fitting
Shape from periodic texture using the eigenvectors of local affine distortion
This paper shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly, without the need for iterative numerical optimization, We work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks. The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces. In particular, the leading eigenvector points in the tilt direction. Although not as geometrically transparent, the direction of the second eigenvector can be used to estimate the slant direction. The required affine distortion matrices are computed using the correspondences between spectral peaks, established on the basis of their energy ordering. We apply the method to a variety of real-world and synthetic imagery
Projection lens scanning laser velocimeter system
A laser Doppler velocimeter system is disclosed that has a laser, a waist position adjusting lens, and a beam splitter which direct laser beams parallel to the optical axis of the negative lens. The negative lens is fixed relative to an afocal lens pair. A pair of planar mirrors intersect at right angles and respectively intersect the optical axis and the optical axis of the afocal lens pair. Mirrors are movable along the optical axis toward and away from the afocal lens pair to focus the laser beams in focus area while maintaining a constant beam waist, crossing angle, and intersection with other laser beams. This produces a constant sensitive volume as the focus is changed
Planar Detonation Wave Initiation in Large-Aspect-Ratio Channels
In this study, two initiator designs are presented that are able to form planar detonations with low input energy in large-aspect-ratio channels over distances corresponding to only a few channel heights. The initiators use a single spark and an array of small channels to shape the detonation wave. The first design, referred to as the static initiator, is simple to construct as it consists of straight channels which connect at right angles. However, it is only able to create planar waves using mixtures that can reliably detonate in its small-width channels. An improved design, referred to as the dynamic initiator, is capable of detonating insensitive mixtures using an oxyacetylene gas slug injected into the initiator shortly before ignition, but is more complex to construct. The two versions are presented next, including an overview of their design and operation. Design drawings of each initiator are available elsewhere [7]. Finally, photographs and pressure traces of the resulting planar waves generated by each device are shown
Constructing elastic distinguishability metrics for location privacy
With the increasing popularity of hand-held devices, location-based
applications and services have access to accurate and real-time location
information, raising serious privacy concerns for their users. The recently
introduced notion of geo-indistinguishability tries to address this problem by
adapting the well-known concept of differential privacy to the area of
location-based systems. Although geo-indistinguishability presents various
appealing aspects, it has the problem of treating space in a uniform way,
imposing the addition of the same amount of noise everywhere on the map. In
this paper we propose a novel elastic distinguishability metric that warps the
geometrical distance, capturing the different degrees of density of each area.
As a consequence, the obtained mechanism adapts the level of noise while
achieving the same degree of privacy everywhere. We also show how such an
elastic metric can easily incorporate the concept of a "geographic fence" that
is commonly employed to protect the highly recurrent locations of a user, such
as his home or work. We perform an extensive evaluation of our technique by
building an elastic metric for Paris' wide metropolitan area, using semantic
information from the OpenStreetMap database. We compare the resulting mechanism
against the Planar Laplace mechanism satisfying standard
geo-indistinguishability, using two real-world datasets from the Gowalla and
Brightkite location-based social networks. The results show that the elastic
mechanism adapts well to the semantics of each area, adjusting the noise as we
move outside the city center, hence offering better overall privacy
Density Functional Theory of a Curved Liquid-Vapour Interface: Evaluation of the rigidity constants
It is argued that to arrive at a quantitative description of the surface
tension of a liquid drop as a function of its inverse radius, it is necessary
to include the bending rigidity k and Gaussian rigidity k_bar in its
description. New formulas for k and k_bar in the context of density functional
theory with a non-local, integral expression for the interaction between
molecules are presented. These expressions are used to investigate the
influence of the choice of Gibbs dividing surface and it is shown that for a
one-component system, the equimolar surface has a special status in the sense
that both k and k_bar are then the least sensitive to a change in the location
of the dividing surface. Furthermore, the equimolar value for k corresponds to
its maximum value and the equimolar value for k_bar corresponds to its minimum
value. An explicit evaluation using a short-ranged interaction potential
between molecules, shows that k is negative with a value around minus 0.5-1.0
kT and that k_bar is positive with a value which is a bit more than half the
magnitude of k. Finally, for dispersion forces between molecules, we show that
a term proportional to log(R)/R^2 replaces the rigidity constants and we
determine the (universal) proportionality constants.Comment: 28 pages; 5 figures; accepted for publication in J. Phys.: Condens.
Matter (2013
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