Ellipse-based Principal Component Analysis for Self-intersecting Curve Reconstruction from Noisy Point Sets

Surface reconstruction from cross cuts usually requires curve reconstruction from planar noisy point samples -- The output curves must form a possibly disconnected 1manifold for the surface reconstruction to proceed -- This article describes an implemented algorithm for the reconstruction of planar curves (1manifolds) out of noisy point samples of a sel-fintersecting or nearly sel-fintersecting planar curve C -- C:[a,b]⊂R→R is self-intersecting if C(u)=C(v), u≠v, u,v∈(a,b) (C(u) is the self-intersection point) -- We consider only transversal self-intersections, i.e. those for which the tangents of the intersecting branches at the intersection point do not coincide (C′(u)≠C′(v)) -- In the presence of noise, curves which self-intersect cannot be distinguished from curves which nearly sel fintersect -- Existing algorithms for curve reconstruction out of either noisy point samples or pixel data, do not produce a (possibly disconnected) Piecewise Linear 1manifold approaching the whole point sample -- The algorithm implemented in this work uses Principal Component Analysis (PCA) with elliptic support regions near the selfintersections -- The algorithm was successful in recovering contours out of noisy slice samples of a surface, for the Hand, Pelvis and Skull data sets -- As a test for the correctness of the obtained curves in the slice levels, they were input into an algorithm of surface reconstruction, leading to a reconstructed surface which reproduces the topological and geometrical properties of the original object -- The algorithm robustly reacts not only to statistical noncorrelation at the self-intersections(nonmanifold neighborhoods) but also to occasional high noise at the nonselfintersecting (1manifold) neighborhood

Properties of Rubble-Pile Asteroid (101955) Bennu from OSIRIS-REx Imaging and Thermal Analysis

Establishing the abundance and physical properties of regolith and boulders on asteroids is crucial for understanding the formation and degradation mechanisms at work on their surfaces. Using images and thermal data from NASA's Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) spacecraft, we show that asteroid (101955) Bennu's surface is globally rough, dense with boulders, and low in albedo. The number of boulders is surprising given Bennu's moderate thermal inertia, suggesting that simple models linking thermal inertia to particle size do not adequately capture the complexity relating these properties. At the same time, we find evidence for a wide range of particle sizes with distinct albedo characteristics. Our findings imply that ages of Bennu's surface particles span from the disruption of the asteroid's parent body (boulders) to recent in situ production (micrometre-scale particles)

Modeling morphological instabilities in lipid membranes with anchored amphiphilic polymers

Anchoring molecules, like amphiphilic polymers, are able to dynamically regulate membrane morphology. Such molecules insert their hydrophobic groups into the bilayer, generating a local membrane curvature. In order to minimize the elastic energy penalty, a dynamic shape instability may occur, as in the case of the curvature-driven pearling instability or the polymer-induced tubulation of lipid vesicles. We review recent works on modeling of such instabilities by means of a mesoscopic dynamic model of the phase-field kind, which take into account the bending energy of lipid bilayers

The dynamic geophysical environment of (101955) Bennu based on OSIRIS-REx measurements

The top-shaped morphology characteristic of asteroid (101955) Bennu, often found among fast-spinning asteroids and binary asteroid primaries, may have contributed substantially to binary asteroid formation. Yet a detailed geophysical analysis of this morphology for a fast-spinning asteroid has not been possible prior to the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) mission. Combining the measured Bennu mass and shape obtained during the Preliminary Survey phase of the OSIRIS-REx mission, we find a notable transition in Bennu’s surface slopes within its rotational Roche lobe, defined as the region where material is energetically trapped to the surface. As the intersection of the rotational Roche lobe with Bennu’s surface has been most recently migrating towards its equator (given Bennu’s increasing spin rate), we infer that Bennu’s surface slopes have been changing across its surface within the last million years. We also find evidence for substantial density heterogeneity within this body, suggesting that its interior is a mixture of voids and boulders. The presence of such heterogeneity and Bennu’s top shape are consistent with spin-induced failure at some point in its past, although the manner of its failure cannot yet be determined. Future measurements by the OSIRIS-REx spacecraft will provide insight into and may resolve questions regarding the formation and evolution of Bennu’s top-shape morphology and its link to the formation of binary asteroids

Evidence for widespread hydrated minerals on asteroid (101955) Bennu

Early spectral data from the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) mission reveal evidence for abundant hydrated minerals on the surface of near-Earth asteroid (101955) Bennu in the form of a near-infrared absorption near 2.7 µm and thermal infrared spectral features that are most similar to those of aqueously altered CM-type carbonaceous chondrites. We observe these spectral features across the surface of Bennu, and there is no evidence of substantial rotational variability at the spatial scales of tens to hundreds of metres observed to date. In the visible and near-infrared (0.4 to 2.4 µm) Bennu’s spectrum appears featureless and with a blue (negative) slope, confirming previous ground-based observations. Bennu may represent a class of objects that could have brought volatiles and organic chemistry to Earth

Flexible Fiber Surfaces: A Reeb-Free Approach

The fiber surface generalizes the popular isosurface to multi-fields, so that pre-images can be visualized as surfaces. As with the isosurface, however, the fiber surface suffers from visual occlusion. We propose to avoid such occlusion by restricting the components to only the relevant ones with a new component-wise flexing algorithm. The approach, flexible fiber surface, generalizes the manipulation idea found in the flexible isosurface for the fiber surface. The flexible isosurface in the original form, however, relies on the contour tree. For the fiber surface, this corresponds to the Reeb space, which is challenging for both the computation and user interaction. We thus take a Reeb-free approach, in which one does not compute the Reeb space. Under this constraint, we generalize a few selected interactions in the flexible isosurface and discuss the implication of the restriction

Loci Periodic Surface Reconstruction from Crystals

Recently a periodic surface (PS) model for computer aided nano design (CAND) was proposed. This implicit surface model can parametrically create Euclidean and hyperbolic geometries at atomic, molecular, and mesoscopic scales while supporting symmetric tiling and crystal packing. In this paper, loci surface reconstruction from crystals is studied based on a generalized PS model. © 2007 by CAD Solutions