106,488 research outputs found
Comparing Features of Three-Dimensional Object Models Using Registration Based on Surface Curvature Signatures
This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison
Curvature in Biological Systems: Its quantification, Emergence and Implications Across the Scales
Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology has been supported by numerous recent experimental and theoretical investigations in recent years. In this review, we first give a brief introduction to the key ideas of surface curvature in the context of biological systems and discuss the challenges that arise when measuring surface curvature. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, we address the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological and mechanical processes but that curvature acts also as a signal that co-determines these processes
Scale-based surface understanding using diffusion smoothing
The research discussed in this thesis is concerned with surface understanding from the
viewpoint of recognition-oriented, scale-related processing based on surface curvatures and
diffusion smoothing. Four problems below high level visual processing are investigated:
1) 3-dimensional data smoothing using a diffusion process;
2) Behaviour of shape features across multiple scales,
3) Surface segmentation over multiple scales; and
4) Symbolic description of surface features at multiple scales.
In this thesis, the noisy data smoothing problem is treated mathematically as a boundary
value problem of the diffusion equation instead of the well-known Gaussian convolution,
In such a way, it provides a theoretical basis to uniformly interpret the interrelationships
amongst diffusion smoothing, Gaussian smoothing, repeated averaging and
spline smoothing. It also leads to solving the problem with a numerical scheme of unconditional
stability, which efficiently reduces the computational complexity and preserves the
signs of curvatures along the surface boundaries.
Surface shapes are classified into eight types using the combinations of the signs of
the Gaussian curvature K and mean curvature H, both of which change at different scale
levels. Behaviour of surface shape features over multiple scale levels is discussed in
terms of the stability of large shape features, the creation, remaining and fading of small
shape features, the interaction between large and small features and the structure of
behaviour of the nested shape features in the KH sign image. It provides a guidance for
tracking the movement of shape features from fine to large scales and for setting up a surface
shape description accordingly.
A smoothed surface is partitioned into a set of regions based on curvature sign
homogeneity. Surface segmentation is posed as a problem of approximating a surface up
to the degree of Gaussian and mean curvature signs using the depth data alone How to
obtain feasible solutions of this under-determined problem is discussed, which includes the
surface curvature sign preservation, the reason that a sculptured surface can be segmented
with the KH sign image alone and the selection of basis functions of surface fitting for
obtaining the KH sign image or for region growing.
A symbolic description of the segmented surface is set up at each scale level. It is
composed of a dual graph and a geometrical property list for the segmented surface. The
graph describes the adjacency and connectivity among different patches as the
topological-invariant properties that allow some object's flexibility, whilst the geometrical
property list is added to the graph as constraints that reduce uncertainty. With this organisation,
a tower-like surface representation is obtained by tracking the movement of
significant features of the segmented surface through different scale levels, from which a
stable description can be extracted for inexact matching during object recognition
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The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature
Clinical imaging modalities are a mainstay of modern disease management, but the full utilization of imaging-based data remains elusive. Aortic disease is defined by anatomic scalars quantifying aortic size, even though aortic disease progression initiates complex shape changes. We present an imaging-based geometric descriptor, inspired by fundamental ideas from topology and soft-matter physics that captures dynamic shape evolution. The aorta is reduced to a two-dimensional mathematical surface in space whose geometry is fully characterized by the local principal curvatures. Disease causes deviation from the smooth bent cylindrical shape of normal aortas, leading to a family of highly heterogeneous surfaces of varying shapes and sizes. To deconvolute changes in shape from size, the shape is characterized using integrated Gaussian curvature or total curvature. The fluctuation in total curvature (δK) across aortic surfaces captures heterogeneous morphologic evolution by characterizing local shape changes. We discover that aortic morphology evolves with a power-law defined behavior with rapidly increasing δK forming the hallmark of aortic disease. Divergent δK is seen for highly diseased aortas indicative of impending topologic catastrophe or aortic rupture. We also show that aortic size (surface area or enclosed aortic volume) scales as a generalized cylinder for all shapes. Classification accuracy for predicting aortic disease state (normal, diseased with successful surgery, and diseased with failed surgical outcomes) is 92.8±1.7%. The analysis of δK can be applied on any three-dimensional geometric structure and thus may be extended to other clinical problems of characterizing disease through captured anatomic changes
Describing whisker morphology of the Carnivora
One of the largest ecological transitions in carnivoran evolution was the shift from terrestrial to aquatic lifestyles, which has driven morphological diversity in skulls and other skeletal structures. In this paper, we investigate the association between those lifestyles and whisker morphology. However, comparing whisker morphology over a range of species is challenging since the number of whiskers and their positions on the mystacial pads vary between species. Also, each whisker will be at a different stage of growth and may have incurred damage due to wear and tear. Identifying a way to easily capture whisker morphology in a small number of whisker samples would be beneficial. Here, we describe individual and species variation in whisker morphology from two-dimensional scans in red fox, European otter and grey seal. A comparison of long, caudal whiskers shows inter-species differences most clearly. We go on to describe global whisker shape in 24 species of carnivorans, using linear approximations of curvature and taper, as well as traditional morphometric methods. We also qualitatively examine surface texture, or the presence of scales, using scanning electron micrographs. We show that gross whisker shape is highly conserved, with whisker curvature and taper obeying simple linear relationships with length. However, measures of whisker base radius, length, and maybe even curvature, can vary between species and substrate preferences. Specifically, the aquatic species in our sample have thicker, shorter whiskers that are smoother, with less scales present than those of terrestrial species. We suggest that these thicker whiskers may be stiffer and able to maintain their shape and position during underwater sensing, but being stiffer may also increase wear
Coupling nonpolar and polar solvation free energies in implicit solvent models
Recent studies on the solvation of atomistic and nanoscale solutes indicate
that a strong coupling exists between the hydrophobic, dispersion, and
electrostatic contributions to the solvation free energy, a facet not
considered in current implicit solvent models. We suggest a theoretical
formalism which accounts for coupling by minimizing the Gibbs free energy of
the solvent with respect to a solvent volume exclusion function. The resulting
differential equation is similar to the Laplace-Young equation for the
geometrical description of capillary interfaces, but is extended to microscopic
scales by explicitly considering curvature corrections as well as dispersion
and electrostatic contributions. Unlike existing implicit solvent approaches,
the solvent accessible surface is an output of our model. The presented
formalism is illustrated on spherically or cylindrically symmetrical systems of
neutral or charged solutes on different length scales. The results are in
agreement with computer simulations and, most importantly, demonstrate that our
method captures the strong sensitivity of solvent expulsion and dewetting to
the particular form of the solvent-solute interactions.Comment: accpted in J. Chem. Phy
Stokesian jellyfish: Viscous locomotion of bilayer vesicles
Motivated by recent advances in vesicle engineering, we consider
theoretically the locomotion of shape-changing bilayer vesicles at low Reynolds
number. By modulating their volume and membrane composition, the vesicles can
be made to change shape quasi-statically in thermal equilibrium. When the
control parameters are tuned appropriately to yield periodic shape changes
which are not time-reversible, the result is a net swimming motion over one
cycle of shape deformation. For two classical vesicle models (spontaneous
curvature and bilayer coupling), we determine numerically the sequence of
vesicle shapes through an enthalpy minimization, as well as the fluid-body
interactions by solving a boundary integral formulation of the Stokes
equations. For both models, net locomotion can be obtained either by
continuously modulating fore-aft asymmetric vesicle shapes, or by crossing a
continuous shape-transition region and alternating between fore-aft asymmetric
and fore-aft symmetric shapes. The obtained hydrodynamic efficiencies are
similar to that of other low Reynolds number biological swimmers, and suggest
that shape-changing vesicles might provide an alternative to flagella-based
synthetic microswimmers
Coalescence of Liquid Drops
When two drops of radius touch, surface tension drives an initially
singular motion which joins them into a bigger drop with smaller surface area.
This motion is always viscously dominated at early times. We focus on the
early-time behavior of the radius \rmn of the small bridge between the two
drops. The flow is driven by a highly curved meniscus of length 2\pi \rmn and
width \Delta\ll\rmn around the bridge, from which we conclude that the
leading-order problem is asymptotically equivalent to its two-dimensional
counterpart. An exact two-dimensional solution for the case of inviscid
surroundings [Hopper, J. Fluid Mech. , 349 (1990)] shows that
\Delta \propto \rmn^3 and \rmn \sim (t\gamma/\pi\eta)\ln [t\gamma/(\eta
R)]; and thus the same is true in three dimensions. The case of coalescence
with an external viscous fluid is also studied in detail both analytically and
numerically. A significantly different structure is found in which the outer
fluid forms a toroidal bubble of radius \Delta \propto \rmn^{3/2} at the
meniscus and \rmn \sim (t\gamma/4\pi\eta) \ln [t\gamma/(\eta R)]. This basic
difference is due to the presence of the outer fluid viscosity, however small.
With lengths scaled by a full description of the asymptotic flow for
\rmn(t)\ll1 involves matching of lengthscales of order \rmn^2, \rmn^{3/2},
\rmn\rmn^{7/4}$.Comment: 36 pages, including 9 figure
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