18 research outputs found
Dichteoptimierung und Strukturanalyse von Hartkugelpackungen
Bei der Verwendung von Hartkugelpackungen als Modelle fĂŒr verschiedene Systeme in Physik, Chemie und den Ingenieurwissenschaften kommen einige Fragen auf, z.B. nach dem Zusammenhang zwischen der Packungsdichte und der Radienverteilung der Kugeln bzw. der Packungsstruktur. Der erste Teil dieser Arbeit beschĂ€ftigt sich mit dem Problem der optimalen Packungsdichte von zufĂ€llig dichten Packungen. Es wird ein Optimierungsalgorithmus vorgestellt, der aus einer vorgegebenen Klasse von Radienverteilungen diejenige bestimmt, fĂŒr die die Packungsdichte maximal wird. Die Packungsstruktur kann man durch verschiedene statistische GröĂen charakterisieren, die im zweiten Teil dieser Arbeit beschrieben werden. Dabei wird die AbhĂ€ngigkeit dieser GröĂen von der Packungsdichte und der Radienverteilung untersucht und gezeigt, dass in monodispersen Packungen mit zunehmender Dichte erhebliche strukturelle VerĂ€nderungen auftreten: Im Dichteintervall zwischen 0,64 und 0,66 erfolgt offenbar ein Ăbergang von ungeordneten zu kristallinen Packungen, bei weiterer Verdichtung entwickelt sich schlieĂlich eine FCC-Struktur
Minimax Estimation of Distances on a Surface and Minimax Manifold Learning in the Isometric-to-Convex Setting
We start by considering the problem of estimating intrinsic distances on a
smooth surface. We show that sharper estimates can be obtained via a
reconstruction of the surface, and discuss the use of the tangential Delaunay
complex for that purpose. We further show that the resulting approximation rate
is in fact optimal in an information-theoretic (minimax) sense. We then turn to
manifold learning and argue that a variant of Isomap where the distances are
instead computed on a reconstructed surface is minimax optimal for the problem
of isometric manifold embedding
Factor Graphs for Computer Vision and Image Processing
Factor graphs have been used extensively in the decoding of error
correcting codes such as turbo codes, and in signal processing.
However, while computer vision and pattern recognition are awash
with graphical model usage, it is some-what surprising that
factor graphs are still somewhat under-researched in these
communities. This is surprising because factor graphs naturally
generalise both Markov random fields and Bayesian networks.
Moreover, they are useful in modelling relationships between
variables that are not necessarily probabilistic and allow for
efficient marginalisation via a sum-product of probabilities.
In this thesis, we present and illustrate the utility of factor
graphs in the vision community through some of the fieldâs
popular problems. The thesis does so with a particular focus on
maximum a posteriori (MAP) inference in graphical
structures with layers. To this end, we are able to break-down
complex problems into factored representations and more
computationally realisable constructions. Firstly, we present a
sum-product framework that uses the explicit factorisation
in local subgraphs from the partitioned factor graph of a layered
structure to perform inference. This provides an efficient method
to perform inference since exact inference is attainable in the
resulting local subtrees. Secondly, we extend this framework to
the entire graphical structure without partitioning, and discuss
preliminary ways to combine outputs from a multilevel
construction. Lastly, we further our endeavour to combine
evidence from different methods through
a simplicial spanning tree reparameterisation of the factor graph
in a way that ensures consistency, to produce an ensembled and
improved result. Throughout the thesis, the underlying feature we
make use of is to enforce adjacency constraints using Delaunay
triangulations computed by adding points dynamically, or using a
convex hull algorithm. The adjacency relationships from Delaunay
triangulations aid the factor graph approaches in this thesis to
be both efficient and
competitive for computer vision tasks. This is because of the low
treewidth they provide in local subgraphs, as well as the
reparameterised interpretation of the graph they form through the
spanning tree of simplexes. While exact inference is known to be
intractable for junction trees obtained from the loopy graphs in
computer vision, in this thesis we are able to effect exact
inference on our spanning tree of simplexes. More importantly,
the approaches presented here are not restricted to the computer
vision and image processing fields, but are extendable to more
general applications that involve distributed computations
3D Non-Rigid Reconstruction with Prior Shape Constraints
3D non-rigid shape recovery from a single uncalibrated camera is a challenging, under-constrained problem in computer vision. Although tremendous progress has been achieved towards solving the problem, two main limitations still exist in most previous solutions. First, current methods focus on non-incremental solutions, that is, the algorithms require collection of all the measurement data before the reconstruction takes place. This methodology is inherently unsuitable for applications requiring real-time solutions. At the same time, most of the existing approaches assume that 3D shapes can be accurately modelled in a linear subspace. These methods are simple and have been proven effective for reconstructions of objects with relatively small deformations, but have considerable limitations when the deformations are large or complex. The non-linear deformations are often observed in highly flexible objects for which the use of the linear model is impractical.
Note that specific types of shape variation might be governed by only a small number of parameters and therefore can be well-represented in a low dimensional manifold. The methods proposed in this thesis aim to estimate the non-rigid shapes and the corresponding camera trajectories, based on both the observations and the prior learned manifold.
Firstly, an incremental approach is proposed for estimating the deformable objects. An important advantage of this method is the ability to reconstruct the 3D shape from a newly observed image and update the parameters in 3D shape space. However, this recursive method assumes the deformable shapes only have small variations from a mean shape, thus is still not feasible for objects subject to large scale deformations. To address this problem, a series of approaches are proposed, all based on non-linear manifold learning techniques. Such manifold is used as a shape prior, with the reconstructed shapes constrained to lie within the manifold. Those non-linear manifold based approaches significantly improve the quality of reconstructed results and are well-adapted to different types of shapes undergoing significant and complex deformations.
Throughout the thesis, methods are validated quantitatively on 2D points sequences projected from the 3D motion capture data for a ground truth comparison, and are qualitatively demonstrated on real example of 2D video sequences. Comparisons are made for the proposed methods against several state-of-the-art techniques, with results shown for a variety of challenging deformable objects. Extensive experiments also demonstrate the robustness of the proposed algorithms with respect to measurement noise and missing data
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Twin Related Domains in Polycrystalline Nickel-Base Superalloys: 3D Structure and Fatigue
Fatigue is the life limiting property of polycrystalline nickel-base superalloys used in turbine disks in the hot section of turbine engines for aerospace and power generation applications. Fabricating components through a powder metallurgy route provides enhanced properties and removes many extrinsic defects associated with fatigue crack formation, driving cracks to initiate at intrinsic microstructrual extremes. Fatigue cracks in the powder metallurgy alloy René 88DT frequently initiate in large grains that are in the tail of the size distribution and contain favorably oriented annealing twin boundaries. Fully characterizing twin boundaries and twin related domains requires 3D microstructural volumes. Datasets of 3D microstructure for René 88DT were collected by TriBeam tomography across a range of resolutions and volumes to characterize microstructure and annealing twins. Algorithms developed to analyze these datasets allow identification of strain localizing sites from 2D cross sections and the frequency of microstructural features amenable to fatigue crack initiation is statistically assessed. Twin related domain structure is quantified via network analysis and leveraged to propose a criterion for identifying fatal fatigue crack sites