43,350 research outputs found
Morphological shape generation through user-controlled group metamorphosis
Morphological shape design is interpreted in this paper as a search for new shapes from a particular application domain represented by a set of selected shape instances. This paper proposes a new foundation for morphological shape design and generation. In contrast to existing generative procedures, an approach based on a user-controlled metamorphosis between functionally based shape models is presented. A formulation of the pairwise metamorphosis is proposed with a variety of functions described for the stages of deformation, morphing and offsetting. This formulation is then extended to the metamorphosis between groups of shapes with user-defined, dynamically correlated and weighted feature elements. A practical system was implemented in the form of plugin to Maya and tested by an industrial designer on a group of representative shapes from a particular domain. Ā© 2013 Elsevier Ltd
Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates
The study of cerebral anatomy in developing neonates is of great importance for
the understanding of brain development during the early period of life. This
dissertation therefore focuses on three challenges in the modelling of cerebral
anatomy in neonates during brain development. The methods that have been
developed all use Magnetic Resonance Images (MRI) as source data.
To facilitate study of vascular development in the neonatal period, a set of image
analysis algorithms are developed to automatically extract and model cerebral
vessel trees. The whole process consists of cerebral vessel tracking from
automatically placed seed points, vessel tree generation, and vasculature
registration and matching. These algorithms have been tested on clinical Time-of-
Flight (TOF) MR angiographic datasets.
To facilitate study of the neonatal cortex a complete cerebral cortex segmentation
and reconstruction pipeline has been developed. Segmentation of the neonatal
cortex is not effectively done by existing algorithms designed for the adult brain
because the contrast between grey and white matter is reversed. This causes pixels
containing tissue mixtures to be incorrectly labelled by conventional methods. The
neonatal cortical segmentation method that has been developed is based on a novel
expectation-maximization (EM) method with explicit correction for mislabelled
partial volume voxels. Based on the resulting cortical segmentation, an implicit
surface evolution technique is adopted for the reconstruction of the cortex in
neonates. The performance of the method is investigated by performing a detailed
landmark study.
To facilitate study of cortical development, a cortical surface registration algorithm
for aligning the cortical surface is developed. The method first inflates extracted
cortical surfaces and then performs a non-rigid surface registration using free-form
deformations (FFDs) to remove residual alignment. Validation experiments using
data labelled by an expert observer demonstrate that the method can capture local
changes and follow the growth of specific sulcus
Space-Time Transfinite Interpolation of Volumetric Material Properties
The paper presents a novel technique based on extension of a general mathematical method of transfinite interpolation to solve an actual problem in the context of a heterogeneous volume modelling area. It deals with time-dependent changes to the volumetric material properties (material density, colour and others) as a transformation of the volumetric material distributions in space-time accompanying geometric shape transformations such as metamorphosis. The main idea is to represent the geometry of both objects by scalar fields with distance properties, to establish in a higher-dimensional space a time gap during which the geometric transformation takes place, and to use these scalar fields to apply the new space-time transfinite interpolation to volumetric material attributes within this time gap. The proposed solution is analytical in its nature, does not require heavy numerical computations and can be used in real-time applications. Applications of this technique also include texturing and displacement mapping of time-variant surfaces, and parametric design of volumetric microstructures
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Customized design of hearing aids using statistical shape learning
3D shape modeling is a crucial component of rapid prototyping systems
that customize shapes of implants and prosthetic devices to a patientās
anatomy. In this paper, we present a solution to the problem of customized 3D
shape modeling using a statistical shape analysis framework. We design a novel
method to learn the relationship between two classes of shapes, which are related
by certain operations or transformation. The two associated shape classes are
represented in a lower dimensional manifold, and the reduced set of parameters
obtained in this subspace is utilized in an estimation, which is exemplified by a
multivariate regression in this paper.We demonstrate our method with a felicitous
application to estimation of customized hearing aid devices
Solving the incompressible surface Navier-Stokes equation by surface finite elements
We consider a numerical approach for the incompressible surface Navier-Stokes
equation on surfaces with arbitrary genus . The approach is
based on a reformulation of the equation in Cartesian coordinates of the
embedding , penalization of the normal component, a Chorin
projection method and discretization in space by surface finite elements for
each component. The approach thus requires only standard ingredients which most
finite element implementations can offer. We compare computational results with
discrete exterior calculus (DEC) simulations on a torus and demonstrate the
interplay of the flow field with the topology by showing realizations of the
Poincar\'e-Hopf theorem on -tori
Solving the time-dependent Schr\"odinger equation with absorbing boundary conditions and source terms in Mathematica 6.0
In recent decades a lot of research has been done on the numerical solution
of the time-dependent Schr\"odinger equation. On the one hand, some of the
proposed numerical methods do not need any kind of matrix inversion, but source
terms cannot be easily implemented into this schemes; on the other, some
methods involving matrix inversion can implement source terms in a natural way,
but are not easy to implement into some computational software programs widely
used by non-experts in programming (e.g. Mathematica). We present a simple
method to solve the time-dependent Schr\"odinger equation by using a standard
Crank-Nicholson method together with a Cayley's form for the finite-difference
representation of evolution operator. Here, such standard numerical scheme has
been simplified by inverting analytically the matrix of the evolution operator
in position representation. The analytical inversion of the N x N matrix let us
easily and fully implement the numerical method, with or without source terms,
into Mathematica or even into any numerical computing language or computational
software used for scientific computing.Comment: 15 pages, 7 figure
Modelling cell movement and chemotaxis pseudopod based feedback
A computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis. An empirical pattern formation model, based on a system of non-linear reaction-diffusion equations, is approximated on an evolving cell boundary using an Arbitrary Lagrangian Eulerian surface finite element method (ALE-SFEM). The solution state is used to drive a mechanical model of the protrusive and retractive forces exerted on the cell boundary. Movement of the cell is achieved using a level set method. Results are presented for cell migration with and without chemotaxis. The simulated behaviour is compared with experimental results of migrating Dictyostelium discoideum cells
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