5,123 research outputs found
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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 patient’s
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
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Mini-Workshop: Analytical and Numerical Methods in Image and Surface Processing
The workshop successfully brought together researchers from mathematical analysis, numerical mathematics, computer graphics and image processing. The focus was on variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, image and surface denoising based on geometric evolution problems in image and surface fairing, physical modeling of surfaces, the restoration of images and surfaces using higher order variational formulations
Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures
The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly
transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit
parametrization of boundary surfaces to impose traction and displacement boundary conditions, which
constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing
traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model
generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as
initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer
all boundary terms in the variational formulation into volumetric terms. We show that in the context of the
voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions
defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field,
the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method
by analyzing stresses in a human femur and a vertebral body
Numerical inversion of SRNFs for efficient elastic shape analysis of star-shaped objects.
The elastic shape analysis of surfaces has proven useful in several application areas, including medical image analysis, vision, and graphics.
This approach is based on defining new mathematical representations of parameterized surfaces, including the square root normal field (SRNF), and then using the L2 norm to compare their shapes. Past work is based on using the pullback of the L2 metric to the space of surfaces, performing statistical analysis under this induced Riemannian metric. However, if one can estimate the inverse of the SRNF mapping, even approximately, a very efficient framework results: the surfaces, represented by their SRNFs, can be efficiently analyzed using standard Euclidean tools, and only the final results need be mapped back to the surface space. Here we describe a procedure for inverting SRNF maps of star-shaped surfaces, a special case for which analytic results can be obtained. We test our method via the classification of 34 cases of ADHD (Attention Deficit Hyperactivity Disorder), plus controls, in the Detroit Fetal Alcohol and Drug Exposure Cohort study. We obtain state-of-the-art results
A novel explicit design method for complex thin-walled structures based on embedded solid moving morphable components
In this article, a novel explicit approach for designing complex thin-walled
structures based on the Moving Morphable Component (MMC) method is proposed,
which provides a unified framework to systematically address various design
issues, including topology optimization, reinforced-rib layout optimization,
and sandwich structure design problems. The complexity of thin-walled
structures mainly comes from flexible geometries and the variation of
thickness. On the one hand, the geometric complexity of thin-walled structures
leads to the difficulty in automatically describing material distribution
(e.g., reinforced ribs). On the other hand, thin-walled structures with
different thicknesses require various hypotheses (e.g., Kirchhoff-Love shell
theory and Reissner-Mindlin shell theory) to ensure the precision of structural
responses. Whereas for cases that do not fit the shell hypothesis, the
precision loss of response solutions is nonnegligible in the optimization
process since the accumulation of errors will cause entirely different designs.
Hence, the current article proposes a novel embedded solid component to tackle
these challenges. The geometric constraints that make the components fit to the
curved thin-walled structure are whereby satisfied. Compared with traditional
strategies, the proposed method is free from the limit of shell assumptions of
structural analysis and can achieve optimized designs with clear load
transmission paths at the cost of few design variables and degrees of freedom
for finite element analysis (FEA). Finally, we apply the proposed method to
several representative examples to demonstrate its effectiveness, efficiency,
versatility, and potential to handle complex industrial structures
Volume-aware design of composite molds
© 2019 Association for Computing Machinery. We propose a novel technique for the automatic design of molds to cast highly complex shapes. The technique generates composite, two-piece molds. Each mold piece is made up of a hard plastic shell and a flexible silicone part. Thanks to the thin, soft, and smartly shaped silicone part, which is kept in place by a hard plastic shell, we can cast objects of unprecedented complexity. An innovative algorithm based on a volumetric analysis defines the layout of the internal cuts in the silicone mold part. Our approach can robustly handle thin protruding features and intertwined topologies that have caused previous methods to fail. We compare our results with state of the art techniques, and we demonstrate the casting of shapes with extremely complex geometry
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