2,595 research outputs found
Placental Flattening via Volumetric Parameterization
We present a volumetric mesh-based algorithm for flattening the placenta to a
canonical template to enable effective visualization of local anatomy and
function. Monitoring placental function in vivo promises to support pregnancy
assessment and to improve care outcomes. We aim to alleviate visualization and
interpretation challenges presented by the shape of the placenta when it is
attached to the curved uterine wall. To do so, we flatten the volumetric mesh
that captures placental shape to resemble the well-studied ex vivo shape. We
formulate our method as a map from the in vivo shape to a flattened template
that minimizes the symmetric Dirichlet energy to control distortion throughout
the volume. Local injectivity is enforced via constrained line search during
gradient descent. We evaluate the proposed method on 28 placenta shapes
extracted from MRI images in a clinical study of placental function. We achieve
sub-voxel accuracy in mapping the boundary of the placenta to the template
while successfully controlling distortion throughout the volume. We illustrate
how the resulting mapping of the placenta enhances visualization of placental
anatomy and function. Our code is freely available at
https://github.com/mabulnaga/placenta-flattening .Comment: MICCAI 201
Spectral Generalized Multi-Dimensional Scaling
Multidimensional scaling (MDS) is a family of methods that embed a given set
of points into a simple, usually flat, domain. The points are assumed to be
sampled from some metric space, and the mapping attempts to preserve the
distances between each pair of points in the set. Distances in the target space
can be computed analytically in this setting. Generalized MDS is an extension
that allows mapping one metric space into another, that is, multidimensional
scaling into target spaces in which distances are evaluated numerically rather
than analytically. Here, we propose an efficient approach for computing such
mappings between surfaces based on their natural spectral decomposition, where
the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS
procedure enables efficient embedding by implicitly incorporating smoothness of
the mapping into the problem, thereby substantially reducing the complexity
involved in its solution while practically overcoming its non-convex nature.
The method is compared to existing techniques that compute dense correspondence
between shapes. Numerical experiments of the proposed method demonstrate its
efficiency and accuracy compared to state-of-the-art approaches
A Metric for genus-zero surfaces
We present a new method to compare the shapes of genus-zero surfaces. We
introduce a measure of mutual stretching, the symmetric distortion energy, and
establish the existence of a conformal diffeomorphism between any two
genus-zero surfaces that minimizes this energy. We then prove that the energies
of the minimizing diffeomorphisms give a metric on the space of genus-zero
Riemannian surfaces. This metric and the corresponding optimal diffeomorphisms
are shown to have properties that are highly desirable for applications.Comment: 33 pages, 8 figure
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