2,574 research outputs found
Localized Manifold Harmonics for Spectral Shape Analysis
The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases
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
VConv-DAE: Deep Volumetric Shape Learning Without Object Labels
With the advent of affordable depth sensors, 3D capture becomes more and more
ubiquitous and already has made its way into commercial products. Yet,
capturing the geometry or complete shapes of everyday objects using scanning
devices (e.g. Kinect) still comes with several challenges that result in noise
or even incomplete shapes. Recent success in deep learning has shown how to
learn complex shape distributions in a data-driven way from large scale 3D CAD
Model collections and to utilize them for 3D processing on volumetric
representations and thereby circumventing problems of topology and
tessellation. Prior work has shown encouraging results on problems ranging from
shape completion to recognition. We provide an analysis of such approaches and
discover that training as well as the resulting representation are strongly and
unnecessarily tied to the notion of object labels. Thus, we propose a full
convolutional volumetric auto encoder that learns volumetric representation
from noisy data by estimating the voxel occupancy grids. The proposed method
outperforms prior work on challenging tasks like denoising and shape
completion. We also show that the obtained deep embedding gives competitive
performance when used for classification and promising results for shape
interpolation
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