59,346 research outputs found
A perturbative approach to the reconstruction of the eigenvalue spectrum of a normal covariance matrix from a spherically truncated counterpart
In this paper we propose a perturbative method for the reconstruction of the
covariance matrix of a multinormal distribution, under the assumption that the
only available information amounts to the covariance matrix of a spherically
truncated counterpart of the same distribution. We expand the relevant
equations up to the fourth perturbative order and discuss the analytic
properties of the first few perturbative terms. We finally compare the proposed
approach with an exact iterative algorithm (presented in Palombi et al. (2017))
in the hypothesis that the spherically truncated covariance matrix is estimated
from samples of various sizes.Comment: 39 pages, 7 figures. v2: version accepted for publication in J. Comp.
Appl. Mat
Shape Generation using Spatially Partitioned Point Clouds
We propose a method to generate 3D shapes using point clouds. Given a
point-cloud representation of a 3D shape, our method builds a kd-tree to
spatially partition the points. This orders them consistently across all
shapes, resulting in reasonably good correspondences across all shapes. We then
use PCA analysis to derive a linear shape basis across the spatially
partitioned points, and optimize the point ordering by iteratively minimizing
the PCA reconstruction error. Even with the spatial sorting, the point clouds
are inherently noisy and the resulting distribution over the shape coefficients
can be highly multi-modal. We propose to use the expressive power of neural
networks to learn a distribution over the shape coefficients in a
generative-adversarial framework. Compared to 3D shape generative models
trained on voxel-representations, our point-based method is considerably more
light-weight and scalable, with little loss of quality. It also outperforms
simpler linear factor models such as Probabilistic PCA, both qualitatively and
quantitatively, on a number of categories from the ShapeNet dataset.
Furthermore, our method can easily incorporate other point attributes such as
normal and color information, an additional advantage over voxel-based
representations.Comment: To appear at BMVC 201
Recognizing Partial Cubes in Quadratic Time
We show how to test whether a graph with n vertices and m edges is a partial
cube, and if so how to find a distance-preserving embedding of the graph into a
hypercube, in the near-optimal time bound O(n^2), improving previous O(nm)-time
solutions.Comment: 25 pages, five figures. This version significantly expands previous
versions, including a new report on an implementation of the algorithm and
experiments with i
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