5,297 research outputs found
Plane-extraction from depth-data using a Gaussian mixture regression model
We propose a novel algorithm for unsupervised extraction of piecewise planar
models from depth-data. Among other applications, such models are a good way of
enabling autonomous agents (robots, cars, drones, etc.) to effectively perceive
their surroundings and to navigate in three dimensions. We propose to do this
by fitting the data with a piecewise-linear Gaussian mixture regression model
whose components are skewed over planes, making them flat in appearance rather
than being ellipsoidal, by embedding an outlier-trimming process that is
formally incorporated into the proposed expectation-maximization algorithm, and
by selectively fusing contiguous, coplanar components. Part of our motivation
is an attempt to estimate more accurate plane-extraction by allowing each model
component to make use of all available data through probabilistic clustering.
The algorithm is thoroughly evaluated against a standard benchmark and is shown
to rank among the best of the existing state-of-the-art methods.Comment: 11 pages, 2 figures, 1 tabl
Approximation of the critical buckling factor for composite panels
This article is concerned with the approximation of the critical buckling factor for thin composite plates. A new method to improve the approximation of this critical factor is applied based on its behavior with respect to lamination parameters and loading conditions. This method allows accurate approximation of the critical buckling factor for non-orthotropic laminates under complex combined loadings (including shear loading). The influence of the stacking sequence and loading conditions is extensively studied as well as properties of the critical buckling factor behavior (e.g concavity over tensor D or out-of-plane lamination parameters). Moreover, the critical buckling factor is numerically shown to be piecewise linear for orthotropic laminates under combined loading whenever shear remains low and it is also shown to be piecewise continuous in the general case. Based on the numerically observed behavior, a new scheme for the approximation is applied that separates each buckling mode and builds linear, polynomial or rational regressions for each mode. Results of this approach and applications to structural optimization are presented
Two Empirical Regimes of the Planetary Mass-Radius Relation
Today, with the large number of detected exoplanets and improved
measurements, we can reach the next step of planetary characterization.
Classifying different populations of planets is not only important for our
understanding of the demographics of various planetary types in the galaxy, but
also for our understanding of planet formation. We explore the nature of two
regimes in the planetary mass-radius (M-R) relation. We suggest that the
transition between the two regimes of "small" and "large" planets, occurs at a
mass of 124 \pm 7, M_Earth and a radius of 12.1 \pm 0.5, R_Earth. Furthermore,
the M-R relation is R \propto M^{0.55\pm 0.02} and R \propto M^{0.01\pm0.02}
for small and large planets, respectively. We suggest that the location of the
breakpoint is linked to the onset of electron degeneracy in hydrogen, and
therefore, to the planetary bulk composition. Specifically, it is the
characteristic minimal mass of a planet which consists of mostly hydrogen and
helium, and therefore its M-R relation is determined by the equation of state
of these materials. We compare the M-R relation from observational data with
the one derived by population synthesis calculations and show that there is a
good qualitative agreement between the two samples.Comment: accepted for publication in A&
Statistical Inference using the Morse-Smale Complex
The Morse-Smale complex of a function decomposes the sample space into
cells where is increasing or decreasing. When applied to nonparametric
density estimation and regression, it provides a way to represent, visualize,
and compare multivariate functions. In this paper, we present some statistical
results on estimating Morse-Smale complexes. This allows us to derive new
results for two existing methods: mode clustering and Morse-Smale regression.
We also develop two new methods based on the Morse-Smale complex: a
visualization technique for multivariate functions and a two-sample,
multivariate hypothesis test.Comment: 45 pages, 13 figures. Accepted to Electronic Journal of Statistic
Caveats for information bottleneck in deterministic scenarios
Information bottleneck (IB) is a method for extracting information from one
random variable that is relevant for predicting another random variable
. To do so, IB identifies an intermediate "bottleneck" variable that has
low mutual information and high mutual information . The "IB
curve" characterizes the set of bottleneck variables that achieve maximal
for a given , and is typically explored by maximizing the "IB
Lagrangian", . In some cases, is a deterministic
function of , including many classification problems in supervised learning
where the output class is a deterministic function of the input . We
demonstrate three caveats when using IB in any situation where is a
deterministic function of : (1) the IB curve cannot be recovered by
maximizing the IB Lagrangian for different values of ; (2) there are
"uninteresting" trivial solutions at all points of the IB curve; and (3) for
multi-layer classifiers that achieve low prediction error, different layers
cannot exhibit a strict trade-off between compression and prediction, contrary
to a recent proposal. We also show that when is a small perturbation away
from being a deterministic function of , these three caveats arise in an
approximate way. To address problem (1), we propose a functional that, unlike
the IB Lagrangian, can recover the IB curve in all cases. We demonstrate the
three caveats on the MNIST dataset
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
Steered mixture-of-experts for light field images and video : representation and coding
Research in light field (LF) processing has heavily increased over the last decade. This is largely driven by the desire to achieve the same level of immersion and navigational freedom for camera-captured scenes as it is currently available for CGI content. Standardization organizations such as MPEG and JPEG continue to follow conventional coding paradigms in which viewpoints are discretely represented on 2-D regular grids. These grids are then further decorrelated through hybrid DPCM/transform techniques. However, these 2-D regular grids are less suited for high-dimensional data, such as LFs. We propose a novel coding framework for higher-dimensional image modalities, called Steered Mixture-of-Experts (SMoE). Coherent areas in the higher-dimensional space are represented by single higher-dimensional entities, called kernels. These kernels hold spatially localized information about light rays at any angle arriving at a certain region. The global model consists thus of a set of kernels which define a continuous approximation of the underlying plenoptic function. We introduce the theory of SMoE and illustrate its application for 2-D images, 4-D LF images, and 5-D LF video. We also propose an efficient coding strategy to convert the model parameters into a bitstream. Even without provisions for high-frequency information, the proposed method performs comparable to the state of the art for low-to-mid range bitrates with respect to subjective visual quality of 4-D LF images. In case of 5-D LF video, we observe superior decorrelation and coding performance with coding gains of a factor of 4x in bitrate for the same quality. At least equally important is the fact that our method inherently has desired functionality for LF rendering which is lacking in other state-of-the-art techniques: (1) full zero-delay random access, (2) light-weight pixel-parallel view reconstruction, and (3) intrinsic view interpolation and super-resolution
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