48,889 research outputs found
A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren & Hauck [29] suggests that the filtered spherical
harmonics method represents an efficient, robust, and accurate method for
radiation transport, at least in the two-dimensional (2D) case. We extend their
work to the three-dimensional (3D) case and find that all of the advantages of
the filtering approach identified in 2D are present also in the 3D case. We
reformulate the filter operation in a way that is independent of the timestep
and of the spatial discretization. We also explore different second- and
fourth-order filters and find that the second-order ones yield significantly
better results. Overall, our findings suggest that the filtered spherical
harmonics approach represents a very promising method for 3D radiation
transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of
Computational Physic
Bilateral Filter: Graph Spectral Interpretation and Extensions
In this paper we study the bilateral filter proposed by Tomasi and Manduchi,
as a spectral domain transform defined on a weighted graph. The nodes of this
graph represent the pixels in the image and a graph signal defined on the nodes
represents the intensity values. Edge weights in the graph correspond to the
bilateral filter coefficients and hence are data adaptive. Spectrum of a graph
is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian
matrix. We use this spectral interpretation to generalize the bilateral filter
and propose more flexible and application specific spectral designs of
bilateral-like filters. We show that these spectral filters can be implemented
with k-iterative bilateral filtering operations and do not require expensive
diagonalization of the Laplacian matrix
Higher-order interference and single-system postulates characterizing quantum theory
We present a new characterization of quantum theory in terms of simple
physical principles that is different from previous ones in two important
respects: first, it only refers to properties of single systems without any
assumptions on the composition of many systems; and second, it is closer to
experiment by having absence of higher-order interference as a postulate, which
is currently the subject of experimental investigation. We give three
postulates -- no higher-order interference, classical decomposability of
states, and strong symmetry -- and prove that the only non-classical
operational probabilistic theories satisfying them are real, complex, and
quaternionic quantum theory, together with 3-level octonionic quantum theory
and ball state spaces of arbitrary dimension. Then we show that adding
observability of energy as a fourth postulate yields complex quantum theory as
the unique solution, relating the emergence of the complex numbers to the
possibility of Hamiltonian dynamics. We also show that there may be interesting
non-quantum theories satisfying only the first two of our postulates, which
would allow for higher-order interference in experiments while still respecting
the contextuality analogue of the local orthogonality principle.Comment: 21 + 6 pages, 1 figure. v4: published version (includes several minor
corrections
Efficient MRF Energy Propagation for Video Segmentation via Bilateral Filters
Segmentation of an object from a video is a challenging task in multimedia
applications. Depending on the application, automatic or interactive methods
are desired; however, regardless of the application type, efficient computation
of video object segmentation is crucial for time-critical applications;
specifically, mobile and interactive applications require near real-time
efficiencies. In this paper, we address the problem of video segmentation from
the perspective of efficiency. We initially redefine the problem of video
object segmentation as the propagation of MRF energies along the temporal
domain. For this purpose, a novel and efficient method is proposed to propagate
MRF energies throughout the frames via bilateral filters without using any
global texture, color or shape model. Recently presented bi-exponential filter
is utilized for efficiency, whereas a novel technique is also developed to
dynamically solve graph-cuts for varying, non-lattice graphs in general linear
filtering scenario. These improvements are experimented for both automatic and
interactive video segmentation scenarios. Moreover, in addition to the
efficiency, segmentation quality is also tested both quantitatively and
qualitatively. Indeed, for some challenging examples, significant time
efficiency is observed without loss of segmentation quality.Comment: Multimedia, IEEE Transactions on (Volume:16, Issue: 5, Aug. 2014
Static/Dynamic Filtering for Mesh Geometry
The joint bilateral filter, which enables feature-preserving signal smoothing
according to the structural information from a guidance, has been applied for
various tasks in geometry processing. Existing methods either rely on a static
guidance that may be inconsistent with the input and lead to unsatisfactory
results, or a dynamic guidance that is automatically updated but sensitive to
noises and outliers. Inspired by recent advances in image filtering, we propose
a new geometry filtering technique called static/dynamic filter, which utilizes
both static and dynamic guidances to achieve state-of-the-art results. The
proposed filter is based on a nonlinear optimization that enforces smoothness
of the signal while preserving variations that correspond to features of
certain scales. We develop an efficient iterative solver for the problem, which
unifies existing filters that are based on static or dynamic guidances. The
filter can be applied to mesh face normals followed by vertex position update,
to achieve scale-aware and feature-preserving filtering of mesh geometry. It
also works well for other types of signals defined on mesh surfaces, such as
texture colors. Extensive experimental results demonstrate the effectiveness of
the proposed filter for various geometry processing applications such as mesh
denoising, geometry feature enhancement, and texture color filtering
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
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