103 research outputs found
Multifractal detrending moving average cross-correlation analysis
There are a number of situations in which several signals are simultaneously
recorded in complex systems, which exhibit long-term power-law
cross-correlations. The multifractal detrended cross-correlation analysis
(MF-DCCA) approaches can be used to quantify such cross-correlations, such as
the MF-DCCA based on detrended fluctuation analysis (MF-X-DFA) method. We
develop in this work a class of MF-DCCA algorithms based on the detrending
moving average analysis, called MF-X-DMA. The performances of the MF-X-DMA
algorithms are compared with the MF-X-DFA method by extensive numerical
experiments on pairs of time series generated from bivariate fractional
Brownian motions, two-component autoregressive fractionally integrated moving
average processes and binomial measures, which have theoretical expressions of
the multifractal nature. In all cases, the scaling exponents extracted
from the MF-X-DMA and MF-X-DFA algorithms are very close to the theoretical
values. For bivariate fractional Brownian motions, the scaling exponent of the
cross-correlation is independent of the cross-correlation coefficient between
two time series and the MF-X-DFA and centered MF-X-DMA algorithms have
comparative performance, which outperform the forward and backward MF-X-DMA
algorithms. We apply these algorithms to the return time series of two stock
market indexes and to their volatilities. For the returns, the centered
MF-X-DMA algorithm gives the best estimates of since its
is closest to 0.5 as expected, and the MF-X-DFA algorithm has the
second best performance. For the volatilities, the forward and backward
MF-X-DMA algorithms give similar results, while the centered MF-X-DMA and the
MF-X-DFA algorithms fails to extract rational multifractal nature.Comment: 15 pages, 4 figures, 2 matlab codes for MF-X-DMA and MF-X-DF
Revisiting Digital Straight Segment Recognition
This paper presents new results about digital straight segments, their
recognition and related properties. They come from the study of the
arithmetically based recognition algorithm proposed by I. Debled-Rennesson and
J.-P. Reveill\`es in 1995 [Debled95]. We indeed exhibit the relations
describing the possible changes in the parameters of the digital straight
segment under investigation. This description is achieved by considering new
parameters on digital segments: instead of their arithmetic description, we
examine the parameters related to their combinatoric description. As a result
we have a better understanding of their evolution during recognition and
analytical formulas to compute them. We also show how this evolution can be
projected onto the Stern-Brocot tree. These new relations have interesting
consequences on the geometry of digital curves. We show how they can for
instance be used to bound the slope difference between consecutive maximal
segments
Unsupervised Polygonal Reconstruction of Noisy Contours by a Discrete Irregular Approach
International audienceIn this paper, we present an original algorithm to build a polygonal reconstruction of noisy digital contours. For this purpose, we first improve an algorithm devoted to the vectorization of discrete irregular isothetic objects. Afterwards we propose to use it to define a reconstruction process of noisy digital contours. More precisely, we use a local noise detector, introduced by Kerautret and Lachaud in IWCIA 2009, that builds a multi-scale representation of the digital contour, which is composed of pixels of various size depending of the local amount of noise. Finally, we compare our approach with previous works, by con- sidering the Hausdorff distance and the error on tangent orientations of the computed line segments to the original perfect contour. Thanks to both synthetic and real noisy objects, we show that our approach has interesting performance, and could be applied in document analysis systems
Analysis of Sample Correlations for Monte Carlo Rendering
Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.publishe
Digital surface regularization by normal vector field alignment
International audienceDigital objects and digital surfaces are isothetic structures per se. Such surfaces are thus not adapted to direct visualization with isothetic quads, or to many geometry processing methods. We propose a new regularization technique to construct a piecewise smooth quad-rangulated surface from a digital surface. More formally we propose a variational formulation which efficiently regularizes digital surface ver-tices while complying with a prescribed, eventually anisotropic, input normal vector field estimated on the digital structure. Beside visualiza-tion purposes, such regularized surface can then be used in any geometry processing tasks which operates on triangular or quadrangular meshes (e.g. compression, texturing, anisotropic smoothing, feature extraction)
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