20,414 research outputs found
Robust motion estimation using connected operators
This paper discusses the use of connected operators for robust motion estimation The proposed strategy involves a motion estimation step extracting the dominant motion and a ltering step relying on connected operators that remove objects that do not fol low the dominant motion. These two steps are iterated in order to obtain an accurate motion estimation and a precise de nition of the objects fol lowing this motion This strategy can be applied on the entire frame or on individual connected components As a result the complete motion oriented segmentation and motion estimation of the frame can be achievedPeer ReviewedPostprint (published version
Gravitational Wave Polarization Modes in Theories
Many studies have been carried out in the literature to evaluate the number
of polarization modes of gravitational waves in modified theories, in
particular in theories. In the latter ones, besides the usual two
transverse-traceless tensor modes present in general relativity, there are two
additional scalar ones: a massive longitudinal mode and a massless transverse
mode (the so-called breathing mode). This last mode has often been overlooked
in the literature, due to the assumption that the application of the Lorenz
gauge implies transverse-traceless wave solutions. We however show that this is
in general not possible and, in particular, that the traceless condition cannot
be imposed due to the fact that we no longer have a Minkowski background
metric. Our findings are in agreement with the results found using the
Newman-Penrose formalism, and thus clarify the inconsistencies found so far in
the literature.Comment: 7 pages; accepted for publication in Phys. Rev.
Dimensions of Copeland-Erdos Sequences
The base- {\em Copeland-Erd\"os sequence} given by an infinite set of
positive integers is the infinite sequence \CE_k(A) formed by concatenating
the base- representations of the elements of in numerical order. This
paper concerns the following four quantities.
The {\em finite-state dimension} \dimfs (\CE_k(A)), a finite-state version
of classical Hausdorff dimension introduced in 2001.
The {\em finite-state strong dimension} \Dimfs(\CE_k(A)), a finite-state
version of classical packing dimension introduced in 2004. This is a dual of
\dimfs(\CE_k(A)) satisfying \Dimfs(\CE_k(A)) \geq \dimfs(\CE_k(A)).
The {\em zeta-dimension} \Dimzeta(A), a kind of discrete fractal dimension
discovered many times over the past few decades.
The {\em lower zeta-dimension} \dimzeta(A), a dual of \Dimzeta(A)
satisfying \dimzeta(A)\leq \Dimzeta(A).
We prove the following.
\dimfs(\CE_k(A))\geq \dimzeta(A). This extends the 1946 proof by Copeland
and Erd\"os that the sequence \CE_k(\mathrm{PRIMES}) is Borel normal.
\Dimfs(\CE_k(A))\geq \Dimzeta(A).
These bounds are tight in the strong sense that these four quantities can
have (simultaneously) any four values in satisfying the four
above-mentioned inequalities.Comment: 19 page
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