55,563 research outputs found
Limits in PMF of Teichmuller geodesics
We consider the limit set in Thurston's compactification PMF of Teichmueller
space of some Teichmueller geodesics defined by quadratic differentials with
minimal but not uniquely ergodic vertical foliations. We show that a) there are
quadratic differentials so that the limit set of the geodesic is a unique
point, b) there are quadratic differentials so that the limit set is a line
segment, c) there are quadratic differentials so that the vertical foliation is
ergodic and there is a line segment as limit set, and d) there are quadratic
differentials so that the vertical foliation is ergodic and there is a unique
point as its limit set. These give examples of divergent Teichmueller geodesics
whose limit sets overlap and Teichmueller geodesics that stay a bounded
distance apart but whose limit sets are not equal. A byproduct of our methods
is a construction of a Teichmueller geodesic and a simple closed curve
so that the hyperbolic length of the geodesic in the homotopy class of gamma
varies between increasing and decreasing on an unbounded sequence of time
intervals along the geodesic.Comment: 39 pages, 4 figure
Multiplicities of Noetherian deformations
The \emph{Noetherian class} is a wide class of functions defined in terms of
polynomial partial differential equations. It includes functions appearing
naturally in various branches of mathematics (exponential, elliptic, modular,
etc.). A conjecture by Khovanskii states that the \emph{local} geometry of sets
defined using Noetherian equations admits effective estimates analogous to the
effective \emph{global} bounds of algebraic geometry.
We make a major step in the development of the theory of Noetherian functions
by providing an effective upper bound for the local number of isolated
solutions of a Noetherian system of equations depending on a parameter
, which remains valid even when the system degenerates at
. An estimate of this sort has played the key role in the
development of the theory of Pfaffian functions, and is expected to lead to
similar results in the Noetherian setting. We illustrate this by deducing from
our main result an effective form of the Lojasiewicz inequality for Noetherian
functions.Comment: v2: reworked last section, accepted to GAF
A Framework for SAR-Optical Stereogrammetry over Urban Areas
Currently, numerous remote sensing satellites provide a huge volume of
diverse earth observation data. As these data show different features regarding
resolution, accuracy, coverage, and spectral imaging ability, fusion techniques
are required to integrate the different properties of each sensor and produce
useful information. For example, synthetic aperture radar (SAR) data can be
fused with optical imagery to produce 3D information using stereogrammetric
methods. The main focus of this study is to investigate the possibility of
applying a stereogrammetry pipeline to very-high-resolution (VHR) SAR-optical
image pairs. For this purpose, the applicability of semi-global matching is
investigated in this unconventional multi-sensor setting. To support the image
matching by reducing the search space and accelerating the identification of
correct, reliable matches, the possibility of establishing an epipolarity
constraint for VHR SAR-optical image pairs is investigated as well. In
addition, it is shown that the absolute geolocation accuracy of VHR optical
imagery with respect to VHR SAR imagery such as provided by TerraSAR-X can be
improved by a multi-sensor block adjustment formulation based on rational
polynomial coefficients. Finally, the feasibility of generating point clouds
with a median accuracy of about 2m is demonstrated and confirms the potential
of 3D reconstruction from SAR-optical image pairs over urban areas.Comment: This is the pre-acceptance version, to read the final version, please
go to ISPRS Journal of Photogrammetry and Remote Sensing on ScienceDirec
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