8,651 research outputs found
An Improved Observation Model for Super-Resolution under Affine Motion
Super-resolution (SR) techniques make use of subpixel shifts between frames
in an image sequence to yield higher-resolution images. We propose an original
observation model devoted to the case of non isometric inter-frame motion as
required, for instance, in the context of airborne imaging sensors. First, we
describe how the main observation models used in the SR literature deal with
motion, and we explain why they are not suited for non isometric motion. Then,
we propose an extension of the observation model by Elad and Feuer adapted to
affine motion. This model is based on a decomposition of affine transforms into
successive shear transforms, each one efficiently implemented by row-by-row or
column-by-column 1-D affine transforms.
We demonstrate on synthetic and real sequences that our observation model
incorporated in a SR reconstruction technique leads to better results in the
case of variable scale motions and it provides equivalent results in the case
of isometric motions
Explicit constructions and properties of generalized shift-invariant systems in
Generalized shift-invariant (GSI) systems, originally introduced by
Hern\'andez, Labate & Weiss and Ron & Shen, provide a common frame work for
analysis of Gabor systems, wavelet systems, wave packet systems, and other
types of structured function systems. In this paper we analyze three important
aspects of such systems. First, in contrast to the known cases of Gabor frames
and wavelet frames, we show that for a GSI system forming a frame, the
Calder\'on sum is not necessarily bounded by the lower frame bound. We identify
a technical condition implying that the Calder\'on sum is bounded by the lower
frame bound and show that under a weak assumption the condition is equivalent
with the local integrability condition introduced by Hern\'andez et al. Second,
we provide explicit and general constructions of frames and dual pairs of
frames having the GSI-structure. In particular, the setup applies to wave
packet systems and in contrast to the constructions in the literature, these
constructions are not based on characteristic functions in the Fourier domain.
Third, our results provide insight into the local integrability condition
(LIC).Comment: Adv. Comput. Math., to appea
Incarnations of Berthelot's conjecture
In this article we give a survey of the various forms of Berthelot's
conjecture and some of the implications between them. By proving some
comparison results between pushforwards of overconvergent isocrystals and those
of arithmetic -modules, we manage to deduce some cases of the
conjecture from Caro's results on the stability of overcoherence under
pushforward via a smooth and proper morphism of varieties. In particular, we
show that Ogus' convergent pushforward of an overconvergent -isocrystal
under a smooth and projective morphism is overconvergent.Comment: 17 pages. Final version, published in J. Number Theor
Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings
This paper is a study of the interaction between the combinatorics of
boundaries of convex polytopes in arbitrary dimension and their metric
geometry.
Let S be the boundary of a convex polytope of dimension d+1, or more
generally let S be a `convex polyhedral pseudomanifold'. We prove that S has a
polyhedral nonoverlapping unfolding into R^d, so the metric space S is obtained
from a closed (usually nonconvex) polyhedral ball in R^d by identifying pairs
of boundary faces isometrically. Our existence proof exploits geodesic flow
away from a source point v in S, which is the exponential map to S from the
tangent space at v. We characterize the `cut locus' (the closure of the set of
points in S with more than one shortest path to v) as a polyhedral complex in
terms of Voronoi diagrams on facets. Analyzing infinitesimal expansion of the
wavefront consisting of points at constant distance from v on S produces an
algorithmic method for constructing Voronoi diagrams in each facet, and hence
the unfolding of S. The algorithm, for which we provide pseudocode, solves the
discrete geodesic problem. Its main construction generalizes the source
unfolding for boundaries of 3-polytopes into R^2. We present conjectures
concerning the number of shortest paths on the boundaries of convex polyhedra,
and concerning continuous unfolding of convex polyhedra. We also comment on the
intrinsic non-polynomial complexity of nonconvex polyhedral manifolds.Comment: 47 pages; 21 PostScript (.eps) figures, most in colo
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