6,916 research outputs found
Uniqueness of the Fisher-Rao metric on the space of smooth densities
MB was supported by ‘Fonds zur F¨orderung der wissenschaftlichen Forschung, Projekt P 24625’
Real-time filtering and detection of dynamics for compression of HDTV
The preprocessing of video sequences for data compressing is discussed. The end goal associated with this is a compression system for HDTV capable of transmitting perceptually lossless sequences at under one bit per pixel. Two subtopics were emphasized to prepare the video signal for more efficient coding: (1) nonlinear filtering to remove noise and shape the signal spectrum to take advantage of insensitivities of human viewers; and (2) segmentation of each frame into temporally dynamic/static regions for conditional frame replenishment. The latter technique operates best under the assumption that the sequence can be modelled as a superposition of active foreground and static background. The considerations were restricted to monochrome data, since it was expected to use the standard luminance/chrominance decomposition, which concentrates most of the bandwidth requirements in the luminance. Similar methods may be applied to the two chrominance signals
Sobolev metrics on shape space of surfaces
Let and be connected manifolds without boundary with , and let compact. Then shape space in this work is either the
manifold of submanifolds of that are diffeomorphic to , or the orbifold
of unparametrized immersions of in . We investigate the Sobolev
Riemannian metrics on shape space: These are induced by metrics of the
following form on the space of immersions: G^P_f(h,k) = \int_{M} \g(P^f h,
k)\, \vol(f^*\g) where \g is some fixed metric on , f^*\g is the
induced metric on , are tangent vectors at to
the space of embeddings or immersions, and is a positive, selfadjoint,
bijective scalar pseudo differential operator of order depending smoothly
on . We consider later specifically the operator , where
is the Bochner-Laplacian on induced by the metric . For
these metrics we compute the geodesic equations both on the space of immersions
and on shape space, and also the conserved momenta arising from the obvious
symmetries. We also show that the geodesic equation is well-posed on spaces of
immersions, and also on diffeomorphism groups. We give examples of numerical
solutions.Comment: 52 pages, final version as it will appea
Optical Polarization M\"obius Strips and Points of Purely Transverse Spin Density
Tightly focused light beams can exhibit electric fields spinning around any
axis including the one transverse to the beams' propagation direction. At
certain focal positions, the corresponding local polarization ellipse can
degenerate into a perfect circle, representing a point of circular
polarization, or C-point. We consider the most fundamental case of a linearly
polarized Gaussian beam, where - upon tight focusing - those C-points created
by transversely spinning fields can form the center of 3D optical polarization
topologies when choosing the plane of observation appropriately. Due to the
high symmetry of the focal field, these polarization topologies exhibit non
trivial structures similar to M\"obius strips. We use a direct physical measure
to find C-points with an arbitrarily oriented spinning axis of the electric
field and experimentally investigate the fully three-dimensional polarization
topologies surrounding these C-points by exploiting an amplitude and phase
reconstruction technique.Comment: 5 pages, 3 figures; additional supplementary materials with 4 pages,
3 figure
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