6,916 research outputs found

    Uniqueness of the Fisher-Rao metric on the space of smooth densities

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    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

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    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

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    Let MM and NN be connected manifolds without boundary with dim(M)<dim(N)\dim(M) < \dim(N), and let MM compact. Then shape space in this work is either the manifold of submanifolds of NN that are diffeomorphic to MM, or the orbifold of unparametrized immersions of MM in NN. 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 NN, f^*\g is the induced metric on MM, h,kΓ(fTN)h,k \in \Gamma(f^*TN) are tangent vectors at ff to the space of embeddings or immersions, and PfP^f is a positive, selfadjoint, bijective scalar pseudo differential operator of order 2p2p depending smoothly on ff. We consider later specifically the operator Pf=1+AΔpP^f=1 + A\Delta^p, where Δ\Delta is the Bochner-Laplacian on MM induced by the metric fgˉf^*\bar g. 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

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    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