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Ricci Curvature of Finsler Metrics by Warped ProductMarcal, Patricia 05 1900 (has links)
Indiana University-Purdue University Indianapolis (IUPUI) / In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.
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Morphological and statistical techniques for the analysis of 3D imagesMeinhardt Llopis, Enric 03 March 2011 (has links)
Aquesta tesi proposa una estructura de dades per
emmagatzemar imatges tridimensionals. L'estructura da dades té
forma d'arbre i codifica les components connexes dels conjunts de
nivell de la imatge. Aquesta estructura és la eina bàsica per
moltes aplicacions proposades: operadors morfològics
tridimensionals, visualització d'imatges mèdiques, anàlisi
d'histogrames de color, seguiment d'objectes en vídeo i detecció
de vores. Motivada pel problema de la completació de vores, la
tesi conté un estudi de com l'eliminació de soroll mitjançant variació
total anisòtropa es pot fer servir per calcular conjunts de
Cheeger en mètriques anisòtropes. Aquests conjunts de Cheeger
anisòtrops es poden utilitzar per trobar òptims globals d'alguns
funcionals per completar vores. També estan relacionats amb
certs invariants afins que s'utilitzen en reconeixement
d'objectes, i en la tesi s'explicita aquesta relació. / This thesis proposes a tree data structure to encode the connected
components of level sets of 3D images. This data structure is applied
as a main tool in several proposed applications: 3D morphological
operators, medical image visualization, analysis of color histograms,
object tracking in videos and edge detection. Motivated by the
problem of edge linking, the thesis contains also an study of
anisotropic total variation denoising as a tool for computing
anisotropic Cheeger sets. These anisotropic Cheeger sets can be used
to find global optima of a class of edge linking functionals. They
are also related to some affine invariant descriptors which are used
in object recognition, and this relationship is laid out explicitly.
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