The tomographic imaging of vector elds on bounded domains is considered. Reconstruction formulas for the probe transform are rst shown to be valid on bounded domains. It is then shown that potential functions reconstructed from these formulas include a component that arises from the harmonic component of the vector eld, which is due to boundary conditions alone. Closed form expressions for the ...

Abstract The variational theory of higher-power energy is developed for mappings between Riemannian manifolds, and more generally sections submersions applied to vector bundles their sphere subbundles. A complete classification then given left-invariant fields on three-dimensional unimodular Lie groups equipped with an arbitrary metric.

The dimensionality of visual motion analysis can be reduced by analyzing projections of ow vector elds. In contrast to motion vector elds, these projections exhibit simple geometric properties which are invariant to the scene structure and depend only on the camera motion. Using these properties, structure and motion can be either completely or partially decoupled. We estimate motion parameters...

This paper considers the problem of vector tomography on an arbitrary bounded domain in three dimensions. The probe transform of a vector eld is the inner product of the Radon transform of a vector eld with a unit vector, called the probe, which may be a function of the projection orientation. Previous work has given reconstruction formulas for arbitrary elds and for those known to be divergenc...

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When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

Visualization of a \ eld", which is a physically invisible concept, is a main subject of scienti c visualization. In this paper described is a method for visualizing a great gravitational eld like a black hole. We assume a velocity vector eld of imaginary uid in the vicinity of the black hole for its e ective visualization. We describe the eld by using equations so called \Eulerian method". Thi...

and Contours from Tagged Magnetic Resonance Images Using Markov Random Field Edge Prior Litao Yan and Thomas S. Denney, Jr. Department of Electrical Engineering Auburn University Auburn University, Alabama 36849, USA [email protected], [email protected] Abstract Magnetic Resonance (MR) tagging has been shown to be a useful method for non-invasively measuring the deformation of the left ...