15,664 research outputs found
Graph-Based Classification of Omnidirectional Images
Omnidirectional cameras are widely used in such areas as robotics and virtual
reality as they provide a wide field of view. Their images are often processed
with classical methods, which might unfortunately lead to non-optimal solutions
as these methods are designed for planar images that have different geometrical
properties than omnidirectional ones. In this paper we study image
classification task by taking into account the specific geometry of
omnidirectional cameras with graph-based representations. In particular, we
extend deep learning architectures to data on graphs; we propose a principled
way of graph construction such that convolutional filters respond similarly for
the same pattern on different positions of the image regardless of lens
distortions. Our experiments show that the proposed method outperforms current
techniques for the omnidirectional image classification problem
Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
We present a new approach to three-dimensional electromagnetic scattering
problems via fast isogeometric boundary element methods. Starting with an
investigation of the theoretical setting around the electric field integral
equation within the isogeometric framework, we show existence, uniqueness, and
quasi-optimality of the isogeometric approach. For a fast and efficient
computation, we then introduce and analyze an interpolation-based fast
multipole method tailored to the isogeometric setting, which admits competitive
algorithmic and complexity properties. This is followed by a series of
numerical examples of industrial scope, together with a detailed presentation
and interpretation of the results
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