Advances in Imaging and Electron Physics, Volume 178 by Peter W. Hawkes

By Peter W. Hawkes

Advances in Imaging and Electron Physics features state of the art articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, photograph technological know-how and electronic photograph processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in these types of domain names.

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* Contributions from major gurus * Informs and updates on the entire newest advancements within the box

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Extra info for Advances in Imaging and Electron Physics, Volume 178

Example text

2009, Shao & Mattivi 2010). Specifically, it was shown in Laptev & Lindeberg (2004c), Lindeberg et al.

VxN ; vt ÞT for the spatio-temporal gradient operator, and with initial condition Lðx; t; 0; 0Þ ¼ f ðx; tÞ for some positive, semi-definite ðN þ 1Þ Â ðN þ 1Þ covariance matrix S0 and for some N þ 1-dimensional vector d0 . ; xN ; tÞT , where the covariance matrix Ss ¼ s S0 constitutes a simultaneous covariance matrix over space and time and ds ¼ s d0 denotes a corresponding translation vector over space and time. Interpretation By a suitable interpretation of the covariance matrix Ss and the offset ds , this non-causal scale-space concept can be used for modeling smoothing operations for spatio-temporal image data.

K, temporal recursivity can, in combination with the requirement of a semigroup property over space, be expressed in terms of a spatio-temporal time-recursive structure of the form Z X K Lðx; t2 ; s2 ; kÞ ¼ Uðx À x; t2 À t1 ; s2 À s1 ; k; zÞLðx; t1 ; s1 ; zÞdz dx x˛RN z¼0 Z Zt2 Bðx À x; t2 À u; s2 ; kÞf ðx; uÞdx du; þ x˛RN u¼t1 where the kernel U updates the internal state, the kernel B incorporates new information, and z constitutes an index over the internal temporal scale 52 Tony Lindeberg levels.

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