Book ChapterDOI
On the Geometric Structure of Spatio-temporal Patterns
Erhardt Barth,Mario Ferraro +1 more
- pp 134-143
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TLDR
The structure of hypersurfaces corresponding to different spatio-temporal patterns is considered, and in particular representations based on geometrical invariants, such as the Riemann and Einstein tensors and the scalar curvature are analyzed.Abstract:
The structure of hypersurfaces corresponding to different spatio-temporal patterns is considered, and in particular representations based on geometrical invariants, such as the Riemann and Einstein tensors and the scalar curvature are analyzed. The spatio-temporal patterns result from translations, Lie-group transformations, accelerated and discontinuous motions and modulations. Novel methods are obtained for the computation of motion parameters and the optical flow. Moreover, results obtained for accelerated and discontinuous motions are useful for the detection of motion boundaries.read more
Citations
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Book ChapterDOI
The Use of Structure Tensors in the Analysis of Seismic Data
Maria Faraklioti,Maria Petrou +1 more
TL;DR: The first and second order structure tensors can be used to quantify the local structure of seismic data and their departure from laminar structure as mentioned in this paper, which can distinguish chaotic regions as well as regions of interest, like mounds and horizon terminations from stratified regions.
Proceedings ArticleDOI
Analysis of motion and curvature in image sequences
TL;DR: In this paper, the authors review a recent development in the area of computer vision and multidimensional signal processing using hypersurfaces, and present methods for the analysis of single and multiple motions, including occluded motions.
Analysis of Motion and Curvature in Image Sequences (invited).
TL;DR: Besides demonstrating the uniqueness of curvature, new methods for the analysis of single and multiple motions are presented including the case of occluded motions.
References
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Book
Applications of Lie Groups to Differential Equations
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
Journal Article
Computer vision
TL;DR: How the field of computer (and robot) vision has evolved, particularly over the past 20 years, is described, and its central methodological paradigms are introduced.
Book
Mathematica: A System for Doing Mathematics by Computer
TL;DR: This book will be released simultaneously with Release 2.0 of Mathematica and will cover all the new features of Release 1.0 as mentioned in this paper, including 16 pages of full-color graphics.
Book
Mathematica: a system for doing mathematics by computer (2nd ed.)
TL;DR: This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users ofMathematica will need this edition.