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- Cammoun, L., et al.
(författare)
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A Review of Tensors and Tensor Signal Processing
- 2009
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Ingår i: Tensors in Image Processing and Computer Vision. - London : Springer London. - 9781848822986 ; , s. 1-32
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Bokkapitel (refereegranskat)abstract
- Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.
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| 2. |
- Cosacov, Andrea, et al.
(författare)
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New insights into the phylogenetic relationships, character evolution, and phytogeographic patterns of Calceolaria (Calceolariaceae)
- 2009
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Ingår i: American Journal of Botany. - : Wiley. - 0002-9122. ; 96:12, s. 1-16
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Tidskriftsartikel (refereegranskat)abstract
- Biogeographical patterns and diversifi cation processes in Andean and Patagonian fl ora are not yet well understood. Calceolaria is a highly diversifi ed genus of these areas, representing one of the most specialized plant – pollinator systems because fl owers produce nonvolatile oils, a very unusual fl oral reward. Phylogenetic analyses with molecular (ITS and matK ) and morphological characters from 103 Calceolaria species were conducted to examine relationships, to understand biogeographic patterns, and to detect evolutionary patterns of fl oral and ecological characters. Total evidence analysis retrieved three major clades, which strongly correspond to the three previously recognized subgenera, although only subgenus Rosula was retrieved as a monophyletic group. A single historical event explains the expansion from the southern to central Andes, while different parallel evolutionary lines show a northward expansion from the central to northern Andes across the Huancabamba Defl ection, an important geographical barrier in northern Peru. Polyploidy, acquisition of elaiophores, and a nototribic pollination mechanism are key aspects of the evolutionary history of Calceolaria . Pollination interactions were more frequently established with Centris than with Chalepoge- nus oil-collecting bee species. The repeated loss of the oil gland and shifts to pollen as the only reward suggest an evolutionary tendency from highly to moderately specialized pollination systems.
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