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, 1966 In this chapter we shall study a variation of so called “decomposition of identity”, a strange and inadequate name for collections E λ of projectors depending on a real (or complex) parameter λ, and strongly related to selfadjoint or normal operators.
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2005
In this paper we propose a novel type of scales-spaces which is emerging from the family of inhomogeneous pseudodifferential equations $(I - \tau\Delta)^{\frac{t}{2}}u$ with τ ≥ 0 and scale parameter t ≥ 0. Since they are connected to the convolution semi-group of Bessel potentials we call the associated operators {R$^{n}_{t,{ \tau}}$ | 0≤ τ,t} either ...
Bernhard Burgeth +2 more
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In this paper we propose a novel type of scales-spaces which is emerging from the family of inhomogeneous pseudodifferential equations $(I - \tau\Delta)^{\frac{t}{2}}u$ with τ ≥ 0 and scale parameter t ≥ 0. Since they are connected to the convolution semi-group of Bessel potentials we call the associated operators {R$^{n}_{t,{ \tau}}$ | 0≤ τ,t} either ...
Bernhard Burgeth +2 more
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The Scaling of Animal Space Use
Science, 2004Space used by animals increases with increasing body size. Energy requirements alone can explain how population density decreases, but not the steep rate at which home range area increases. We present a general mechanistic model that predicts the frequency of interaction, spatial overlap, and loss of resources to neighbors. Extensive empirical evidence
Chris Carbone +11 more
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Spaces and Scales of Leadership
2016This chapter analyzes the various scales (meaning the different geographical levels; cf. Glossary for the definition of geography) at which leaders are involved and to which they are related. Leaders are, in fact, influenced by, and influence, the transformation and emergence of numerous spaces.
Frannie Léautier +1 more
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Image and Vision Computing, 1997
It is argued that image measurements should satisfy two requirements of physical plausibility: the measurements are of non-zero scale and non-zero imprecision; and two required invariances, nothing is lost by expanding the image and nothing is lost by increasing the contrast of the image.
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It is argued that image measurements should satisfy two requirements of physical plausibility: the measurements are of non-zero scale and non-zero imprecision; and two required invariances, nothing is lost by expanding the image and nothing is lost by increasing the contrast of the image.
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1995
So far we have studied linear parabolic evolution equations in a fixed Banach space. However, we have already seen, in connection with considerations of higher regularity and problems with variable domains, that it is useful and necessary to consider induced equations in interpolation spaces as well.
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So far we have studied linear parabolic evolution equations in a fixed Banach space. However, we have already seen, in connection with considerations of higher regularity and problems with variable domains, that it is useful and necessary to consider induced equations in interpolation spaces as well.
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1997
The conclusion reached at the end of Chapter 3 can be summarised by the following scale-space paradigm.
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The conclusion reached at the end of Chapter 3 can be summarised by the following scale-space paradigm.
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Scale-Space Theory in Computer Vision
Lecture Notes in Computer Science, 1993Tony Lindeberg
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Proceedings of 13th International Conference on Pattern Recognition, 1996
Viewing images as distributions of light quanta enables an information theoretic study of image structures on different scales. This article combines Shannon's entropy and Witkin and Koenderink's scale-space to establish a precise connection between the heat equation and the thermodynamic entropy in scale-space.
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Viewing images as distributions of light quanta enables an information theoretic study of image structures on different scales. This article combines Shannon's entropy and Witkin and Koenderink's scale-space to establish a precise connection between the heat equation and the thermodynamic entropy in scale-space.
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