Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modal...

For many Markov semigroups dilations in the sense of Hudson and Parthasarathy, that is a dilation which is a cocycle perturbation of a noise, have been constructed with the help of quantum stochastic calculi. In these notes we show that every Markov semigroup on the algebra of all bounded operators on a separable Hilbert space that is spatial in the sense of Arveson, admits a Hudson-Parthasarat...

Morphological image processing is well known as an efficient methodology for image processing and computer vision. With the wide use of color in many areas, the interest on the color perception and processing has been growing rapidly. Many models have been proposed to extend morphological operators to the field of color images, dealing with some new problems not present previously in the binary...

AIM To evaluate repeatability and reproducibility of macular thickness measurements in visually normal eyes using the Topcon 3D OCT-1000. METHODS Phase 1 investigated scan repeatability, the effect of age and pupil dilation. Two groups (6 younger and 6 older participants) had one eye scanned 5 times pre and post- dilation by 1 operator. Phase 2 investigated between-operator, within and betwee...

Morphological image processing filters preserve shapes related to the structuring element shape of the operator. The basic morphological operators are minimum (erosion) and maximum (dilation) operations performed on the pixels within a structuring element. Although these operators (and the compound operators formed from them) are able to smooth noise, they also introduce a statistical and deter...

Spectral representations of the dilation and translation operators on L 2 (R) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes.

The Markov dilation of diffusion type processes is defined. Infinitesimal operators and stochastic differential equations for the obtained Markov processes are described. Some applications to the integral representation for functionals of diffusion type processes and to the construction of a replicating portfolio for a non-terminal contingent claim are considered.

Dilation theory is a paradigm for studying operators by way of exhibiting an operator as compression another which in some sense well behaved. For example, every contraction can be dilated to (i.e., of) unitary operator, and on this simple fact penetrating non-normal has been developed. In the first part survey, I will leisurely review key classical results dilation single or several commuting ...

We define the concept of instability index of an isolated eigenvalue of a non-self-adjoint operator, and prove some of its general properties. We also describe a stable procedure for computing this index for Schrödinger operators in one dimension, and apply it to the complex resonances of a typical operator with a dilation analytic potential. AMS subject classification: 34L05, 35P05, 47A75, 49R...

Two procedures to compute the output distribution φS of certain stack filters S (so called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S and also yields the rank selection probabilities. The other is based on inclusion-exclusion and e.g. yields φS for some important LULU -operators S. Properties of φS can be used to characterize smoothing properties.