Classical morphology is built up in such a way that all operators occur in pairs, e.g., dilation and erosion, opening and closing, etc. This phenomenon, which is a straightforward consequence of the duality principle, often prohibits the construction of tools that treat foreground and background of signals in exactly the same way. In this paper we discuss an alternative framework for morphologi...

In this text we show how points, point pairs, lines, planes, circles, spheres, and rotation, translation and dilation operators and their uncertainty can be evaluated from uncertain data in a unified manner using the Geometric Algebra of conformal space. This extends previous work by Förstner et al. [3] from points, lines and planes to non-linear entities and operators, while keeping the linear...

We prove that the maximal functions associated with a Zygmund dilation dyadic structure in three-dimensional Euclidean space, and flag two-dimensional cannot be bounded by multiparameter sparse operators corresponding grid. also obtain supplementary results about absence of domination for strong function.

We construct efficient approximations for the eigenfunctions of non-selfadjoint Schrödinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrödinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable ad...

In the Hilbert space ?2 ?(Z; E) (Z := {0,? 1, ? 2, ...}, dim E = N < ?), maximal dissipative singular second-order matrix difference operators that extensions of a minimal symmetric operator with deficiency indices (2N, 2N) (in limit-circle cases at ?) are considered. The general boundary conditions investigated. For operator, self-adjoint dilation and is its incoming outgoing spectral repre...

We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators dilation and erosion, opening and closing, as well as the much more complex top-hat transform, for which we report a real-world application from the steel i...

In this paper, classified and comparative study of edge detection algorithms are presented. Experimental results prove that Boie-Cox, ShenCastan and Canny operators are better than Laplacian of Gaussian (LOG), while LOG is better than Prewitt and Sobel in case of noisy image. Subjective and objective methods are used to evaluate the different edge operators. The morphological filter is more imp...

and the corresponding inversion formula analyze the frequency content of f . Underlying many finer decompositions into simpler pieces are the fundamental invariance properties of R and the corresponding operators. For harmonic analysis on R these are the translations t → t+x and the dilations t → at, where t, x ∈ R and a ∈ R. The corresponding operators are the translation operator Tx (2) Txf(t...

We prove a covering lemma for rectangles in Rn which has connections to a problem of Zygmund and its solution in three dimensions by Cordoba. One of the objectives of this note is to revive interest in a collection of problems in differentiation theory related to a conjecture of Zygmund. We shall also give another proof of the sharp mapping properties near L of the strong maximal operator by pr...