A quasi-conformal mapping of the parametric domain onto the underlying physical domain is used to generate a 2D structured mesh with required properties: grid line orthogonality and prescribed mesh point clustering near the domain boundary. The functions implementing the mapping are sought by solving the Dirichlet problem for the elliptic partial differential equations. An additional control fo...

For the past two decades, fractals (e.g., the Hilbert and Peano space-filling curves) have been considered the natural method for providing a locality-preserving mapping. The idea behind a locality-preserving mapping is to map points that are nearby in the multi-dimensional space into points that are nearby in the one-dimensional space. In this paper, we argue against the use of fractals in loc...

We address the problem of simplifying two-dimensional polygonal partitions that exhibit strong regularities. Such are relevant for reconstructing urban scenes in a concise way. Preserving long linear structures spanning several partition cells motivates point-line projective duality approach which points represent line intersections, and lines possibly carry multiple points. propose simplificat...

We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

Let (pn)n be a given monic orthogonal polynomial sequence (OPS) and k a fixed positive integer number such that k ≥ 2. We discuss conditions under which this OPS originates from a polynomial mapping in the following sense: to find another monic OPS (qn)n and two polynomials πk and θm , with degrees k and m (resp.), with 0 ≤ m ≤ k − 1, such that pnk+m(x) = θm(x)qn(πk(x)) (n = 0, 1, 2, . . .). In...

An orthogonality space is a set equipped with symmetric and irreflexive binary relation. We consider spaces the additional property that any collection of mutually orthogonal elements gives rise to structure Boolean algebra. Together maps preserve substructures, we are led category NOS normal spaces. Moreover, an finite rank called linear if for two distinct e f there third one g such exactly p...

ARPA Image Understanding Workshop 1996 As an alternative to texture segmentation for the description of the images, we propose a method for coalescing descriptors of adjacent image patches with similar textural content into tight clusters. We achieve this result by extending the notion of edge-preserving smoothing and anisotropic di usion from gray-level and color images to vector-valued images...