We show how to represent a simple polygon P by a grid (pixel-based) polygon Q that is simple and whose Hausdorff or Fréchet distance to P is small. For any simple polygon P , a grid polygon exists with constant Hausdorff distance between their boundaries and their interiors. Moreover, we show that with a realistic input assumption we can also realize constant Fréchet distance between the bounda...

We present and implement an error estimation protocol in the Insight Toolkit (ITK) for assessing the accuracy of image alignment. We base this error estimation on a robust version of the Hausdorff Distance (HD) metric applied to the recovered edges of the images. The robust modifications we introduce to the HD metric significantly reduce the amount of outliers in the local distance error estima...

Buried archeological features show up as crop marks that are mostly visible using high-resolution image data. Such data are costly and restricted to small regions and time domains. However, a time series of freely available medium resolution imagery can be employed to detect crop growth changes to reveal subtle surface marks in large areas. This paper aims to study the classical Chinese settlem...

p. 3 Tesselations by Connection in Orders p. 15 A Concise Characterization of 3D Simple Points p. 27 Digital n-Pseudomanifold and n-Weakmanifold in a Binary (n+1)-Digital Image p. 37 Digital Jordan Curve Theorems p. 46 A New Means for Investigating 3-Manifolds p. 57 Nearness in Digital Images and Proximity Spaces p. 69 Morphological Operators with Discrete Line Segments p. 78 Hausdorff Discreti...

Confining strings in 4D are effective, thick strings describing the confinement phase of compact U(1) and, possibly, also non-Abelian gauge fields. We show that these strings are dual to the gauge fields, inasmuch their perturbative regime corresponds to the strong coupling (e ≫ 1) regime of the gauge theory. In this regime they describe smooth surfaces with long-range correlations and Hausdorf...

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dL is a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the ...

For a closed cocompact subgroup Γ of a locally compact group G, given a compact abelian subgroup K of G and a homomorphism ρ : K̂ → G satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deformations C∗(Ĝ/Γ, ρ) of the homogeneous space G/Γ, generalizing Rieffel’s construction of quantum Heisenberg manifolds. We show that when G is a Lie group and G/Γ is conn...

We consider several distances between two sets of points, which are modifications of the Hausdorff metric, and apply them to describe some fractals such as δ-quasi-self-similar sets, and some other geometric notions in Euclidean space, such as tilings with quasi-prototiles and patterns with quasi-motifs. For the δ-quasi-self-similar sets satisfying the open set condition we obtain the same resu...

Abstraca. The main object of the paper is to study the distance betwecn Banach spaces introduced by Kadets. For Banach spaccs Xand y. thc lGders distancc is denned to be rhe infimum of the Hausdorfl distance d(Bx, rr) betwecn the respoctive closed unit balls over all isomctric linear embeddings of f and yinto a common Banach space Z. This is comparcd with the Gromov-Hausdorff distance which is ...

It is well known from differential geometry that an n-dimensional Riemannian manifold can be isometrically embedded in a Euclidean space of dimension 2n+1 [Nas54]. Though the proof by Nash is intuitive, it is not clear whether such a construction is achievable by an algorithm that only has access to a finite-size sample from the manifold. In this paper, we study Nash’s construction and develop ...