Consider a problem where we are given a bipartite graph H with vertices arranged on two horizontal lines in the plane, such that the two sets of vertices placed on the two lines form a bipartition of H . We additionally require that H admits a perfect matching and assume that edges of H are embedded in the plane as segments. The goal is to compute the minimal number of intersecting edges in a p...

Retinal vessel segmentation algorithms play an important role for the detection of numerous diseases, such as diabetic retinopathy, glaucoma and many others. The aim of this paper is report an automated method for segmentation of retinal blood vessels using the crest lines and morphological operations. Initially, each image is preprocessed and the green channel is obtained. Then, we extract the...

We study the possibility of the existence of a Katona type proof for the Erdős-Ko-Rado theorem for 2and 3-intersecting families of sets. An Erdős-Ko-Rado type theorem for 2-intersecting integer arithmetic progressions and a model theoretic argument show that such an approach works in the 2-intersecting case.

We apply the entropy formalism to the study of the near-horizon geometry of extremal black p-brane intersections in D > 5 dimensional supergravities. The scalar flow towards the horizon is described in terms an effective potential given by the superposition of the kinetic energies of all the forms under which the brane is charged. At the horizon active scalars get fixed to the minima of the eff...

We describe two tests of the hypothesis that human judgments of the proximity of colors are consistent with a Euclidean geometry on color matching space. The first test uses proximity judgments to measure the angle between any two intersecting lines in color space. Pairwise estimates of the angles between three lines in a plane were made in order to test the additivity of angles. Three differen...

We present a novel algorithm for the geometric extraction of stream volume segmentation for visualization of grid-less flow simulation. Our goal is the segmentation of different paths through a mixing tube where the flow is represented by scattered point sets approximated with moving least squares. The key challenges are the watertight construction of boundary representations from separatrices....

Texture has been one of the most popular representations in image retrieval. Our image database retrieval system uses two sets of textural features, first one being the line-angle-ratio statistics which is a texture histogram computed from the properties of the surroundings and the spatial relationships of intersecting lines, second one being the variances of gray level spatial dependencies com...

With the exception of pure data-driven methods, reconstruction approaches for 3D building models from aerial point clouds often incorporate some level of model information to construct regularized and well-formed roof structures. In the proposed feature-driven approach, low-level roof features like ridge lines, gable and (half-) hip ends, intersecting ridge lines, dormers etc. are detected in a...

A proper non-empty subset C of the points of a linear space S = (P; L) is called line-closed if any two intersecting lines of S , each meeting C at least twice, have their intersection in C. We show that when every line has k points and every point lies on r lines the maximum size for such sets is r + k ? 2. In addition it is shown that this cannot happen for projective spaces PG(n; q) unless q...

Ahlswede and Khachatrian's diametric theorem is a weighted version of their complete intersection theorem, which is itself a well known extension of the t-intersecting Erd˝ os-Ko-Rado theorem. The complete intersection theorem says that the maximum size of a family of subsets of [n] = {1,. .. , n}, every pair of which intersects in at least t elements, is the size of certain trivially intersect...