On the coarseness of bicolored point sets

New results on the coarseness of bicolored point sets

Let S be a 2-colored (red and blue) set of n points in the plane. A subset I of S is an island if there exits a convex set C such that I = C∩S. The discrepancy of an island is the absolute value of the number of red minus the number of blue points it contains. A convex partition of S is a partition of S into islands with pairwise disjoint convex hulls. The discrepancy of a convex partition is t...

On Hamiltonian alternating cycles and paths

We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to be plane. In this paper, we relax the constraint on the cycles and paths from being plane to being 1-plane, and deal with the same type of questions as those for the plane case...

Fuzzy Sets for Image Texture Modelling Based on Human Distinguishability of Coarseness

In this paper, the “coarseness” texture property is modelled by means of fuzzy sets, relating representative coarseness measures (our reference set) with the human perception of this type of feature. In our study, a wide variety of measures are analyzed, and the coarseness human perception are collected from polls filled by subjects. The capability of each measure to discriminate different coar...

Texture descriptors by a fractal analysis of three-dimensional local coarseness

9 This work proposes a new method of extracting texture descriptors from digital images based on local scaling properties of the greyscale function using constraints to define connected local sets. The texture is first mapped onto a three-dimensional cloud of points and the local coarseness under different scales is assigned to each point p. This measure is obtained from the size of the largest...

Monochromatic geometric k-factors for bicolored point sets with auxiliary points