Using the Interval Metric for Modeling Entities Geometrics in R2 – Case Study Interval Circumference - Aguiar, Sergio S.; Trindade, Roque M. P.; Andrade, Alexsandra O.; Silva, Alzira F.; Cerquiera, Gonçalo R. (Trends in Computational and Applied Mathematics, 2020)
The study of some distances provide science away to separate two entities.It has applications in various ﬁelds such as remote sensing, datamining, pattern recognition and multivariate data analysis and others. If the distance is a Hausdorff metric, the guarantee is that all individuals are available. With the use of the distance of Trindade et al, we intend to extend the real topology to an interval topology, since the interval distance preserves the uncertainties and exits noise in the data. The present work proposes an interval circumference using an interval distance of a point to the center (pixel), like a set of pixels obeying certain distances to the center. With the interval circumference we intend to extend the notion of open ball and the concepts of neighborhood for the construction of the interval topology. A circumference separates a space into three regions, inner region, border region and outer region, where we construct our notion of neighborhood. In this work we will explore only the geometric properties of the intervalcircumference, we will extrapolate the notion from point to pixel by providing a differentiated frontier region for the clustering area.