Geodesics of Triangulated Image Object Shapes. Approximating Image Shapes via Rectilinear and Curvilinear Triangulations

Abstract: This paper introduces the geodesics of triangulated image object shapes. Both rectilinear and curvilinear triangulations of shapes are considered. The triangulation of image object shapes leads to collections of what are known as nerve complexes that provide a workable basis for the study of shape geometry.A nerve complex is a collection of filled triangles with a common vertex. Each nerve complex triangle has an extension called a spoke, which provides an effective means of covering shape interiors. This leads to a geodesic-based metric for shape approximation which offers a straightforward means of assessing, comparing and classifying the shapes of image objects with high acuity.