  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.
