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This paper introduces the geodesics of triangulated image object shapes. Bothrectilinear and curvilinear triangulations of shapes are considered. Thetriangulation of image object shapes leads to collections of what are known asnerve complexes that provide a workable basis for the study of shape geometry.Anerve complex is a collection of filled triangles with a common vertex. Eachnerve complex triangle has an extension called a spoke, which provides aneffective means of covering shape interiors. This leads to a geodesic-basedmetric for shape approximation which offers a straightforward means ofassessing, comparing and classifying the shapes of image objects with highacuity.

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