Discrete Morse theory segmentation on high-resolution 3D lithic artifacts

Motivated by the question of understanding the roots of tool making by anatomically modern humans and coexisting Neanderthals in the Paleolithic, a number of shape classification methods have been tested on photographs and drawings of stone tools. Since drawings contain interpretation and photographs fool both human and computational methods by color and shadows on the surface, we propose an approach using 3D datasets as best means for analyzing shape, and rely on first open access repositories on lithic tools. The goal is to not only analyze shape on an artifact level, but allow a more detailed analysis of stone tools on a scar and ridge level. A Morse-Smale complex (MS complex) extracted from the triangular mesh of a 3D model is a reduced skeleton consisting of linked lines on the mesh. Discrete Morse theory makes it possible to obtain such a MS complex from a scalar function. Thus, we begin with Multi-Scale Integral Invariant filtering on the meshes of lithic artifacts, which provides curvature measures for ridges, which are convex, and scars, which are concave. The resulting values on the vertices can be used as our discrete Morse function and the skeleton we get is build up from lines that will coincide with the ridges and, implicitly, contains the scars as enclosed regions of those lines on the mesh. As this requires a few parameters, we provide a graphical user interface (GUI) to allow altering the predefined parameters to quickly find a good result. In addition, a stone tool may have areas that do not belong to the scar/ridge class. These can be masked and we use conforming MS complexes to ensure that the skeleton keeps these areas whole. Finally, results are shown on real and open access datasets. The source code and manually annotated ground truth for the evaluation are provided as Open Access with a Creative Commons license.