Graph-Based M-tortuosity Estimation

The sinuosity of a porous microstructure may be quantified by geometric tortuosity characterization, namely the ratio of geodesic and euclidean distances. The assessment of geometric tortuosity, among other descriptors, is of importance for rigorous characterization of complex materials. This paper proposes a new way of calculation, based on a graph structure, of the topological descriptor M-tortuosity introduced in [3]. The original M-tortuosity descriptor is based on a geodesic distance computation algorithm. A pore network partition [7] method is used to extract pores and construct a graph from the void of a porous microstructure. Through this scheme, pores are the nodes, distances between pores are the arcs between nodes and the goal boils down to the determination of the shortest paths between nodes. Solving this on a graph requires a tree search formulation of the problem. Our results have shown a drastic time complexity decrease while preserving good agreement with the original results. The added value of our method consists in its simplicity of implementation and its reduced execution time.