The application of morphological algorithms on 3-dimensional porous structures for identifying pores and gathering statistical data

Thinning algorithms and related methods have been used to examine the void structure of porous materials. While the goal is to divide the porous media into separate entities called pores, these algorithms tend to introduce problems with robustness and falsely identified pores due to digitalisation errors. In this paper we apply methods from mathematical morphology and studies on voids in sedimentary rocks to pore structure characterization of pigment coated paper. The Maximal Balls algorithm is subjected to various modifications and additions in order to make it more suitable for the needs of coated paper research, where porosities are typically relatively high. These modifications include methods for the removal of falsely identified pores inside the media, caused by digitalisation problems. Furthermore, we present different approaches to improve speed, such as the use of pre-calculated data and removal of unnecessary calculations. It is also evident that the previously proposed algorithms consume vast amounts of memory and in order to overcome this we present an approach that removes redundant information and avoids using objects for data representation. The most CPU-intense subalgorithm was reduced from O(n²) Complexity to O(1) for nested calculations. Basic memory optimisations done allowed for a decrease in memory usage to around one half while a fundamental improvement was found in changing data structures. This allows for a closer to linear increase in memory consumption as a function of data size, while the original algorithm showed an unpredictable behaviour linking memory consumption to porosity of the set and the hierarchical structure and used data structures of considerable size.