Volume segmentation of synthetically generated data of porous chalk rocks – University of Copenhagen

Volume segmentation of synthetically generated data of porous chalk rocks

Master's Defense by Jacob Daniel Kirstejn Hansen April 15th.

Abstract

This thesis presents a complete pipeline for the automatised generation of synthetic 3-dimensional porous chalk rock data, from X-ray com- puterised microtomography (X-ray μCT) data. Generated datasets are based on two experimental datasets with voxel sizes of 25 and 50 nm, collected from the ID22 beamline, at the European Synchrotron Research Facility. The pipeline shows great potential for reconstructing dataset with similar petrophysical parameters.

Two process based data generation strategies are proposed, for low- and high-energy environment sedimentation of spherical shaped and irregularly shaped grains respectively. An automatic shape prior extraction routine, based on the watershed transform has been implemented for the generation of grain size distributions. A randomized extraction of grain radii from grain size distributions, for sedimentation, has been done using the inverse transform sampling. A variational segmenta- tion algorithm, as an extension of the classic Chan and Vese algorithm ([Chan and Vese, 2001]) has been derived and implemented. The algorithm is without level sets and has a regularization term based on the dual formulation of total variation, which is relaxed to make the min- imization problem convex, inspired by the recent work of Chambolle, Cremers and Pock ([Chambolle et al., 2012]).

The pipeline encompasses functionality for adding blurring, noise, bias field, and ringing effects artefacts, at variable controllable strength and nature. Two pairs of synthetic datasets have been created, based on the two proposed strategies, each pair with voxel sizes of 25 and 50 nm. All four artefacts have been added to each pair and segmented using our proposed method, to test the feasibility of our pipeline. A module for computing petrophysical quality indicators and measures has also been developed, that comprises the Sørensen-Dice coefficient, porosity, grain surface voxel ratio, pore phase connectivity, and the total surface area shared between grain and pore space. All Dice scores were reported over 97% and relative ratios of segmented volumes and ground truth show near perfect restoration of porosity and connectivity.

Relative ratios of recovered surface voxels and total surface area are near 80%. Furthermore, a meshing module has been used to gener- ate surface meshes for visualization, but can also be used to generate volume meshes for future fluid simulations to determine important petrophysical parameters.

This first iteration of the pipeline looks very promising as a testbed for future comparative studies and segmentation parameter tuning, to test feasibility and accuracy of segmentation algorithms.