The OPTIMAL project will introduce a novel change detection method, based on optimal transport, to automatically identify looting activities, allowing wide spatial contexts to be swiftly and accurately analysed. The key steps of the research methodology are detailed below:

1) User case scenario and data collection.The user case scenario was carefully drafted with the Center for Cultural Heritage Technology (CCHT) of the Istituto Italiano di Tecnologia (IIT), the European host institution. The first multi-temporal LiDAR dataset for looting identification was created in this step. As reported in the Data Management Plan (DMP), the raw data made available to the fellow by the owner under a specific data usage agreement were pre-processed during the first year of the project. The daset contains co-registered LiDAR point cloud pairs, ( PC(t), PC(t+ Δt)), captured at two successive equally spaced points in time, t and t+ Δt. The identification of suitable case study locations, where looting is known to happen representing diverse environmental settings to trial the proposed ML approach. 

2) Design of two unsupervised change detection algorithms on LiDAR. The recent new trend in the study of how to apply optimal transport (OT) to ML problems makes this a favourable moment to apply the OPT theory for detecting changes on non-registered complex and time-evolving LiDAR point clouds. The optimal transport theory provides a natural way to detect changes between a pair of point clouds enabling to computation of the geometric discrepancy between two distributions (the pair of clouds) and evaluating Wasserstein distances (also known as Earth Mover’s) between them. In this project, an unsupervised change detection approach based on unbalanced optimal transport was developed. Specifically, OT provides us with a methodology to project the first point cloud on the support of the second one through the so-called displacement interpolation by considering both clouds as two uniform probability distributions. The changes are then computed point-wise between the projected and the second cloud. The OPTIMAL change detection method was tailored to detect the presence of looting pits, holes and trenches (which have well-known patterns and shapes) spread over and around archaeological sites to track illegal activities and their rate over time. The design and implementation of this approach will be performed at Kyoto University under the supervision of Prof Makoto Yamada.

In collaboration with Kyoto University and RIKEN AIP, another novel change detection algorithm was developed. This method is based on neural implicit representation learning to encode a bi-temporal pair of LiDAR point clouds as a continuous function of both time and space. This function is estimated using the total variation norm to enforce discontinuities along the time dimension to model sharp temporal changes and increase robustness to noisy measurements. In the second step, the changes in altitude are characterised using the Gaussian mixture model.

3) Evaluation of change detection algorithm. Hypothetical target sites that were identified from the OPTIMAL detection pipeline were tested using image-based manual inspection. The direct check of the proposed optimal transport technique was possible for a limited number of sites through the support of several CCHT archaeologists and external collaborators who have committed to undertake targeted surveys on the ground to ascertain the looting activities and collect intelligence to determine the exact period of the pillaging.