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Mathematical Modelling of Beach Litter Distributions using Drone Images

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Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2026.  Director: Ana Alejandra Cabaña Nigro, Niclas Rieger i Estrella Olmedo

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Given that plastic pollution has increased worldwide, accurate quantification of marine litter is essential to develop effective remediation and preventive strategies. However, conducting effective monitoring surveys is difficult due to the inherent spatial variation and laborious nature of current sampling methods. Classic survey protocols often rely on counting items in small sample areas, which may fail to accurately represent overall pollution levels given the tendency of litter to accumulate in clusters. This thesis develops a probabilistic framework using empirical data derived from drone images to quantify the uncertainty of different beach litter sampling protocols in estimating mean litter densities.
Data analysis of provided beach samples demonstrated that litter counts exhibit significant overdispersion and scatteredness, requiring probabilistic distributions beyond standard Poisson models. After extensive model comparisons, a Zero-Inflated Negative Binomial Log-Gaussian Cox Process (ZINB-LGCP) model was implemented, since it best captured the overdispersion and sparsity observed in the empirical data. The model was developed within a Bayesian machine learning framework, employing Penalized Complexity (PC) priors and Hilbert Space Gaussian Process (HSGP) approximations to ensure stable convergence and computational efficiency.
Three representative beaches were chosen to approximate the distinct spatial clustering patterns observed across samples. Using posterior predictive distributions from the fitted model, we generated 5000 synthetic beach realizations that replicate the statistical properties and spatial structure of the three chosen ones. These synthetic samples served as a controlled ground truth to simulate and evaluate the performance of two widely used monitoring protocols: the transect-based National Oceanic and Atmospheric Administration (NOAA) protocol and the station-based Científicos de la Basura (CdB) protocol. The bias, accuracy and precision of both protocols were quantified by comparing their
estimates against known baselines of synthetic beaches. This analysis provides insights into the uncertainties of in-situ measurements and demonstrates that generative Bayesian modeling offers a rigorous validation tool for environmental sampling designs, enabling the optimization of survey efforts without the need for exhaustive physical collection.

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Mathematical Modelling of Beach Litter Distributions using Drone Images