Discrete Gaussian Process Representations for Optimising UAV-based Precision Weed Mapping

Accurate agricultural weed mapping using UAVs is crucial for precision farming applications. Traditional methods rely on orthomosaic stitching from rigid flight paths, which is computationally intensive and time-consuming. Gaussian Process (GP)-based mapping offers continuous modelling of the underlying variable (i.e. weed distribution) but requires discretisation for practical tasks like path planning or visualisation. Current implementations often default to quadtrees or gridmaps without systematically evaluating alternatives. This study compares five discretisation methods: quadtrees, wedgelets, top-down binary space partition (BSP) trees using least square error (LSE), bottom-up BSP trees using graph merging, and variable-resolution hexagonal grids. Evaluations on real-world weed distributions measure visual similarity, mean squared error (MSE), and computational efficiency. Results show quadtrees perform best overall, but alternatives excel in specific scenarios: hexagons or BSP LSE suit fields with large, dominant weed patches, while quadtrees are optimal for dispersed small-scale distributions. These findings highlight the need to tailor discretisation approaches to weed distribution patterns (patch size, density, coverage) rather than relying on default methods. By choosing representations based on the underlying distribution, we can improve mapping accuracy and efficiency for precision agriculture applications.