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

Jacob Swindell, Madeleine Darbyshire, Marija Popovic, Riccardo Polvara

TL;DR

This paper tackles the challenge of efficiently mapping weed distributions from UAV imagery by using Gaussian process (GP) regression and discretising the continuous GP state for practical tasks such as path planning. It systematically evaluates five discrete GP representations—quadtrees, wedgelets, BSP with least-squares error (LSE), BSP with region-based pruning, and hexagonal grids—against a high-resolution gridmap reference across real-world WeedMap datasets, using metrics like SSIM, HD, and MSE along with time and memory. The study finds that quadtrees perform best on average, but hexagonal grids and BSP-LSE excel for fields with large dominant patches, while quadtrees are robust for many small patches; BSP-LSE offers the best mean squared error at the cost of higher computation, and BSP Region tends to be the most memory- and time-efficient. These results demonstrate that discretisation should be tailored to weed patch patterns to improve mapping fidelity and computational efficiency, guiding practitioners in selecting representations based on field distribution and planning needs, with implications for online UAV mapping and adaptive surveys.

Abstract

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.

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

TL;DR

This paper tackles the challenge of efficiently mapping weed distributions from UAV imagery by using Gaussian process (GP) regression and discretising the continuous GP state for practical tasks such as path planning. It systematically evaluates five discrete GP representations—quadtrees, wedgelets, BSP with least-squares error (LSE), BSP with region-based pruning, and hexagonal grids—against a high-resolution gridmap reference across real-world WeedMap datasets, using metrics like SSIM, HD, and MSE along with time and memory. The study finds that quadtrees perform best on average, but hexagonal grids and BSP-LSE excel for fields with large dominant patches, while quadtrees are robust for many small patches; BSP-LSE offers the best mean squared error at the cost of higher computation, and BSP Region tends to be the most memory- and time-efficient. These results demonstrate that discretisation should be tailored to weed patch patterns to improve mapping fidelity and computational efficiency, guiding practitioners in selecting representations based on field distribution and planning needs, with implications for online UAV mapping and adaptive surveys.

Abstract

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.

Paper Structure

This paper contains 14 sections, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Dataset / Data processing
  5. Continuous Weed Distribution
  6. Discrete GP Representations
  7. Evaluation Metrics
  8. Experimental Evaluation
  9. Qualitative Results
  10. Quantitative Results
  11. Computational and Memory Performance
  12. Correlation
  13. Discussion
  14. Conclusion

Figures (2)

  • Figure 1: Conventional weed mapping uses UAV orthomosaics and deep learning to label coverage, yet pixel-level segmentation may be superfluous. We show that a Gaussian process regressor, trained from uniform samples of the orthomosaic, can capture the underlying weed distribution, and compare multiple discretised representations for computational and statistical advantages.
  • Figure 2: Representations for 000_gt orthomosaic in the WeedMap dataset. Bright spots show a high weed presence while dark spots show low weed presence.