Optimizing the Spatial Layout of Agricultural Irrigation Sprinklers Using Remote Sensing Data: An Adaptive Incremental $K$-Means Clustering Algorithm

The layout of sprinklers is crucial in agricultural irrigation systems, and agricultural remote sensing technology plays a key role in extracting plant distribution data for designing efficient sprinkler layouts. However, traditional manual methods struggle to handle the complexity and scale of plant distribution data. To address this, we propose an adaptive incremental <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula>-means (AIK-means) clustering algorithm for sprinkler layout optimization. AIK-means partitions plant objects into clusters, determining a centroid for each cluster. By placing sprinklers at these centroids, the algorithm ensures high irrigation coverage and minimizes water waste. AIK-means iteratively updates the centroids, assigning plant objects to clusters based on distance constraints to guarantee full coverage within each cluster. New centroids are introduced for plant objects not yet irrigated, and the centroids are updated within these new clusters to ensure validity. In addition, AIK-means integrates an adaptive adjustment mechanism to prevent excessive clustering of centroids, thereby minimizing overlapping sprinkler coverage. Experimental results on real plant distribution datasets extracted from agricultural remote sensing images demonstrate that AIK-means outperforms widely-used clustering algorithms, achieving a significant improvement of at least 90% in the coverage-to-overlap ratio metric.