Continuous Version of the Previously Introduced Discrete Distance
Version continue de la distance discrète précédemment introduite
Résumé
This article provides a detailed exploration of a measure-based distance metric, denoted as d µ , designed for comparing arbitrary measurable subsets. This metric is a continuous generalization of the discrete distance introduced in prior work [2]. We investigate its theoretical properties, including its metric space characteristics and behavior across various measure spaces. Comparisons with established metrics such as the Hausdorff and Wasserstein distances highlight d µ 's unique advantages in flexibility and interpretability. The metric's practical utility is demonstrated through applications in image processing and land use analysis using Geographic Information Systems (GIS). This work contributes new insights and examples, establishing d µ as a versatile instrument for set comparison.
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