Tobler's First Law in GeoAI: A Spatially Explicit Deep Learning Model for Terrain Feature Detection Under Weak Supervision

Recent interest in geospatial artificial intelligence (GeoAI) has fostered a wide range of applications using artificial intelligence (AI), especially deep learning, for geospatial problem solving. However, major challenges such as a lack of training data and the neglect of spatial principles and spatial effects in AI model design remain, significantly hindering the in-depth integration of AI with geospatial research. This paper reports our work in developing a deep learning model that enables object detection, particularly of natural features, in a weakly supervised manner. Our work makes three contributions: First, we present a method of object detection using only weak labels. This is achieved by developing a spatially explicit model based on Tobler's first law of geography. Second, we incorporate attention maps into the object detection pipeline and develop a multistage training strategy to improve performance. Third, we apply this model to detect impact craters on Mars, a task that previously required extensive manual effort. The model generalizes to both natural and human-made features on the surfaces of Earth and other planets. This research advances the theoretical and methodological foundations of GeoAI.