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

arXiv: https://arxiv.org/abs/2508.03745 · HTML: https://mlsanity.com/paper/2508.03745/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 57 references that are in the map.
- First posted on arXiv 1 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [AID: A Benchmark Dataset for Performance Evaluation of Aerial Scene Classification](https://mlsanity.com/paper/1608.05167/) (2016)
- [Weakly Supervised Deep Detection Networks](https://mlsanity.com/paper/1511.02853/) (2015)
- [Object Detectors Emerge in Deep Scene CNNs](https://mlsanity.com/paper/1412.6856/) (2014)
- [Multiple Instance Detection Network with Online Instance Classifier Refinement](https://mlsanity.com/paper/1704.00138/) (2017)
- [PatternNet: A Benchmark Dataset for Performance Evaluation of Remote Sensing Image Retrieval](https://mlsanity.com/paper/1706.03424/) (2017)
- [Rotation-Sensitive Regression for Oriented Scene Text Detection](https://mlsanity.com/paper/1803.05265/) (2018)
- [What makes for effective detection proposals?](https://mlsanity.com/paper/1502.05082/) (2015)
- [Learning RoI Transformer for Detecting Oriented Objects in Aerial Images](https://mlsanity.com/paper/1812.00155/) (2018)
- [C-WSL: Count-guided Weakly Supervised Localization](https://mlsanity.com/paper/1711.05282/) (2017)
- [RSI-CB: A Large Scale Remote Sensing Image Classification Benchmark via Crowdsource Data](https://mlsanity.com/paper/1705.10450/) (2017)
- [Learning from Counting: Leveraging Temporal Classification for Weakly Supervised Object Localization and Detection](https://mlsanity.com/paper/2103.04009/) (2021)

## Built on by (most cited first, 1 of 1)

- [Physics-Informed Spectral Modeling for Hyperspectral Imaging](https://mlsanity.com/paper/2508.21618/) (2025)

## Abstract (arXiv)

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.