# A Weakly Supervised Approach for Estimating Spatial Density Functions from High-Resolution Satellite Imagery

arXiv: https://arxiv.org/abs/1810.09528 · HTML: https://mlsanity.com/paper/1810.09528/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2018.

## Built on by (most cited first, 6 of 6)

- [Fine-grained Population Mapping from Coarse Census Counts and Open Geodata](https://mlsanity.com/paper/2211.04039/) (2022)
- [High-resolution Population Maps Derived from Sentinel-1 and Sentinel-2](https://mlsanity.com/paper/2311.14006/) (2023)
- [Handling Image and Label Resolution Mismatch in Remote Sensing](https://mlsanity.com/paper/2211.15790/) (2022)
- [A weakly supervised framework for high-resolution crop yield forecasts](https://mlsanity.com/paper/2205.09016/) (2022)
- [Fine-Grained Property Value Assessment using Probabilistic Disaggregation](https://mlsanity.com/paper/2306.00246/) (2023)
- [Probabilistic Image-Driven Traffic Modeling via Remote Sensing](https://mlsanity.com/paper/2403.05521/) (2024)

## Abstract (arXiv)

We propose a neural network component, the regional aggregation layer, that makes it possible to train a pixel-level density estimator using only coarse-grained density aggregates, which reflect the number of objects in an image region. Our approach is simple to use and does not require domain-specific assumptions about the nature of the density function. We evaluate our approach on several synthetic datasets. In addition, we use this approach to learn to estimate high-resolution population and housing density from satellite imagery. In all cases, we find that our approach results in better density estimates than a commonly used baseline. We also show how our housing density estimator can be used to classify buildings as residential or non-residential.