Satellite images contain fewer independent samples than pixel count suggests
How Many Independent Samples Does a Satellite Image Contain? Generalization Bounds for Spatially Dependent Data
Computer Vision and Pattern RecognitionMachine Learning
Summary
When using satellite images for machine learning, people often treat every pixel as a separate data point. The authors show that because nearby pixels tend to be similar, the actual number of independent data points is much lower. They prove mathematically how the size of this effect depends on the image size and how far spatial correlation extends. Their results help improve the way algorithms are tested to better reflect real accuracy and confidence.
What this means in practice
- •For remote sensing engineers: Design cross-validation schemes for satellite image classifiers that properly account for spatial correlation and produce reliable confidence estimates.
- •For geospatial data platform developers: Build satellite image data pipelines that correctly estimate effective sample size to avoid overestimating confidence in machine learning models.
Authors
Robin Young
Abstract
Machine learning classifiers for remote sensing imagery are typically evaluated as though every pixel were an independent sample. Spatial autocorrelation violates this assumption, since neighboring pixels carry redundant information which inflates sample sizes. How many independent samples does a satellite image actually contain? For an $n \times n$ image whose spatial correlation persists over a range of $r$ pixels, the effective sample size is $Θ(n^2/r^2)$, not $n^2$. We prove this as a finite-sample upper bound for classifiers on spatially correlated data, and show via a matching lower bound that the rate is tight, and no algorithm can do better. We extend the results to images with directional correlation and spatially varying correlation structure. Our result justifies spatial cross-validation since block holdout with separation proportional to the correlation range achieves optimal generalization guarantees, while random holdout can underestimate confidence interval widths by a factor proportional to $r$. We validate the theory on synthetic data and satellite image tiles from three sensors (Landsat 8, Sentinel-2, and Sentinel-1).