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To extract information at scale, researchers increasingly apply semantic segmentation techniques to remotely-sensed imagery. While fully-supervised learning enables accurate pixel-wise segmentation, compiling the exhaustive datasets required is often prohibitively expensive. As a result, many non-urban settings lack the ground-truth needed for accurate segmentation. Existing open source infrastructure data for these regions can be inexact and non-exhaustive. Open source infrastructure annotations like OpenStreetMaps (OSM) are representative of this issue: while OSM labels provide global insights to road and building footprints, noisy and partial annotations limit the performance of segmentation algorithms that learn from them. In this paper, we present a novel and generalizable two-stage framework that enables improved pixel-wise image segmentation given misaligned and missing annotations. First, we introduce the Alignment Correction Network to rectify incorrectly registered open source labels. Next, we demonstrate a segmentation model -- the Pointer Segmentation Network -- that uses corrected labels to predict infrastructure footprints despite missing annotations. We test sequential performance on the AIRS dataset, achieving a mean intersection-over-union score of 0.79; more importantly, model performance remains stable as we decrease the fraction of annotations present. We demonstrate the transferability of our method to lower quality data, by applying the Alignment Correction Network to OSM labels to correct building footprints; we also demonstrate the accuracy of the Pointer Segmentation Network in predicting cropland boundaries in California from medium resolution data. Overall, our methodology is robust for multiple applications with varied amounts of training data present, thus offering a method to extract reliable information from noisy, partial data.