Daily Papers

Local heights are arithmetic invariants used in the quadratic Chabauty method for determining the rational points on curves. We present an algorithm to compute these local heights for hyperelliptic curves at odd primes ellneq p. This algorithm significantly broadens the applicability of quadratic Chabauty to curves which were previously inaccessible due to the presence of non-trivial local heights. We provide numerous examples, including the first quadratic Chabauty computation for a curve having two primes with non-trivial local heights.

Information on trees at the individual level is crucial for monitoring forest ecosystems and planning forest management. Current monitoring methods involve ground measurements, requiring extensive cost, time and labor. Advances in drone remote sensing and computer vision offer great potential for mapping individual trees from aerial imagery at broad-scale. Large pre-trained vision models, such as the Segment Anything Model (SAM), represent a particularly compelling choice given limited labeled data. In this work, we compare methods leveraging SAM for the task of automatic tree crown instance segmentation in high resolution drone imagery in three use cases: 1) boreal plantations, 2) temperate forests and 3) tropical forests. We also study the integration of elevation data into models, in the form of Digital Surface Model (DSM) information, which can readily be obtained at no additional cost from RGB drone imagery. We present BalSAM, a model leveraging SAM and DSM information, which shows potential over other methods, particularly in the context of plantations. We find that methods using SAM out-of-the-box do not outperform a custom Mask R-CNN, even with well-designed prompts. However, efficiently tuning SAM end-to-end and integrating DSM information are both promising avenues for tree crown instance segmentation models.

We introduce GlobalBuildingAtlas, a publicly available dataset providing global and complete coverage of building polygons, heights and Level of Detail 1 (LoD1) 3D building models. This is the first open dataset to offer high quality, consistent, and complete building data in 2D and 3D form at the individual building level on a global scale. Towards this dataset, we developed machine learning-based pipelines to derive building polygons and heights (called GBA.Height) from global PlanetScope satellite data, respectively. Also a quality-based fusion strategy was employed to generate higher-quality polygons (called GBA.Polygon) based on existing open building polygons, including our own derived one. With more than 2.75 billion buildings worldwide, GBA.Polygon surpasses the most comprehensive database to date by more than 1 billion buildings. GBA.Height offers the most detailed and accurate global 3D building height maps to date, achieving a spatial resolution of 3x3 meters-30 times finer than previous global products (90 m), enabling a high-resolution and reliable analysis of building volumes at both local and global scales. Finally, we generated a global LoD1 building model (called GBA.LoD1) from the resulting GBA.Polygon and GBA.Height. GBA.LoD1 represents the first complete global LoD1 building models, including 2.68 billion building instances with predicted heights, i.e., with a height completeness of more than 97%, achieving RMSEs ranging from 1.5 m to 8.9 m across different continents. With its height accuracy, comprehensive global coverage and rich spatial details, GlobalBuildingAltas offers novel insights on the status quo of global buildings, which unlocks unprecedented geospatial analysis possibilities, as showcased by a better illustration of where people live and a more comprehensive monitoring of the progress on the 11th Sustainable Development Goal of the United Nations.