Abstract. Learned local descriptors based on Convolutional Neural Networks (CNNs) have achieved significant improvements on patch-based benchmarks, whereas not having demonstrated strong generalization ability on recent benchmarks of image-based 3D reconstruction. In this paper, we mitigate this limitation by proposing a novel local descriptor learning approach that integrates geometry constraints from multi-view reconstructions, which benefits the learning process in terms of data generation, data sampling and loss computation. We refer to the proposed descriptor as GeoDesc, and demonstrate its superior performance on various large-scale benchmarks, and in particular show its great success on challenging reconstruction tasks. Moreover, we provide guidelines towards practical integration of learned descriptors in Structurefrom-Motion (SfM) pipelines, showing the good trade-off that GeoDesc delivers to 3D reconstruction tasks between accuracy and efficiency