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Given raster imagery features and imperfect vector training labels with registration uncertainty, this paper studies a deep learning framework that can quantify and reduce the registration uncertainty of training labels as well as train neural network parameters simultaneously. The problem is important in broad applications such as streamline classification on Earth imagery or tissue segmentation on medical imagery, whereby annotating precise vector labels is expensive and time-consuming. However, the problem is challenging due to the gap between the vector representation of class labels and the raster representation of image features and the need for training neural networks with uncertain label locations. Existing research on uncertain training labels often focuses on uncertainty in label class semantics or characterizes label registration uncertainty at the pixel level (not contiguous vectors). To fill the gap, this paper proposes a novel learning framework that explicitly quantifies vector labels' registration uncertainty. We propose a registration-uncertainty-aware loss function and design an iterative uncertainty reduction algorithm by re-estimating the posterior of true vector label locations distribution based on a Gaussian process. Evaluations on real-world datasets in National Hydrography Dataset refinement show that the proposed approach significantly outperforms several baselines in the registration uncertainty estimations performance and classification performance. 

Given earth imagery with spectral features on a terrain surface, this paper studies surface segmentation based on both explanatory features and surface topology. The problem is important in many spatial and spatiotemporal applications such as flood extent mapping in hydrology. The problem is uniquely challenging for several reasons: first, the size of earth imagery on a terrain surface is often much larger than the input of popular deep convolutional neural networks; second, there exists topological structure dependency between pixel classes on the surface, and such dependency can follow an unknown and non-linear distribution; third, there are often limited training labels. Existing methods for earth imagery segmentation often divide the imagery into patches and consider the elevation as an additional feature channel. These methods do not fully incorporate the spatial topological structural constraint within and across surface patches and thus often show poor results, especially when training labels are limited. Existing methods on semi-supervised and unsupervised learning for earth imagery often focus on learning representation without explicitly incorporating surface topology. In contrast, we propose a novel framework that explicitly models the topological skeleton of a terrain surface with a contour tree from computational topology, which is guided by the physical constraint (e.g., water flow direction on terrains). Our framework consists of two neural networks: a convolutional neural network (CNN) to learn spatial contextual features on a 2D image grid, and a graph neural network (GNN) to learn the statistical distribution of physics-guided spatial topological dependency on the contour tree. The two models are co-trained via variational EM. Evaluations on the real-world flood mapping datasets show that the proposed models outperform baseline methods in classification accuracy, especially when training labels are limited.