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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. 

In recent years, deep learning has achieved tremendous success in image segmentation for computer vision applications. The performance of these models heavily relies on the availability of large-scale high-quality training labels (e.g., PASCAL VOC 2012). Unfortunately, such large-scale high-quality training data are often unavailable in many real-world spatial or spatiotemporal problems in earth science and remote sensing (e.g., mapping the nationwide river streams for water resource management). Although extensive efforts have been made to reduce the reliance on labeled data (e.g., semi-supervised or unsupervised learning, few-shot learning), the complex nature of geographic data such as spatial heterogeneity still requires sufficient training labels when transferring a pre-trained model from one region to another. On the other hand, it is often much easier to collect lower-quality training labels with imperfect alignment with earth imagery pixels (e.g., through interpreting coarse imagery by non-expert volunteers). However, directly training a deep neural network on imperfect labels with geometric annotation errors could significantly impact model performance. Existing research that overcomes imperfect training labels either focuses on errors in label class semantics or characterizes label location errors at the pixel level. These methods do not fully incorporate the geometric properties of label location errors in the vector representation. To fill the gap, this article proposes a weakly supervised learning framework to simultaneously update deep learning model parameters and infer hidden true vector label locations. Specifically, we model label location errors in the vector representation to partially reserve geometric properties (e.g., spatial contiguity within line segments). Evaluations on real-world datasets in the National Hydrography Dataset (NHD) refinement application illustrate that the proposed framework outperforms baseline methods in classification accuracy. 

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. 

Spatial classification with limited observations is important in geographical applications where only a subset of sensors are deployed at certain spots or partial responses are collected in field surveys. For example, in observation-based flood inundation mapping, there is a need to map the full flood extent on geographic terrains based on earth imagery that partially covers a region. Existing research mostly focuses on addressing incomplete or missing data through data cleaning and imputation or modeling missing values as hidden variables in the EM algorithm. These methods, however, assume that missing feature observations are rare and thus are ineffective in problems whereby the vast majority of feature observations are missing. To address this issue, we recently proposed a new approach that incorporates physics-aware structural constraint into the model representation. We design efficient learning and inference algorithms. This paper extends our recent approach by allowing feature values of samples in each class to follow a multi-modal distribution. Evaluations on real-world flood mapping applications show that our approach significantly outperforms baseline methods in classification accuracy, and the multi-modal extension is more robust than our early single-modal version. Computational experiments show that the proposed solution is computationally efficient on large datasets. 

Accurate maps of regional surface water features are integral for advancing ecologic, atmospheric and land development studies. The only comprehensive surface water feature map of Alaska is the National Hydrography Dataset (NHD). NHD features are often digitized representations of historic topographic map blue lines and may be outdated. Here we test deep learning methods to automatically extract surface water features from airborne interferometric synthetic aperture radar (IfSAR) data to update and validate Alaska hydrographic databases. U-net artificial neural networks (ANN) and high-performance computing (HPC) are used for supervised hydrographic feature extraction within a study area comprised of 50 contiguous watersheds in Alaska. Surface water features derived from elevation through automated flow-routing and manual editing are used as training data. Model extensibility is tested with a series of 16 U-net models trained with increasing percentages of the study area, from about 3 to 35 percent. Hydrography is predicted by each of the models for all watersheds not used in training. Input raster layers are derived from digital terrain models, digital surface models, and intensity images from the IfSAR data. Results indicate about 15 percent of the study area is required to optimally train the ANN to extract hydrography when F1-scores for tested watersheds average between 66 and 68. Little benefit is gained by training beyond 15 percent of the study area. Fully connected hydrographic networks are generated for the U-net predictions using a novel approach that constrains a D-8 flow-routing approach to follow U-net predictions. This work demonstrates the ability of deep learning to derive surface water feature maps from complex terrain over a broad area.