Accurate and prompt mapping of flood extent is important for effective disaster management. Prior terrain-guided methods utilizing digital elevation model (DEM) data to improve segmentation quality, but are only applicable to small areas with restricted assumptions. We propose ZoneGraph, a scalable flood mapping approach that is generally applicable to any area. Since water level varies a lot from upstream to downstream, and an Earth image may contain multiple river channels or branches, ZoneGraph partitions an Earth image into localized zones each with a consistent water level for intra-region inference using hidden Markov trees (HMTs), and uses a zone adjacency graph for inter-zone regularization to enforce flow direction consistency across adjacent zones. Parallelization techniques are applied to speed up the zonal water level computations. Experiments show ZoneGraph achieves higher accuracy than existing methods, scale to a large area with 24,805 × 40,129 pixels, and yields up to 14.3× parallelization speedup on 32 threads.

Flood inundation mapping from Earth imagery plays a vital role in rapid disaster response and national water forecasting. However, the problem is non-trivial due to significant imagery noise and obstacles, complex spatial dependency on 3D terrains, spatial non-stationarity, and high computational cost. Existing machine learning approaches are mostly terrain-unaware and are prone to produce spurious results due to imagery noise and obstacles, requiring significant efforts in post-processing. Recently, several terrain- aware methods were proposed that incorporate complex spatial dependency (e.g., water flow directions on 3D terrains) but they assume that the inferred flood surface level is spatially stationary, making them insufficient for a large heterogeneous geographic area. To address these limitations, this paper proposes a novel spatial learning framework called hidden Markov forest, which decomposes a large heterogeneous area into local stationary zones, represents spatial dependency on 3D terrains via zonal trees (forest), and jointly infers the class map in different zonal trees with spatial regularization. We design efficient inference algorithms based on dynamic programming and multi-resolution filtering. Evaluations on real-world datasets show that our method outperforms baselines and our proposed computational refinement significantly reduces the time cost.

Accurate and timely mapping of flood extent plays a crucial role in disaster management such as damage assessment and relief activities. In recent years, high-resolution optical imagery becomes increasingly available with the wide deployment of satellites and drones. However, analyzing such imagery data to extract flood extent poses unique challenges due to noises such as obstacles (e.g., tree canopies, clouds). In this paper, we propose an elevation-guided annotation tool for flood extent mapping, which allows annotators to provide the flooded/dry labels for just a few pixels to cover a large area where the labels of most other pixels are automatically inferred. The physical rule we use here to guide the automatic label inference is that if a location is flooded (resp. dry), then its adjacent locations with a lower (resp. higher) elevation must also be flooded (resp. dry). In this way, annotators just need to label the pixels that they are confident with, and the true labels of many ambiguous pixels such as tree-canopy ones can be automatically inferred. We demonstrate the usage of our annotation tool using high-resolution aerial imagery from National Oceanic and Atmospheric Administration (NOAA) National Geodetic Survey (NGS) together with the corresponding Digital Elevation Model (DEM) data. The annotated data can be used to train machine learning models for flood extent mapping, and we train U-Net models to infer the flood map for an unseen region and achieve a high accuracy. Our annotation tool is open-sourced at https://github.com/SaugatAdhikari/Flood-Annotation-Tool.

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.

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.

Spatial structured models are predictive models that capture dependency structure between samples based on their locations in the space. Learning such models plays an important role in many geoscience applications such as water surface mapping, but it also poses significant challenges due to implicit dependency structure in continuous space and high computational costs. Existing models often assume that the dependency structure is based on either spatial proximity or network topology, and thus cannot incorporate complex dependency structure such as contour and flow direction on a 3D potential surface. To fill the gap, we recently proposed a novel spatial structured model called hidden Markov contour tree (HMCT), which generalizes the traditional hidden Markov model from a total order sequence to a partial order polytree. HMCT also advances existing work on hidden Markov trees through capturing complex contour structures on a 3D surface. We proposed efficient model construction and learning algorithms. This paper extends our initial HMCT model into a post-processor that can refine the classified results from other existing models. We analyzed the theoretical properties of the extended model. Evaluations on real-world flood mapping datasets show that HMCT outperforms multiple baseline methods in classification performance and the HMCT can also effectively enhance the results of other baseline methods. Computational experiments also show that HMCT is scalable to large data sizes (e.g., classifying millions of samples in seconds).

Given a 3D surface defined by an elevation function on a 2D grid as well as non-spatial features observed at each pixel, the problem of surface segmentation aims to classify pixels into contiguous classes based on both non-spatial features and surface topology.The problem has important applications in hydrology, planetary science, and biochemistry but is uniquely challenging for several reasons.First, the spatial extent of class segments follows surface contours in the topological space, regardless of their spatial shapes and directions.Second, the topological structure exists in multiple spatial scales based on different surface resolutions.Existing widely successful deep learning models for image segmentation are often not applicable due to their reliance on convolution and pooling operations to learn regular structural patterns on a grid.In contrast, we propose to represent surface topological structure by a contour tree skeleton, which is a polytree capturing the evolution of surface contours at different elevation levels.We further design a graph neural network based on the contour tree hierarchy to model surface topological structure at different spatial scales.Experimental evaluations based on real-world hydrological datasets show that our model outperforms several baseline methods in classification accuracy.

Given a spatial raster framework with explanatory feature layers, a spatial contextual layer (e.g., a potential field), as well as a set of training samples with class labels, the spatial prediction problem aims to learn a model that can predict a class layer. The problem is important in societal applications such as flood extent mapping for disaster response and national water forecasting, but is challenging due to the noise, obstacles, and heterogeneity in feature maps, implicit spatial dependency between locations based on the contextual layer (e.g., gradient directions on a potential field), and the large number of sample locations. Existing work often assumes undirected spatial dependency, or directed dependency with a total order, and thus cannot reflect complex directed dependency with a partial order. In contrast, we recently proposed geographical hidden Markov tree, a probabilistic graphical model that generalizes the common hidden Markov model from a one-dimensional sequence to a two-dimensional map. Partial order class dependency is incorporated in the hidden class layer with a reverse tree structure. We also investigated computational algorithms for reverse tree construction, model parameter learning and class inference. This paper extends our recent model with overlaying class nodes between observation nodes and underlying hidden class nodes. The additional overlaying class layer makes the model more robust to large scale feature obstacles. We also proposed corresponding learning and inference methods. Extensive evaluations on real world datasets show that our models outperform multiple baselines in flood mapping applications, our algorithms are scalable on large data sizes, and the proposed extension enhances classification performance.

Over the last decade, deep learning research has achieved tremendous success in computer vision and natural language processing. The current widely successful deep learning models are largely based on convolution and pooling operations on a Euclidean plane with a regular grid (e.g., image and video data) and thus cannot be directly applied to the non-Euclidean surface. Geometric deep learning aims to fill the gap by generalizing deep learning models from a 2D Euclidean plane to a 3D geometric surface. The problem has important applications in human-computer interaction, biochemistry, and mechanical engineering, but is uniquely challenging due to the lack of a regular grid framework and the difficulties in learning geometric features on a non-Euclidean manifold. Existing works focus on generalizing deep learning models from 2D image to graphs (e.g., graph neural networks) or 3D mesh surfaces but without fully learning geometric features from a differential geometry perspective. In contrast, this paper proposes a novel geometric deep learning model called CurvaNet that integrates differential geometry with graph neural networks. The key idea is to learn direction sensitive 3D shape features through directional curvature filters. We design a U-Net like architecture with downsampling and upsampling paths based on mesh pooling and unpooling operations. Evaluation on real-world datasets shows that the proposed model outperforms several baseline methods in classification accuracy.

Spatial structured models are predictive models that capture dependency structure between samples based on their locations in the space. Learning such models plays an important role in many geoscience applications such as water surface mapping, but it also poses significant challenges due to implicit dependency structure in continuous space and high computational costs. Existing models often assume that the dependency structure is based on either spatial proximity or network topology, and thus cannot incorporate complex dependency structure such as contour and flow direction on a 3D potential surface. To fill the gap, this paper proposes a novel spatial structured model called hidden Markov contour tree (HMCT), which generalizes the traditional hidden Markov model from a total order sequence to a partial order polytree. HMCT also advances existing work on hidden Markov trees through capturing complex contour structures on a 3D surface. We propose efficient model construction and learning algorithms. Evaluations on real world hydrological datasets show that our HMCT outperforms multiple baseline methods in classification performance and that HMCT is scalable to large data sizes (e.g., classifying millions of samples in seconds).

Class ambiguity refers to the phenomenon whereby similar features correspond to different classes at different locations. Given heterogeneous geographic data with class ambiguity, the spatial ensemble learning (SEL) problem aims to find a decomposition of the geographic area into disjoint zones such that class ambiguity is minimized and a local classifier can be learned in each zone. The problem is important for applications such as land cover mapping from heterogeneous earth observation data with spectral confusion. However, the problem is challenging due to its high computational cost. Related work in ensemble learning either assumes an identical sample distribution (e.g., bagging, boosting, random forest) or decomposes multi-modular input data in the feature vector space (e.g., mixture of experts, multimodal ensemble) and thus cannot effectively minimize class ambiguity. In contrast, we propose a spatial ensemble framework that explicitly partitions input data in geographic space. Our approach first preprocesses data into homogeneous spatial patches and uses a greedy heuristic to allocate pairs of patches with high class ambiguity into different zones. We further extend our spatial ensemble learning framework with spatial dependency between nearby zones based on the spatial autocorrelation effect. Both theoretical analysis and experimental evaluations on two real world wetland mapping datasets show the feasibility of the proposed approach.

Flood extent mapping plays a crucial role in disaster management and national water forecasting. Unfortunately, traditional classification methods are often hampered by the existence of noise, obstacles and heterogeneity in spectral features as well as implicit anisotropic spatial dependency across class labels. In this paper, we propose geographical hidden Markov tree, a probabilistic graphical model that generalizes the common hidden Markov model from a one dimensional sequence to a two dimensional map. Partial order class dependency is incorporated in the hidden class layer with a reverse tree structure. We also investigate computational algorithms for reverse tree construction, model parameter learning and class inference. Extensive evaluations on both synthetic and real world datasets show that proposed model outperforms multiple baselines in flood mapping, and our algorithms are scalable on large data sizes.