A Hidden Markov Contour Tree Model for Spatial Structured Prediction

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).

Automated summary

This paper introduces a novel spatial structured model that captures the dependency structure between samples based on their locations in space. The model outperforms existing methods in classification performance and can be used as a post-processor to refine the results of other models.