Abstract
The development of novel remote sensing techniques, based on interferometric synthetic aperture RADAR (InSAR), currently allows for millimetric precision measurements of Earth surface deformation over time. One of the major challenges posed by these techniques, known as persistent scatterer interferometry (PSI), is the inherent sparsity of the data resulting from the RADAR scatterer selection process.
In this work we present an automated image analysis framework aimed at the detection of model-defined spatiotemporal features within sparse point cloud datasets, and we show how this framework can be tailored to the early detection of hazardous geophysical features within InSAR-derived data. In particular, we developed a spatiotemporal model describing the evolution of subsiding features, we verified its validity by using discrete element method simulations, and applied it, within our framework, to the early detection of sinkholes.
The ground truth dataset, used to develop the spatiotemporal model, was obtained by imaging a sinkhole prone area for a period of 70months. The relevance of this dataset for our research is due to the fact that it contains four active features of which one (W1) collapsed before the data was taken, and one (W2) collapsed after the data was taken providing ground truth measurements.
We first approached the detection as a graph segmentation problem. By assigning each PSI scatterer within the ground truth dataset to a vertex and enforcing connectivity by the Delaunay triangulation, we obtained a graph that reflected the local neighborhood relationship. We then constructed an edge-weighting function designed to favor low weights for edges traversing boundaries of regions displaying signs of subsidence. The segmentation resulting from the application of the min-cut algorithm to this graph captured 27% and 94% of the collapsed area of W1 and W2 respectively.
Since we had at our disposal the time series of the displacements of each scatterer, we expanded our approach to leverage this information by developing a model-based spatiotemporal detection method. The parameters regulating the behavior of the model were used to generate a multidimensional parameter space that was then scanned with user-defined resolution. At each point, a spatiotemporal template was reconstructed based on the original model and the currently selected parameters. This template was used to analyze the point cloud dataset for regions with matching behavior. This method provided an improvement by identifying as high risk 52.6% and 81.6% of the collapsed area of W1 and W2 respectively against the values of 37.5% and 17.6% obtained from the graph cut approach. We also applied this method to a 40km x 40km area of interest located in western Virginia. The ground validation on a subset of the detected features showed that 78% of the locations presented strong evidence of subsidence.
To improve on the computational burden imposed by the direct application of this exploration method with complex models over large datasets, we developed an activity detection approach where large datasets were subdivided into smaller blocks. The average and standard deviation of the displacements of the scatterers contained in each block were used as elements of each block feature vector. Outliers in the feature space, corresponding to actively subsiding regions, were identified using their Mahalanobis distance. When applied to the ground truth dataset this screening method provided a x15 increase in the detection speed while still maintaining accurate results. To further reduce the impact of larger datasets and complex models, we introduced a second screening stage, based on the evaluation of the normalized mutual information between model and data, to pinpoint the location of features requiring full spatiotemporal analysis.
Finally, to leverage the inherent sparsity of the PSI data, we took advantage of the tools provided by the emerging field of graph signal processing and developed a graph-based scale space analysis approach that provided results comparable to those obtained by previous methods.
