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This paper describes an interdisciplinary approach to geometry modeling ofgeospatial boundaries. The objective is to extract surfaces from irregularspatial patterns using differential geometry and obtain coherent directionalpredictions along the boundary of extracted surfaces to enable more targetedsampling and exploration. Specific difficulties of the data include sparsity,incompleteness, causality and resolution disparity. Surface slopes areestimated using only sparse samples from cross-sections within a geologicaldomain with no other information at intermediate depths. From boundarydetection to subsurface reconstruction, processes are automated in between. Thekey problems to be solved are boundary extraction, region correspondence andpropagation of the boundaries via contour morphing. Established techniques fromcomputational physics, computer vision and signal processing are used withappropriate modifications to address challenges in each area. To facilitateboundary extraction, an edge map synthesis procedure is presented. This workswith connected component analysis, anisotropic diffusion and active contours toconvert unordered points into regularized boundaries. For regioncorrespondence, component relationships are handled via graphicaldecomposition. FFT-based spatial alignment strategies are used in regionmerging and splitting scenarios. Shape changes between aligned regions aredescribed by contour metamorphosis. Specifically, local spatial deformation ismodeled by PDE and computed using level-set methods. Directional predictionsare obtained using particle trajectories by following the evolving boundary.However, when a branching point is encountered, particles may lose track of thewavefront. To overcome this, a curvelet backtracking algorithm has beenproposed to recover information for boundary segments without particle coverageto minimize shape distortion.

Subsurface Boundary Geometry Modeling: Applying Computational Physics, Computer Vision and Signal Processing Techniques to Geoscience