Implicit Reconstruction of Complex Geological Surfaces

@inproceedings{FrankRM2005,
 abstract = { In this paper we introduce a new, precise and adaptive method for the implicit reconstruction of discontinuous surfaces from scattered, unorganized points as extracted from seismic data. We embed the point set into a 3D complex on which a 3D implicit function is interpolated. The 3D complex is a set of tetrahedra and the implicit function represents a surface that lies as close as possible to the input data points. The density of the 3D complex can be adapted to efficiently control both the precision of the implicit function and the size of triangles of the reconstructed surface. Discontinuities in the topology of the tetrahedral mesh make it possible to reconstruct discontinuous, bounded surfaces and very close parallel patches without introducing unwanted connections (topological “handles”) between these regions. The value of the implicit function is computed so that it is zero at data points that the reconstructed surface will fit, negative on one side of that surface and positive on the other side. To compute the implicit function we use the Discrete Smooth Interpolation (DSI) method with a set of boundary, off-boundary and smoothness constraints. The interpolation problem does not primarily depend on the number of input data points but on the magnitude of the 3D complex, and it can handle a huge number of constraints. Once the implicit function is computed, a surface where the value of the function is zero is extracted from the tessellated model using a marching tetrahedra algorithm. Then the triangulation of the surface is improved. Contrary to other methods, our approach does not require computing normals on the input point set, even for sparse data. },
 author = { Frank, Tobias AND Tertois, Anne-Laure AND Mallet, Jean-Laurent },
 booktitle = { 25th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { Implicit Reconstruction of Complex Geological Surfaces },
 year = { 2005 }
}