Iterative Thickness Regularization of Stratigraphic Layers in Discrete Implicit Modeling

@article{laurent:hal-01338981,
 abstract = {Discrete implicit modeling consists in representing structural surfaces as isovalues of three-dimensional piecewise linear scalar fields, which are interpolated from available data points. Data are expressed as local constraints that can enforce the value of the scalar fields as well as their gradients. This paper illustrates some limitations of published discrete implicit methods, related to the difficulty of controlling the norm of scalar field gradient and its evolution over the interpolated domain. It is shown that important artifacts may arise due to the intrinsic dependence between variations in the norm and the direction of the scalar field gradient, from one element to its neighbors. Evidence that these artifacts are related to mesh facet direction with respect to gradient direction are given. The artifacts lead to rapid and uncontrolled variations of thickness that may induce erroneous interpolations. This paper proposes two original approaches to overcome these problems. The first one consists in iteratively adjusting the norm of scalar field gradients in the direction obtained after previous iterations. The second solution consists in optimizing the mesh used by the interpolation. This requires finding appropriate mesh facet orientationwith respect to scalar field gradient. These methods demonstrate that the results of discrete implicit surface interpolation can be improved and call for further development of available interpolation schemes.},
 author = {Laurent, Gautier},
 doi = {10.1007/s11004-016-9637-y},
 hal_id = {hal-01338981},
 hal_version = {v1},
 journal = {{Mathematical Geosciences}},
 keywords = {Discrete scheme ; Structural modeling ; Interpolation ; Mesh ; Norm constraint ; Iterative process},
 pdf = {https://hal.univ-lorraine.fr/hal-01338981v1/file/Laurent_2016_Iterative_thickness_regularisation_author_version.pdf},
 publisher = {{Springer Verlag}},
 title = {{Iterative Thickness Regularization of Stratigraphic Layers in Discrete Implicit Modeling}},
 url = {https://hal.univ-lorraine.fr/hal-01338981},
 year = {2016}
}