Improved atomic meshes

SUMMARYThis work describes several improvements over the technique known as Atomic Meshes introducedby Hale[8], which aims at producing numerical meshes from image data “directly”, i.e., bypassingany image segmentation step. We propose two modifications to Hale’s original idea: (1) a procedurewhereby atoms are initially projected onto perceived features, and (2) the introduction of a Laplaciancomponent to the formulation of the energy field governing atom movement. These aim at improvingthe adaptation of the mesh to the image while producing better shaped triangles. True to Hale’sidea, no image segmentation is ever tried, but since the atom placement and movement criteria aremore sensitive to image borders, experiments indicate that the resulting meshes tend to conform moreclosely to the image features. Copyright °c 2000 John Wiley & Sons, Ltd.key words: Numerical meshes; seismic data; image processing 1. IntroductionCreating meshes which approximate or are in some way conformal to the features of a givenimage has captured the attention of many researchers over the last years. The idea is thatthe resulting mesh contains much of the information of the underlying image which makes itideal for applications such as image compression, image modeling, medical image analysis andothers [13].A particularly interesting application is the creation of meshes from seismic images.Traditionally,thegeologicalinterpretationofseismicdataresultsinasetofcurvesandsurfaces,which are used to construct a consistent earth model. This model can then be used to generatediscrete meshes for several kinds of numerical simulations, such as a reservoir simulation,the propagation of acoustic waves, or large-scale fluid and heat flow within saturated poroussediments.The geological model must contain all of the geological features, such as horizons (separatingsurfaces between geological layers) and faults (discontinuities caused by the brittle behavior