An algorithm for segmentation under interpolation conditions using deformable models. (English) Zbl 1013.65068
Summary: We present a deformable model technique for geophysical image analysis. Deformable model approaches have been developed extensively in the literature, including prior applications to geophysical or medical image interpretation. In this paper we propose a method to segment a geophysical image under interpolation conditions (well data). The originality of this segmentation method is that it considers the deformable model as a set of articulated curves, which corresponds to the interfaces between different regions. Moreover, the interpolation conditions permit some geometric constraints to be made on the model. The theoretical aspect of the method is given in the case of a three-dimensional image. Numerical results are given.
MSC:
| 65K10 | Numerical optimization and variational techniques |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49M15 | Newton-type methods |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 86A22 | Inverse problems in geophysics |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
Keywords:
inverse problems; finite elements; snakes; deformable models; energy integral minimization; level set methods; viscosity solution; numerical results; geophysical image analysis; interpolation; segmentation methodReferences:
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| [6] | DOI: 10.1016/0021-9991(88)90002-2 · Zbl 0659.65132 · doi:10.1016/0021-9991(88)90002-2 |
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