Sebastien Guillon

Adaptive nonlinear filters for 2D and 3D image enhancement

Abstract Unsharp masking method is a popular approach for image enhancement, in which a highpass version of an image is added to the original one. This method is easy to run, but is very sensitive to noise. Suppressing noise is generally performed with lowpass filters, and leads to edge blurring. So, an approach which is a combination of a nonlinear lowpass and highpass filters is proposed. These filters are based on an adaptive filter mask. We demonstrate that this approach performs noise reduction as well as edge enhancement. It also improves the contrast enhancement in comparison with other methods. These results are illustrated by processing blurred and noisy images. The method is then extended for 3D data processing and used on 3D seismic images.

Seismic Fault Preserving Diffusion

This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non linear diffusion filtering leading to a better detection of seismic faults. The non linear diffusion approaches are based on the definition of a partial differential equation that allows us to simplify the images without blurring relevant details or discontinuities. Computing the structure tensor which provides information on the local orientation of the geological layers, we propose to drive the diffusion along these layers using a new approach called SFPD (Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor are fixed according to a confidence measure that takes into account the regularity of the local seismic structure. Results on both synthesized and real 3-D blocks show the efficiency of the proposed approach.

Robust nonlinear contrast enhancement filters

This paper is devoted to a new adaptive class of nonlinear contrast enhancement filters. These filters are referred to as nonstationary filters because the filter mask depends on the local pixel values. First we show how to find the adaptive filter mask, i.e. the set of surrounding pixels the more similar, in a sense which is defined, to the current pixel. Then we define a new class of quadratic filters based on the so defined filter mask. Finally, processing of blurred and noisy images by these algorithms demonstrates the contrast enhancement improvement in comparison to other quadratic filters.

Discontinuous seismic horizon tracking based on a poisson equation with incremental dirichlet boundary conditions

We propose a new method to track a seismic horizon with a discontinuity due to a fault throw assumed to be quasi-vertical. Our approach requires the knowledge of the two points delimiting the horizon as well as the discontinuity location and jump. We deal with a non linear partial derivative equation relied on the estimated local dip. Its iterative resolution is based on a Poisson equation with incremental Dirichlet boundary conditions. By exploiting a coherence criterion, we finally present an efficient method even when the discontinuity location and jump are unknown.

A PDE-Based Approach to Three-Dimensional Seismic Data Fusion

We present a new method for the denoising and fusion, which is dedicated to multiazimuth seismic data. We propose to combine low-level fusion and diffusion processes through the use of a unique model based on partial differential equations. The denoising process is driven by the seismic fault preserving diffusion equation. Meanwhile, relevant information (as seismic faults) is injected in the fused 3-D images by an inverse diffusion process. One of the advantages of such an original approach is to improve the quality of the results in case of noisy inputs, which are frequently occurring in seismic unprocessed data. Some examples on synthetic and real seismic data will demonstrate the efficiency of our method.

A robust framework for GeoTime cube

This paper presents a robust unsupervised framework for 3D seismic data flattening. The resulting volume, called GeoTime cube, brings to light history of sedimentary deposits which is a key issue in petroleum prospecting. The proposed method makes it possible to obtain the transformation by transcribing fundamental principles of geophysics in image processing. The first step is a sedimentary layer reconstruction, the second one consists in numbering them according to their relative geological age and the last one computes a transformation in order to clearly represent them in a flattened way. Finally, the results obtained by our method compared to an existing one show that many relevant information can be extracted from GeoTime cubes and the final flattened data enhances the seismic structures identification.

3D Seismic Data Fusion and Filtering using a PDE-Based Approach

In order to aid the interpretation of seismic data, we present a new method for the denoising and fusion of multiple 3D registered blocks of the same area of subsoil. We propose to combine low-level fusion and diffusion processes through the use of a unique model based on partial differential equations (PDE). The denoising process is driven by the seismic fault enhancing diffusion equation. Meanwhile, relevant information (as seismic faults) is injected in the fused blocks by an inverse diffusion process. One of the advantages of such an original approach is to improve the quality of the results in case of noisy inputs, frequently occurring in seismic unprocessed data. Finally, two examples will demonstrate the efficiency of our method on synthetic and real seismic data.

Discontinuous seismic horizon reconstruction based on local dip transformation

We present a method to reconstruct a seismic horizon with a finite number of discontinuities due to oriented fault throws. Our approach requires the knowledge of the two points delimiting the horizon as well as the discontinuities orientations, locations and jumps. We deal with an accurate and noise robust global optimization technique based on a non-linear partial derivative equation relied on the local dip. The key point is the expression of the local dip in a basis in which the discontinuities are vertical. This basis is obtained by a bijective transformation composed of several transformations applied part-by-part in areas defined by the number and the sequence of the discontinuities. By exploiting a fault attribute, we finally propose an efficient method even when the discontinuities parameters are unknown.

Seismic Image Restoration Using Nonlinear Least Squares Shape Optimization

In this article we present a new method for seismic image restoration. When observed, a seismic image is the result of an initial deposit system that has been transformed by a set of successive geological deformations (flexures, fault slip, etc) that occurred over a large period of time. The goal of seismic restoration consists in inverting the deformations to provide a resulting image that depicts the geological deposit system as it was in a previous state. Providing a tool that quickly generates restored images helps the geophysicists to recognize geological features that may be too strongly altered in the observed image. The proposed approach is based on a minimization process that expresses geological deformations in terms of geometrical constraints. We use a quickly converging Gauss-Newton approach to solve the system. We provide results to illustrate the seismic image restoration process on real data and present how the restored version can be used in a geological interpretation framework.