Marc Donias

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.

Curvature of oriented patterns: 2-D and 3-D estimation from differential geometry

This paper presents a method that estimates curvature of both 2-D and 3-D oriented patterns at different scales even if the structures are very close. Assuming that a structure is locally defined by an implicit isointensity contour, the curvature is obtained by a direct computation stemming from the differential geometry. The method is applied to curvature estimation of seismic image for geological interpretation.

New fault attribute based on robust directional scheme

We present a steered data-analysis approach to measure coherence for fault detection. In contrast with conventional coherence, which detects discontinuities without distinction, our approach aims to identify faults only. Assuming the local linearity of fault geometry, the method performs a continuity test using a steered data-analysis window over a set of dip/azimuth directions. A robust, selective directional continuity test is achieved by combining measures of coherence computed from a few aligned, steered windows. Finally, fault detection consists of finding the maximum directional response and accumulating it into an attribute volume. A comparison between results obtained on both synthetic and real seismic images indicates the new method is superior to the conventional coherence measure in isolating faults from stratigraphic signature and noise. Undesired scale, staircase, and mislocation effects are reduced noticeably.

Texture Synthesis Using the Structure Tensor

This paper proposes a two-stage texture synthesis algorithm. At the first stage, a structure tensor map carrying information about the local orientation is synthesized from the exemplars data and used at the second stage to constrain the synthesis of the texture. Keeping in mind that the algorithm should be able to reproduce as faithfully as possible the visual aspect, statistics, and morphology of the input sample, the method is tested on various textures and compared objectively with existing methods, highlighting its strength in successfully synthesizing the output texture in many situations where traditional algorithms fail to reproduce the exemplars patterns. The promising results pave the way towards the synthesis of accurately large and multi-scale patterns as it is the case for carbon material samples showing laminar structures, for example.

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.

Structure tensor based synthesis of directional textures for virtual material design

Exemplar-based texture synthesis schemes are promising for virtual material design. They provide impressive results in many cases, but fail in difficult situations with large and multi-scale patterns, or with long range directional variations. Since a prior synthesis of a geometric layer may help in the synthesis of the texture layer, a two-stage structure/texture synthesis algorithm is proposed. At the first stage, a structure tensor map carrying information about the local orientation is synthesized from the exemplars data, and at the second stage, the synthesized tensor field is used to constrain the synthesis of the texture. Results show that the proposed approach not only yields better synthesized textures, but also successfully synthesizes the output texture in many situations where traditional algorithms fail to reproduce the exemplars patterns, which paves the way towards the synthesis of accurately large and multi-scale patterns as it is the case for pyrolytic carbon samples showing laminar structures observed by Transmission Electronic Microscopy.

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.

Axis detection of cylindrical objects in three-dimensional images

We introduce an algorithm dedicated to the detection of the axes of cylindrical objects in a 3D block. The proposed algorithm performs 3D axis detection without prior segmentation of the block. This approach is specifically appropriate when the gray levels of the cylindrical objects are not homogeneous and are thus difficult to distinguish from the background. The method relies on gradient and curvature estimation and operates in two main steps. The first one selects candidate voxels for the axes, and the second one refines the determination of the axis of each cylindrical object. Applied to fiber-reinforced composite materials, this algorithm detects the axes of fibers in order to obtain the geometrical characteristics of the reinforcement. Knowing the reinforcement characteristics is an important issue in the quality control of the material but also in the prediction of the thermal and mechanical performances. We detail the various steps of the algorithm and then present some results, obtained with both synthetic blocks and real data acquired by synchrotron X-ray micro-tomography on carbon-fiber-reinforced carbon composites.

Modelling Infiltration of Fibre Preforms From X-Ray Tomography Data

The production of high-quality Ceramic-Matrix Composites often includes matrix deposition by Chemical Vapour Infiltration (CVI), a process which involves many phenomena such as gas transport, chemical reactions, and structural evolution of the preform. Control and optimization of this high-tech process are demanding for modelling tools. In this context, a numerical simulation of CVI in complex 3D images, acquired e.g. by X-ray Computerized Microtomography, has been developed. The approach addresses the two length scales which are inherent to a composite with woven textile reinforcement (i.e. inter- and intra-bundle), with two numerical tools. The small-scale program allows direct simulation of CVI in small intra-bundle pores. Effective laws for porosity, internal surface area and transport properties as infiltration proceeds are produced by averaging. They are an input for the next modelling step. The second code is a large-scale solver which accounts for the locally heterogeneous and anisotropic character of the pore space. Simulation of the infiltration of a whole composite material part is possible with this program. Validation of these tools on test cases, as well as some examples on actual materials, are shown and discussed.

Structure Tensor Riemannian Statistical Models for CBIR and Classification of Remote Sensing Images

This paper deals with parametric techniques for the description of texture on very high resolution (VHR) remote sensing images. These techniques focus on the property of anisotropy as described by the local structure tensor (LST). The novelty of this paper consists in proposing several comprehensive statistical frameworks to handle LST fields for rotation-invariant texture discrimination tasks. These frameworks are all based on probability models defined on the Riemannian manifold of positive definite matrices: a recent Riemannian Gaussian model on the affine-invariant metric space and a multivariate Gaussian distribution on the Log-Euclidean space. A thorough comparison of the proposed methods is performed with respect to some state-of-the-art texture analysis methods. Three experimental protocols are considered based on VHR remote sensing data. The first one consists of a content-based image retrieval (CBIR) protocol for browsing oyster field patches. The second one concerns a supervised classification protocol for grouping maritime pine forest stands in different age classes. The third one is, again, a CBIR protocol performed on the UC Merced land use/land cover patch collection. Tensor-based approaches show similar or even better results than the state-of-the-art texture analysis methods considered for comparison in all the experimental contexts.