Sorin Pop

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.

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.

Low-level fusion: a PDE-based approach

In this paper, we present a new general method for image fusion based on partial differential equation (PDE). We propose to combine pixel-level fusion and diffusion processes through one single powerful equation. The insertion of the relevant information contained in sources is achieved in the fused image by reversing the diffusion process. To solve the well-known instability problem of an inverse diffusion process, we introduce two additional constraints. Then, we propose a general PDE, which integrates one of these constraints as a regularization term. One of the advantages of such an original approach is to improve the quality of the results in case of noisy input images. To answer to the requirements of a 3D specific fusion application, we also propose an extension of the general equation. Finally, few examples and comparisons with classical fusion models will demonstrate the efficiency of our method both on 2D and 3D cases.

A PDE-based approach for image fusion

In this paper, we present a new general method for image fusion based on Partial Differential Equation (PDE).We propose to combine pixel-level fusion and diffusion processes through one single powerful equation. The insertion of the relevant information contained in sources is achieved in the fused image by reversing the diffusion process. To solve the well-known instability problem of an inverse diffusion process, a regularization term is added. One of the advantages of such an original approach is to improve the quality of the results in case of noisy input images. Finally, few examples and comparisons with classical fusion models will demonstrate the efficiency of our method both on blurred and noisy images.

3-D Directional Diffusion

In this paper we propose a 3D filter for denoising and enhancing strongly oriented data. Our approach is based on 2D directional diffusion model proposed by Terebes et al. (2004). The diffusion process is modulated by a non-linear function depending on the absolute values of the directional derivatives in the 3 orthogonal directions of the space. These directions are the eigenvectors of a structure tensor. We compare this extension with an existing 3D extension designed by Dargent et al. (2004)

Asymmetric directional diffusion based image filtering and enhancement

This paper introduces a new method for directional diffusion based image filtering and enhancement. The main novelty of our approach consists in considering asymmetric orientation information for steering a diffusion process along the main directions of the constituent structures of an image. The diffusion process is obtained by generalizing an existing approach defined on a symmetric framework. The increased efficiency of the method for the preservation and enhancement of junctions and corners, coupled with good noise filtering capabilities, is illustrated through an experimental setup involving both synthetic and real images.

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.

Image enhancement using hybrid shock filters

We present a new approach based on Partial Differential Equations (PDEs) and shock filter theory for image enhancement in “Gaussian Blur (GB) + Additive White Gaussian Noise (AWGN)” scenarios. The main disadvantage of classic shock filters, inability of successfully filtering noisy images, is overcome by the introduction of a complex domain shock filter framework. Furthermore, the proposed method allows for better control and anisotropic, contour-driven shock filtering, via its control functions f1 and f2. The main advantages of our method consist in the ability of successfully enhancing GB+AWGN images while preserving a stable-convergent time behavior.

Asymmetric anisotropic diffusion

We introduce a new anisotropic diffusion based approach for image filtering and enhancement. The main novelty of our method consists in considering a modulo 2π based definition of the diffusion axis along the main directions of the processed image. Such an asymmetric formulation of the filter induces better junction and corner preservation properties coupled with a good noise removal capacity.

A new discrete PDE-based fusion model

Recently, we have proposed a PDE-based fusion approach for noisy images. In this paper, we describe our continuous model and we insist on the numerical model. A new discretization scheme is introduced in order to obtain a faster time of convergence and more reliable results. We compare our model (implemented by 2 discretization schemes) with the classical multi-resolution fusion methods in the case of noisy-free 2D images. The results are obtained after an optimization in the space of parameters and are compared on 3 different applications (2 classical and 1 synthesized) by the means of a quality factor.