Variational Autoencoders have gained considerable attention due to their capacity of encoding high dimensional data into a lower dimensional latent space. In this context, several methods have been proposed with the objective of producing disentangled representations. In this work, we propose a weakly supervised model that explicitly disentangles the factors of variation of a dataset in separate subspaces using a pairwise architecture. We also create a framework that encourages conditional image generation according to the desired factor of variation, by controlling these subspaces. This is achieved by introducing an additional network trained with a triplet loss. Its output approximates representations of images generated from the same factor and push the ones of images generated from different factors apart. Experiments are carried out on widely used datasets, and show that our model is able to disentangle specified factors of variation, and to generate new data while constraining desired properties, even when these factors have small influence on reconstruction loss.

The most common scheme for estimating the orientation field of space-varying directional textures is based on a local nonlinear spatial averaging of the gradient field. This leads to locally biased orientations, especially in regions of nonlinearly distributed convergence, asymmetrically distributed curvature, or geometry superposition. In this paper, we propose an orientation estimation framework that is invariant toward the local geometry. Instead of applying the spatial averaging in the initial space, it is performed in a flattened space which is obtained from a parametric space transformation model deduced from the reconstruction of local hypersurfaces. The flattening can either be applied to the initial gradient field or to the intensity image, on which the flattened gradient field is computed. The process is iterated in order to define more accurate space transformations leading to refined orientation estimation. The computational efficiency is improved without noticeable loss of orientation accuracy by a patch-based approach. Experiments, both on synthetic as well as real-life fingerprint and fibrous material images, exhibit enhanced performance in comparison with conventional methods such as the structure tensor method.

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.

Methods of seismic horizon reconstruction based on the solution of a partial derivative equation are generally robust to noise. However, they can only reconstruct horizons on rectangular domains when using fast iterative methods which is inconvenient in regions of uncertainty or irrelevant data in the seismic image. In this paper, we propose a method to reconstruct seismic horizons on any polygonal domain based on a succession of Schwarz-Christoffel transformations which conserve the angles locally. Since these are conformal transformations, the form of the equation is preserved and the solution on the polygonal domain corresponds to the solution on the rectangular domain using the grid data transformed from the rectangular into the polygonal domain.

This paper presents local structure tensor (LST) based methods for extracting the anisotropy and orientation information characterizing a textured image sample. A Log-Euclidean (LE) multivariate Gaussian model is proposed for representing the marginal distribution of the LST field of a texture. An extended model is considered as well for describing its spatial dependencies. The potential of these approaches are tested in a rotation invariant content based image retrieval (CBIR) context. Experiments are conducted on real data presenting anisotropic textures: very high resolution (VHR) remote sensing maritime pine forest images and material images representing dense carbons at nanometric scale.

Estimating the local orientations of a directional structure may prove to be complicated especially for complex geometries for which conventional methods, including those based on the gradient, are unsuitable. In this paper, we propose a recursive method of orientation estimation based on the reconstruction of hypersurfaces and the definition of a model of the structure in these so-called complex areas. The estimation proves to be more accurate when executed on the flattened data and driven to the initial referential. This process recursively leads to a more accurate orientation field estimation. When applied to synthetic data, the method reduces significantly the estimation bias. For real directional textures, the resulting orientation field coincides better with the perceptual orientation of the directional structures.

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 exemplar's 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 exemplar's 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.

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 exemplar's 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 exemplar's 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.

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.

We propose a fast method to reconstruct a seismic horizon with respect to a set of picked input points. The reconstruction domain is subdivided in quadrilateral domains which are determined from input points while the entire horizon is obtained part-by-part by juxtaposing independent partial reconstructions. Each quadrilateral domain is mapped onto a rectangular domain on which a non-linear partial derivative equation relied on local dip is solved by an iterative process based on a Poisson equation. The key point is the transformation of the local dip, which allows to carry out a direct Fourier method with a low computational cost.

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.

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.

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.

7-9 novembre 2005

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.