Yann Gousseau

Random Phase Textures: Theory and Synthesis

This paper explores the mathematical and algorithmic properties of two sample-based texture models: random phase noise (RPN) and asymptotic discrete spot noise (ADSN). These models permit to synthesize random phase textures. They arguably derive from linearized versions of two early Julesz texture discrimination theories. The ensuing mathematical analysis shows that, contrarily to some statements in the literature, RPN and ADSN are different stochastic processes. Nevertheless, numerous experiments also suggest that the textures obtained by these algorithms from identical samples are perceptually similar. The relevance of this study is enhanced by three technical contributions providing solutions to obstacles that prevented the use of RPN or ADSN to emulate textures. First, RPN and ADSN algorithms are extended to color images. Second, a preprocessing is proposed to avoid artifacts due to the nonperiodicity of real-world texture samples. Finally, the method is extended to synthesize textures with arbitrary size from a given sample.

Are natural images of bounded variation

The bounded variation assumption is the starting point of many methods in image analysis and processing. However, one common drawback of these methods is their inability to handle textures and small structures properly. Here we precisely show why natural images are incompletely represented by BV functions. Through an experimental study of the distribution of bilevels of natural images, we show that their total variation blows up to infinity with the increasing of resolution. To reach these conclusions, we compute bounds on the total variation, and we model convolution and sampling under quite general assumptions.

SAR-SIFT: A SIFT-Like Algorithm for SAR Images

The scale-invariant feature transform (SIFT) algorithm and its many variants are widely used in computer vision and in remote sensing to match features between images or to localize and recognize objects. However, mostly because of speckle noise, it does not perform well on synthetic aperture radar (SAR) images. In this paper, we introduce a SIFT-like algorithm specifically dedicated to SAR imaging, which is named SAR-SIFT. The algorithm includes both the detection of keypoints and the computation of local descriptors. A new gradient definition, yielding an orientation and a magnitude that are robust to speckle noise, is first introduced. It is then used to adapt several steps of the SIFT algorithm to SAR images. We study the improvement brought by this new algorithm, as compared with existing approaches. We present an application of SAR-SIFT to the registration of SAR images in different configurations, particularly with different incidence angles.

Shape-based Invariant Texture Indexing

This paper introduces a new texture analysis scheme, which is invariant to local geometric and radiometric changes. The proposed methodology relies on the topographic map of images, obtained from the connected components of level sets. This morphological tool, providing a multi-scale and contrast-invariant representation of images, is shown to be well suited to texture analysis. We first make use of invariant moments to extract geometrical information from the topographic map. This yields features that are invariant to local similarities or local affine transformations. These features are invariant to any local contrast change. We then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases. The obtained experimental results outperform the current state of the art in locally invariant texture analysis.

Geometrically Guided Exemplar-Based Inpainting

Exemplar-based methods have proven their efficiency for the reconstruction of missing parts in a digital image. Texture as well as local geometry are often very well restored by such methods. Some applications, however, require the ability to reconstruct nonlocal geometric features, e.g., long edges. In order to do so, we propose to first compute a geometric sketch, which is then interpolated and used as a guide for the global reconstruction. In comparison with other related approaches, the originality of our work relies on the following points: (1) The geometric sketch computation is parameter-free and based on level lines, which provides a complete, reliable, and stable representation of the image. (2) The completion of the geometric sketch is fully automatic. It is done using a new—and interesting on its own—geometric inpainting approach that interpolates level lines with Euler spirals. Euler spirals are natural curves for shape completion and have been used already for edge completion and inpainting. It is the first time, however, that these curves are used for completing the whole level lines structure. (3) The general reconstruction is performed using a guided version of a classical exemplar-based method. However, we do not constrain the exemplar-based reconstruction to strictly follow the geometric guide. We actually use a new metric between blocks that consists of the sum of the classical

An A Contrario Decision Method for Shape Element Recognition

{{\mathrm L}^2}

A Bias-Variance Approach for the Nonlocal Means

metric between any two blocks of the general image plus an

Accurate Junction Detection and Characterization in Natural Images

{{\mathrm L}^2}

The TVL1 Model: A Geometric Point of View

metric between the corresponding blocks in the completed geometric image. This is equivalent to a Lagrangian relaxation of a strictly guided reconstruction. We discuss in the paper the details of the method and some related mathematical issues, and we illustrate its efficiency on several examples.

A Statistical Approach to the Matching of Local Features

Shape recognition is the field of computer vision which addresses the problem of finding out whether a query shape lies or not in a shape database, up to a certain invariance. Most shape recognition methods simply sort shapes from the database along some (dis-)similarity measure to the query shape. Their main weakness is the decision stage, which should aim at giving a clear-cut answer to the question: “do these two shapes look alike?” In this article, the proposed solution consists in bounding the number of false correspondences of the query shape among the database shapes, ensuring that the obtained matches are not likely to occur “by chance”. As an application, one can decide with a parameterless method whether any two digital images share some shapes or not.