Study of pointwise regularity and application to trade data

In this paper we focus on the pointwise Lipschitz regularity in 1D and 2D. We put the emphasis on its invariance properties to a wide range of transformations. Wavelets algorithms provide fast computations, which is desirable in the applications. In addition to theoretical properties, a practical evaluation of its robustness is possible in practice. This leads to the conclusion that the regularity stands out as a robust pointwise features in 1D as well as in 2D. As an application, we use it to extract features that are indicators of potential fraud, through the processing of trade data. Keywords: Lipschitz regularity, wavelets, feature extractionJRC.G.2-Global security and crisis managemen

Detection of abnormal behavior in trade data using Wavelets, Kalman Filter and Forward Search

In this paper we address the issue of the automatic detection of abnormal behavior in time series extracted from international trade data. We motivate, review and use three specific methods, based on solid frameworks: Wavelets, Kalman Filter and Forward Search. These methods have been successfully applied to an important EU policy issue: the analysis of trade data for antifraud and antimoney-laundering, fields in which specialists are often confronted with massive datasets. Our contribution consists in an in-depth study of these approaches to assess their performance, qualitatively and quantitatively. On the one hand, we present these three approaches, underline their specific aspects and detail the used algorithms. On the other hand, we put forward a rigorous assessment methodology. We use this methodology to evaluate each method and also to compare them, on simulated time series and also on real datasets. Results show each method has its specific advantages. Their joint use could be of a high operational impact for our applications, to deal with the variety of patterns occurring in trade data.JRC.G.2-Global security and crisis managemen

Identification of outliers in simultaneous time series using Wavelets and Forward Search

In this paper we present an original methodology for the processing of simultaneous time series. It allows to identify times at which two time series present different patterns - these being outliers in a certain sense. We first apply wavelet techniques to transform data into representations focusing on singular locations. Several approaches are proposed to obtain such representations of the data. Then we explore these with a modern tool in robust statistics, the Forward Search, which allows in particular to evidence outliers.JRC.G.2-Global security and crisis managemen

Study of Lipschitz regularity - Feature extraction on regular and irregular grids

In this paper we study the pointwise Lipschitz regularity, covering several aspects: theoretical and practical, methods for its estimation on regular and irregular grids. The relevance of this value of regularity lies in its invariance properties to several transformations, and its fast computation thanks to wavelets. We study the influence of scale on wavelets transforms and show invariance properties this value of regularity. We also put forward an original technique for its estimation on regular grids. We also address the issue of irregular grids, based on the behavior of smoothing kernels with respect to scale. The obtained results emphasize the usefulness of such features for the applications, and motivate further work on this topic. Keywords: Lipschitz regularity, wavelets, smoothing kernels, robust feature extraction, regular and irregular gridsJRC.G.2-Global security and crisis managemen

Statistics on EU trade: Highlight on its heterogeneous structure and recommendations for practical applications

We present here an analysis of trade data, which highlights differences between Member States of the European Union, and also differences between chapters of traded products. We carry out a statistical description of quantity and value of traded products between the EU and third countries. This allows in particular to obtain specific threshold values, which are useful for filtering huge datasets. We present the results obtained on a dataset covering a wide area of trade involving the EU. These results make up a relevant source of information for specialists of antifraud and antimoney-laundering.JRC.G.2-Global security and crisis managemen

Ondelettes pour la détection de caractéristiques en traitement d'images. Application à la détection de région d'intérêt.

This thesis in image processing addresses the problem of the highlight of some remarquable structures, such as objects we perceive visually. These can be monodimensional, like contours, as well as bidimensional, corresponding to more complex objects. An important problem in computer vision consists on detecting such structures, and also extracting characteristic features from them. In many applications, such as object recognition, image matching, motion tracking or the enhancement of some particular elements, it is a first step before other high-level operations. Thereby, the formulation of performant detectors appears as essential. We show that this can be carried out using wavelet decompositions; in particular, it is possible to define some maxima lines, which turn out as relevant to this problem : one the one hand, so as to detect objects (given by some regions of interest), and, on the other hand, in order to characterize them (computations of Lipschitz regularity and of characteristic scale). This original approach for detection, based on maxima lines, can thus be compared to classical approches.Cette thèse en traitement d'images aborde le problème de la mise en évidence de certaines structures remarquables, comme des objets que nous percevons visuellement. Celles-ci peuvent être autant monodimensionnelles, comme des contours, que bidimensionnelles, ce qui correspond des objets plus complexes. Un problème important issu de la vision par ordinateur est de détecter de telles structures, ainsi que d'extraire des grandeurs caractéristiques de celles-ci. Dans diverses applications, comme la reconnaissance d'objets, l'appariement d'images, le suivi de mouvement ou le rehaussement de certains éléments particuliers, il s'agit d'une première étape avant d'autres opérations de plus haut niveau. Ainsi, la formulation de détecteurs performants apparaît comme essentielle. Nous montrons que cela peut être réalisé grâce des décompositions en ondelettes ; en particulier, il est possible de définir certaines lignes de maxima, qui s'avèrent pertinentes vis à vis de ce problème : d'une part, pour détecter des objets (par des régions d'intérêt), et, d'autre part, afin de les caractériser (calculs de régularité Lipschitzienne et d'échelle caractéristique). Cette approche originale de détection fondée sur des lignes de maxima peut alors être comparée aux approches classiques

Notes sur la régularité Lipschitzienne

This paper describes some properties of the Lipschitz regularity in 2D. We explain how the Lipschitz regularity can be computed on the basis of maxima lines. We also show that this regularity is robust to some tranformations of the image such as noise addition or affine deformations

Highlight on a feature extracted at fine scales: the pointwise Lipschitz regularity

International audienceThe aim of this paper is to study the robustness of the pointwise Lipschitz regularity in 2D, which is a measure of the local regularity of the intensity function associated to an image. This regularity can be efficiently computed by an approach based on fine scales. We assess its robustness when the image undergoes various transformations, especially geometric ones. The results we obtain show that the pointwise Lipschitz regularity is a suitable feature for applications in computer vision

Computation of Blob-like Structures Characteristic Scale with Wavelet Maxima Lines

International audienc