Inner-Cheeger Opening and Applications

International audienceThe aim of this paper is to study an optimal opening in the sense of minimize the relationship perimeter over area. We analyze theoretical properties of this opening by means of classical results from variational calculus. Firstly, we explore the optimal radius as attribute in morphological attribute filtering for grey scale images. Secondly, an application of this optimal opening that yields a decomposition into meaningful parts in the case of binary image is explored. We provide different examples of 2D, 3D images and mesh-points datasets

Wikipedia vandalism detection

Wikipedia is an online encyclopedia that anyone can edit. The fact that there are almost no restrictions to contributing content is at the core of its success. However, it also attracts pranksters, lobbysts, spammers and other people who degradatesWikipedia's contents. One of the most frequent kind of damage is vandalism, which is defined as any bad faith attempt to damage Wikipedia's integrity. For some years, the Wikipedia community has been fighting vandalism using automatic detection systems. In this work, we develop one of such systems, which won the 1st International Competition on Wikipedia Vandalism Detection. This system consists of a feature set exploiting textual content of Wikipedia articles. We performed a study of different supervised classification algorithms for this task, concluding that ensemble methods such as Random Forest and LogitBoost are clearly superior. After that, we combine this system with two other leading approaches based on different kind of features: metadata analysis and reputation. This joint system obtains one of the best results reported in the literature. We also conclude that our approach is mostly language independent, so we can adapt it to languages other than English with minor changes.Mola Velasco, SM. (2011). Wikipedia vandalism detection. http://hdl.handle.net/10251/1587

Morphological scale-space for hyperspectral images and dimensionality exploration using tensor modeling

International audienceThis paper proposes a framework to integrate spatial information into unsupervised feature extraction for hyperspectral images. In this approach a nonlinear scale-space representation using morphological levelings is formulated. In order to apply feature extraction, tensor principal components are computed involving spatial and spectral information. The proposed method has shown significant gain over the conventional schemes used with real hyperspectral images. In addition, the proposed framework opens a wide field for future developments in which spatial information can be easily integrated into the feature extraction stage. Examples using real hyperspectral images with high spatial resolution showed excellent performance even with a low number of training samples

Vector ordering and multispectral morphological image processing

International audienceThis chapter illustrates the suitability of recent multivariate ordering approaches to morphological analysis of colour and multispectral images working on their vector representation. On the one hand, supervised ordering renders machine learning no-tions and image processing techniques, through a learning stage to provide a total ordering in the colour/multispectral vector space. On the other hand, anomaly-based ordering, automatically detects spectral diversity over a majority background, al-lowing an adaptive processing of salient parts of a colour/multispectral image. These two multivariate ordering paradigms allow the definition of morphological operators for multivariate images, from algebraic dilation and erosion to more advanced techniques as morphological simplification, decomposition and segmentation. A number of applications are reviewed and implementation issues are discussed in detail

Parameters Selection Of Morphological Scale-Space Decomposition For Hyperspectral Images Using Tensor Modeling

International audienceDimensionality reduction (DR) using tensor structures in morphological scale-space decomposition (MSSD) for HSI has been investigated in order to incorporate spatial information in DR.We present results of a comprehensive investigation of two issues underlying DR in MSSD. Firstly, information contained in MSSD is reduced using HOSVD but its nonconvex formulation implicates that in some cases a large number of local solutions can be found. For all experiments, HOSVD always reach an unique global solution in the parameter region suitable to practical applications. Secondly, scale parameters in MSSD are presented in relation to connected components size and the influence of scale parameters in DR and subsequent classification is studied

Riemannian mathematical morphology

This paper introduces mathematical morphology operators for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance used for the adjoint dilation/erosion. We then extend the canonic case to a most general framework of Riemannian operators based on the notion of admissible Riemannian structuring function. An alternative paradigm of morphological Riemannian operators involves an external structuring function which is parallel transported to each point on the manifold. Besides the definition of the various Riemannian dilation/erosion and Riemannian opening/closing, their main properties are studied. We show also how recent results on Lasry-Lions regularization can be used for non-smooth image filtering based on morphological Riemannian operators. Theoretical connections with previous works on adaptive morphology and manifold shape morphology are also considered. From a practical viewpoint, various useful image embedding into Riemannian manifolds are formalized, with some illustrative examples of morphological processing real-valued 3D surfaces

Statistical Shape Modeling Using Morphological Representations

ISBN : 978-1-4244-7542-1International audienceThe aim of this paper is to propose tools for statistical analysis of shape families using morphological operators. Given a series of shape families (or shape categories), the approach consists in empirically computing shape statistics (i.e., mean shape and variance of shape) and then to use simple algorithms for random shape generation, for empirical shape confidence boundaries computation and for shape classification using Bayes rules. The main required ingredients for the present methods are well known in image processing, such as watershed on distance functions or log-polar transformation. Performance of classification is presented in a well-known shape database

Random projection depth for multivariate mathematical morphology

International audienceThe open problem of the generalization of mathematical morphology to vector images is handled in this paper using the paradigm of depth functions. Statistical depth functions provide from the "deepest" point a "center-outward ordering" of a multidimensional data distribution and they can be therefore used to construct morphological operators. The fundamental assumption of this data-driven approach is the existence of "background/foreground" image representation. Examples in real color and hyperspectral images illustrate the results