Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel

A Marker-Based Approach for the Automated Selection of a Single Segmentation from a Hierarchical Set of Image Segmentations

The Hierarchical SEGmentation (HSEG) algorithm, which combines region object finding with region object clustering, has given good performances for multi- and hyperspectral image analysis. This technique produces at its output a hierarchical set of image segmentations. The automated selection of a single segmentation level is often necessary. We propose and investigate the use of automatically selected markers for this purpose. In this paper, a novel Marker-based HSEG (M-HSEG) method for spectral-spatial classification of hyperspectral images is proposed. Two classification-based approaches for automatic marker selection are adapted and compared for this purpose. Then, a novel constrained marker-based HSEG algorithm is applied, resulting in a spectral-spatial classification map. Three different implementations of the M-HSEG method are proposed and their performances in terms of classification accuracies are compared. The experimental results, presented for three hyperspectral airborne images, demonstrate that the proposed approach yields accurate segmentation and classification maps, and thus is attractive for remote sensing image analysis

Hyperspectral Image Segmentation Using a New Spectral Unmixing-Based Binary Partition Tree Representation

International audienceThe Binary Partition Tree (BPT) is a hierarchical region-based representation of an image in a tree structure. BPT allows users to explore the image at different segmentation scales. Often, the tree is pruned to get a more compact representation and so the remaining nodes conform an optimal partition for some given task. Here, we propose a novel BPT construction approach and pruning strategy for hyperspectral images based on spectral unmixing concepts. Linear Spectral Unmixing (LSU) consists of finding the spectral signatures of the materials present in the image (endmembers) and their fractional abundances within each pixel. The proposed methodology exploits the local unmixing of the regions to find the partition achieving a global minimum reconstruction error. Results are presented on real hyperspectral data sets with different contexts and resolutions

Hyperspectral image segmentation using a new spectral mixture-based binary partition tree representation

International audienceThe Binary Partition Tree (BPT) is a hierarchical region-based representation of an image in a tree structure. BPT allows users to explore the image at different segmentation scales, from fine partitions close to the leaves to coarser partitions close to the root. Often, the tree is pruned so the leaves of the resulting pruned tree conform an optimal partition given some optimality criterion. Here, we propose a novel BPT construction approach and pruning strategy for hyperspectral images based on spectral unmixing concepts. The proposed methodology exploits the local unmixing of the regions to find the partition achieving a global minimum reconstruction error. We successfully tested the proposed approach on the well-known Cuprite hyperspectral image collected by NASA Jet Propulsion Laboratory's Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). This scene is considered as a standard benchmark to validate spectral unmixing algorithms

Lossless compact histogram representation for multi-component images: application to histogram equalization

The problem of histogram representation is addressed. In the case of multi-component images, this problem is not trivial: the theoretical "naive" required memory space goes exponentially beyond todays technical capacities. To overcome this problem, we present a lossless compact representation of vector histograms. It is based on the use of a space filling curve to index the data space. The application of this representation to vector histogram equalization is then considered

Segmentation of time-frequency images for the separation of seismic waves

This paper deals with the use of image processing techniques for tiling the time-frequency plane. This technique is applied on seismic wave separation. We consider data recorded by a linear array of sensors. For each recorded signal, the application of a time-frequency transform allows a two dimensional representation where the different seismic events are well localized and isolated. The segmentation by the watershed algorithm applied on each representation enables the definition of the time-frequency filters leading to the separation of the different waves. Then, in order to apply the separation algorithm to all the different recorded signals, we use the continuity from one signal to the other to perform the tracking of the different waves from one image to the next. After an initialisation step, this leads to an automatic algorithm. This algorithm is validated on a real data set and compared with a classical method. In comparison, the proposed method has the advantage to separate all the different waves simultaneously and without introducing artefact in the spatial domain. The limit of the algorithm is reached when the patterns associated to the different waves are not correctly separated in the time-frequency representation.Ce papier illustre l'utilisation de techniques de traitement d'image pour segmenter le plan temps-fréquence (et temps-échelle). Cette étude est appliquée à la séparation d'ondes sismiques. On considère des données issues d'une rangée de capteurs. Pour chaque signal enregistré, l'application d'une transformée temps-fréquence décrit l'information dans une image sur laquelle les différentes ondes sont localisées et séparées. La segmentation par Ligne de Partage des Eaux (LPE) de ces représentations à deux dimensions permet une caractérisation automatique des filtres temps-fréquence menant à la séparation des différentes ondes. Ensuite, pour appliquer cet algorithme de séparation à l'ensemble des signaux issus des différents capteurs, on utilise la continuité d'un signal à l'autre pour effectuer le suivi des différentes ondes d'une image à l'autre. Hormis une phase d'initialisation, on obtient ainsi un algorithme automatique. Cet algorithme est validé et comparé à une méthode classique en sismique sur un jeu de données réelles. En comparaison, l'algorithme proposé a l'avantage de séparer toutes les ondes simultanément, et sans introduire d'artefacts. Les limites de l'algorithme sont atteintes lorsque les motifs caractérisant chacune des ondes ne sont plus convenablement séparés dans la représentation temps-fréquence