Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing

Hyperspectral imaging provides the capability of increased sensitivity and discrimination over traditional imaging methods by combining standard digital imaging with spectroscopic methods. For each individual pixel in a hyperspectral image (HSI), a continuous spectrum is sampled as the spectral reflectance/radiance signature to facilitate identification of ground cover and surface material. The abundant spectrum knowledge allows all available information from the data to be mined. The superior qualities within hyperspectral imaging allow wide applications such as mineral exploration, agriculture monitoring, and ecological surveillance, etc. The processing of massive high-dimensional HSI datasets is a challenge since many data processing techniques have a computational complexity that grows exponentially with the dimension. Besides, a HSI dataset may contain a limited number of degrees of freedom due to the high correlations between data points and among the spectra. On the other hand, merely taking advantage of the sampled spectrum of individual HSI data point may produce inaccurate results due to the mixed nature of raw HSI data, such as mixed pixels, optical interferences and etc. Fusion strategies are widely adopted in data processing to achieve better performance, especially in the field of classification and clustering. There are mainly three types of fusion strategies, namely low-level data fusion, intermediate-level feature fusion, and high-level decision fusion. Low-level data fusion combines multi-source data that is expected to be complementary or cooperative. Intermediate-level feature fusion aims at selection and combination of features to remove redundant information. Decision level fusion exploits a set of classifiers to provide more accurate results. The fusion strategies have wide applications including HSI data processing. With the fast development of multiple remote sensing modalities, e.g. Very High Resolution (VHR) optical sensors, LiDAR, etc., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems

Analyse hiérarchique d'images multimodales

There is a growing interest in the development of adapted processing tools for multimodal images (several images acquired over the same scene with different characteristics). Allowing a more complete description of the scene, multimodal images are of interest in various image processing fields, but their optimal handling and exploitation raise several issues. This thesis extends hierarchical representations, a powerful tool for classical image analysis and processing, to multimodal images in order to better exploit the additional information brought by the multimodality and improve classical image processing techniques. %when applied to real applications. This thesis focuses on three different multimodalities frequently encountered in the remote sensing field. We first investigate the spectral-spatial information of hyperspectral images. Based on an adapted construction and processing of the hierarchical representation, we derive a segmentation which is optimal with respect to the spectral unmixing operation. We then focus on the temporal multimodality and sequences of hyperspectral images. Using the hierarchical representation of the frames in the sequence, we propose a new method to achieve object tracking and apply it to chemical gas plume tracking in thermal infrared hyperspectral video sequences. Finally, we study the sensorial multimodality, being images acquired with different sensors. Relying on the concept of braids of partitions, we propose a novel methodology of image segmentation, based on an energetic minimization framework.Il y a un intérêt grandissant pour le développement d’outils de traitements adaptés aux images multimodales (plusieurs images de la même scène acquises avec différentes caractéristiques). Permettant une représentation plus complète de la scène, ces images multimodales ont de l'intérêt dans plusieurs domaines du traitement d'images, mais les exploiter et les manipuler de manière optimale soulève plusieurs questions. Cette thèse étend les représentations hiérarchiques, outil puissant pour le traitement et l’analyse d’images classiques, aux images multimodales afin de mieux exploiter l’information additionnelle apportée par la multimodalité et améliorer les techniques classiques de traitement d’images. Cette thèse se concentre sur trois différentes multimodalités fréquemment rencontrées dans le domaine de la télédétection. Nous examinons premièrement l’information spectrale-spatiale des images hyperspectrales. Une construction et un traitement adaptés de la représentation hiérarchique nous permettent de produire une carte de segmentation de l'image optimale vis-à-vis de l'opération de démélange spectrale. Nous nous concentrons ensuite sur la multimodalité temporelle, traitant des séquences d’images hyperspectrales. En utilisant les représentations hiérarchiques des différentes images de la séquence, nous proposons une nouvelle méthode pour effectuer du suivi d’objet et l’appliquons au suivi de nuages de gaz chimique dans des séquences d’images hyperspectrales dans le domaine thermique infrarouge. Finalement, nous étudions la multimodalité sensorielle, c’est-à-dire les images acquises par différents capteurs. Nous appuyant sur le concept des tresses de partitions, nous proposons une nouvelle méthodologie de segmentation se basant sur un cadre de minimisation d’énergie

Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations

The study of low-dimensional, noisy manifolds embedded in a higher dimensional space has been extremely useful in many applications, from the chemical analysis of multi-phase flows to simulations of galactic mergers. Building a probabilistic model of the manifolds has helped in describing their essential properties and how they vary in space. However, when the manifold is evolving through time, a joint spatio-temporal modelling is needed, in order to fully comprehend its nature. We propose a first-order Markovian process that propagates the spatial probabilistic model of a manifold at fixed time, to its adjacent temporal stages. The proposed methodology is demonstrated using a particle simulation of an interacting dwarf galaxy to describe the evolution of a cavity generated by a Supernov