The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

The Multiscale Morphology Filter: Identifying and Extracting Spatial Patterns in the Galaxy Distribution

We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in redshift surveys or from particles in cosmological N-body simulations: it makes no prior assumptions about the scale or shape of the structures.}Comment: Replacement with higher resolution figures. 28 pages, 17 figures. For Full Resolution Version see: http://www.astro.rug.nl/~weygaert/tim1publication/miguelmmf.pd

Filtering of image sequences: on line edge detection and motion reconstruction

L'argomento della Tesi riguarda líelaborazione di sequenze di immagini, relative ad una scena in cui uno o pi˘ oggetti (possibilmente deformabili) si muovono e acquisite da un opportuno strumento di misura. A causa del processo di misura, le immagini sono corrotte da un livello di degradazione. Si riporta la formalizzazione matematica dellíinsieme delle immagini considerate, dellíinsieme dei moti ammissibili e della degradazione introdotta dallo strumento di misura. Ogni immagine della sequenza acquisita ha una relazione con tutte le altre, stabilita dalla legge del moto della scena. Líidea proposta in questa Tesi Ë quella di sfruttare questa relazione tra le diverse immagini della sequenza per ricostruire grandezze di interesse che caratterizzano la scena. Nel caso in cui si conosce il moto, líinteresse Ë quello di ricostruire i contorni dellíimmagine iniziale (che poi possono essere propagati attraverso la stessa legge del moto, in modo da ricostruire i contorni della generica immagine appartenente alla sequenza in esame), stimando líampiezza e del salto del livello di grigio e la relativa localizzazione. Nel caso duale si suppone invece di conoscere la disposizione dei contorni nellíimmagine iniziale e di avere un modello stocastico che descriva il moto; líobiettivo Ë quindi stimare i parametri che caratterizzano tale modello. Infine, si presentano i risultati dellíapplicazione delle due metodologie succitate a dati reali ottenuti in ambito biomedicale da uno strumento denominato pupillometro. Tali risultati sono di elevato interesse nellíottica di utilizzare il suddetto strumento a fini diagnostici