[...]... methods, and by dimensionality mapping methods Multiband images can be taken as a particular case Such methods are pivotal in Chapter 6 on multichannel data, 8 on catalog analysis, and 9 on data storage and retrieval Hough and Radon transforms, leading to 3D tomography and other applications: Detection of alignments and curves is necessary for many classes of segmentation and feature analysis, and for... Gonzalez and Woods (1992), Jain (1990), Pratt (1991), Parker (1996), Castleman (1995), Petrou and Bosdogianni (1999), Bovik (2000) A text of ours on image processing and pattern recognition is available on-line (Campbell and Murtagh, 2001) Data analysis texts of importance include Bishop (1995), and Ripley (1995) 1.2 Transformation and Data Representation Many different transforms are used in data processing,... identifying and locating object position In this schema we start off with raw data (an array of grey-levels) and we end up with information – the identification and position of an object As we progress, the data and processing move from low-level to high-level Haralick and Shapiro (1985) give the following wish-list for segmentation: “What should a good image segmentation be? Regions of an image segmentation... selection of data to keep long-term, including the appropriate resolution and refinement levels The vast quantities of visual data collected now and in the future present us with new problems and opportunities Critical needs in our software systems include compression and progressive transmission, support for differential detail and user navigation in data spaces, and “thinwire” transmission and visualization... facts point to the importance of effective and efficient compression technology In Chapter 5, the state of the art in astronomical image compression will be surveyed Mathematical morphology: Combinations of dilation and erosion operators, giving rise to opening and closing operations, in boolean images and in greyscale images, allow for a truly very esthetic and immediately practical processing framework... a key factor in human understanding of the real world, as mediated through our computing and networking base We need to receive condensed, summarized data first, and we can be aided in our understanding of the data by having more detail added progressively A hyperlinked and networked world makes this need for summarization more 2 1 Introduction to Applications and Methods and more acute We need to take... social amnesia The positive implication is the ever-increasing complementarity of professional observational astronomy with education and public outreach Astronomy’s data centers and image and catalog archives play an important role in our society’s collective memory For example, the SIMBAD database of astronomical objects at Strasbourg Observatory contains data on 3 million objects, based on 7.5 million... Galaxy cluster: sub-structure detection (Pierre and Starck, 1998; Krywult et al., 1999; Arnaud et al., 2000), hierarchical clustering (Pando et al., 1998a), distribution of superclusters of galaxies (Kalinkov et al., 1998) – Cosmic Microwave Background: evidence for scale-scale correlations in the Cosmic Microwave Background radiation in COBE data (Pando et al., 1998b), large-scale CMB non-Gaussian statistics... corona, and by Ragazzoni and Barbieri (1994) for the study of astronomical light curve time series 1.2.5 The Ridgelet Transform The two-dimensional continuous ridgelet transform in R2 can be defined as follows (Cand`s and Donoho, 1999) We pick a smooth univariate function e ψ : R → R with sufficient decay and satisfying the admissibility condition ˆ |ψ(ξ)|2 /|ξ|2 dξ < ∞, (1.24) 1.2 Transformation and Data. .. (Donoho and Duncan, 2000; Cand`s and Donoho, e 2000a; Starck et al., 2003a) opens the possibility to analyze an image with different block sizes, but with a single transform The idea is to first decompose the image into a set of wavelet bands, and to analyze each band with a local ridgelet transform The block size can be changed at each scale level Roughly speaking, different levels of the multi-scale . 2006930922 ISSN 094 1-7 834 ISBN-10 3-5 4 0-3 302 4-0 2nd Edition Springer Berlin Heidelberg New York ISBN-13 97 8-3 -5 4 0-3 302 4-0 2nd Edition Springer Berlin Heidelberg New York ISBN 3-5 4 0-4 288 5-2 1st Edition. Sauverny, Switzerland V.Trimble, College Park, MD, and Irvine, CA, USA J L. Starck F. Murtagh Astronomical Image and Data Analysis Second Edition With 119 Figures 123 Jean- Luc Starck Service. on image processing and pattern recognition is available on-line (Campbell and Murtagh, 2001). Data analysis texts of importance include Bishop (1995), and Ripley (1995). 1.2 Transformation and