Connections in image processing are an important notion that describes how pixels can be grouped together according to their spatial relationships and/or their gray-level values. In recent years, several works were devoted to the development of new theories of connections among which hyperconnection (h-connection) is a very promising notion. This paper addresses two major issues of this theory. First, we propose a new axiomatic that ensures that every h-connection generates decompositions that are consistent for image processing and, more precisely, for the design of h-connected filters. Second, we develop a general framework to represent the decomposition of an image into h-connections as a tree that corresponds to the generalization of the connected component tree. Such trees are indeed an efficient and intuitive way to design attribute filters or to perform detection tasks based on qualitative or quantitative attributes. These theoretical developments are applied to a particular fuzzy h-connection, and we test this new framework on several classical applications in image processing, i.e., segmentation, connected filtering, and document image binarization. The experiments confirm the suitability of the proposed approach: It is robust to noise, and it provides an efficient framework to design selective filters.

In this paper, we investigate the possibilities offered by the extension of the connected component trees (cc-trees) to multivariate images. We propose a general framework for image processing using the cc-tree based on the lattice theory and we discuss the possible applications depending on the properties of the underlying ordered set. This theoretical reflexion is illustrated by two applications in multispectral astronomical imaging: source separation and object detection.

We propose to apply a marked point process to detect a galaxy filament network. From the "quality candy" model, initially developed for road network extraction in remotely sensed images, we adapt the data term to the filament detection. The optimization is realized by a simulated annealing using a reversible jump Markov Chain Monte Carlo algorithm. Results are presented on a numerical simulation and on an astronomical survey

The large-scale distribution of galaxies in the Universe exhibits structures at various scales, these so-called groups, clusters, and superclusters of galaxies being more or less hierarchically organized. A specific vision model is needed in order to detect, describe, and classify each component of this hierarchy. To do so, we have developed a multiscale vision model based on an unfolding into a scale space allowing us to detect structures of different sizes. A discrete wavelet transform is done by the a trous algorithm. The algorithm is implemented for astronomical images and also for lists of object positions, currently called catalogues in astronomical literature. Some applications on astrophysical data of cosmological interest are briefly described: (1) inventory procedures for galaxy counts on wide-field images, (2) processing of X-ray cluster images lending to the analyses of the total matter distribution, and (3) detection of large-scale structures from galaxy counts, From the analyses of N-body simulations we show that the vision model from the wavelet transform provides a new statistical indicator on cosmological scenarios.