Radu Stoica

A Gibbs Point Process for Road Extraction from Remotely Sensed Images

In this paper we propose a new method for the extraction of roads from remotely sensed images. Under the assumption that roads form a thin network in the image, we approximate such a network by connected line segments.To perform this task, we construct a point process able to simulate and detect thin networks. The segments have to be connected, in order to form a line-network. Aligned segments are favored whereas superposition is penalized. These constraints are enforced by the interaction model (called the Candy model). The specific properties of the road network in the image are described by the data term. This term is based on statistical hypothesis tests.The proposed probabilistic model can be written within a Gibbs point process framework. The estimate for the network is found by minimizing an energy function. In order to avoid local minima, we use a simulated annealing algorithm, based on a Monte Carlo dynamics (RJMCMC) for finite point processes. Results are shown on SPOT, ERS and aerial images.

Case studies in spatial point process modeling

Point process statistics is successfully used in fields such as material science, human epidemiology, social sciences, animal epidemiology, biology, and seismology. Its further application depends greatly on good software and instructive case studies that show the way to successful work. This book satisfies this need by a presentation of the spatstat package and many statistical examples. Researchers, spatial statisticians and scientists from biology, geosciences, materials sciences and other fields will use this book as a helpful guide to the application of point process statistics. No other book presents so many well-founded point process case studies.

Evidence for spin alignment of spiral and elliptical/S0 galaxies in filaments

ABSTRACT Galaxies are not distributed randomly in the cosmic web but are instead arranged infilaments and sheets surrounding cosmic voids. Observationally there is still no con-vincing evidence of a link between the properties of galaxies and their host structures.However, by the tidal torque theory (our understanding of the origin of galaxy angularmomentum), such a link should exist. Using the presently largest spectroscopic galaxyredshift survey (SDSS) we study the connection between the spin axes of galaxies andthe orientation of their host filaments.We use a three dimensional field of orientations to describe cosmic filaments. Torestore the inclination angles of galaxies, we use a 3D photometric model of galaxiesthat gives these angles more accurately than traditional 2D models.We found evidence thatthe spin axesofbrightspiralgalaxieshavea weaktendencyto be aligned parallel to filaments. For elliptical/S0 galaxies, we have a statisticallysignificant result that their spin axes are aligned preferentially perpendicular to thehost filaments; we show that this signal practically does not depend on the accuracyof the estimated inclination angles for elliptical/S0 galaxies.Key words: methods: statistical – galaxies: general – galaxies: statistics – galaxies:evolution – large-scale structure of Universe.

Detection of cosmic filaments using the Candy model

We propose to apply a marked point process to automatically delineate filaments of the large-scale structure in redshift catalogues. We illustrate the feasibility of the idea on an example of simulated catalogues, describe the procedure, and characterize the results. We find the distribution of the length of the filaments, and suggest how to use this approach to obtain other statistical characteristics of filamentary networks.

Filaments in observed and mock galaxy catalogues

Context. The main feature of the spatial large-scale galaxy distribution is an intricate network of galaxy filaments. Although many attempts have been made to quantify this network, there is no unique and satisfactory recipe for that yet. Aims. The present paper compares the filaments in the real data and in the numerical models, to see if our best models reproduce statistically the filamentary network of galaxies. Methods. We apply an object point process with interactions (the Bisous process) to trace and describe the filamentary network both in the observed samples (the 2dFGRS catalogue) and in the numerical models that have been prepared to mimic the data. We compare the networks. Results. We find that the properties of filaments in numerical models (mock samples) have a large variance. A few mock samples display filaments that resemble the observed filaments, but usually the model filaments are much shorter and do not form an extended network. Conclusions. We conclude that although we can build numerical models that are similar to observations in many respects, they may fail yet to explain the filamentary structure seen in the data. The Bisous-built filaments are a good test for such a structure.

The two-dimensional Wold decomposition for segmentation and indexing in image libraries

This paper presents a method for indexing and retrieval of multimedia data through texture segmentation, using the Wold decomposition. The texture field is assumed to be a realisation of a regular homogeneous random field. On the basis of a 2-D Wold-like decomposition, the field is represented as the sum of a purely indeterministic component, a harmonic component and a countable number of evanescent fields. A new rigorous distance measure between textures is derived, using Wold parameters. Adopting the MRF framework, we construct a segmentation procedure using the Wold parameters.

Image retrieval and indexing: a hierarchical approach in computing the distance between textured images

This paper presents a method for indexing and retrieval of multimedia data. The proposed indexing and retrieval strategy is based on the usage of textural information contained in the data imagery components as the indexing keys. On the basis of a 2-D Wold-like decomposition, the texture field is represented as the sum of purely indeterministic, harmonic, and evanescent fields. A new rigorous distance measure between textures which employs their estimated parametric models, is developed. This distance measure is then applied to retrieve multimedia records that contain images with textured segments which are similar to those in a given image. Evaluation of this distance measure is computationally efficient, and hence highly suitable for data base retrieval applications.

Tracing the cosmic web

The cosmic web is one of the most striking features of the distribution of galaxies and dark matter on the largest scales in the Universe. It is composed of dense regions packed full of galaxies, long filamentary bridges, flattened sheets and vast low-density voids. The study of the cosmic web has focused primarily on the identification of such features, and on understanding the environmental effects on galaxy formation and halo assembly. As such, a variety of different methods have been devised to classify the cosmic web - depending on the data at hand, be it numerical simulations, large sky surveys or other. In this paper, we bring 12 of these methods together and apply them to the same data set in order to understand how they compare. In general, these cosmic-web classifiers have been designed with different cosmological goals in mind, and to study different questions. Therefore, one would not a priori expect agreement between different techniques; however, many of these methods do converge on the identification of specific features. In this paper, we study the agreements and disparities of the different methods. For example, each method finds that knots inhabit higher density regions than filaments, etc. and that voids have the lowest densities. For a given web environment, we find a substantial overlap in the density range assigned by each web classification scheme. We also compare classifications on a halo-by-halo basis; for example, we find that 9 of 12 methods classify around a third of group-mass haloes (i.e. M-halo similar to 10(13.5) h(-1) M-circle dot) as being in filaments. Lastly, so that any future cosmic-web classification scheme can be compared to the 12 methods used here, we have made all the data used in this paper public.

The Candy model : properties and inference

In this paper we study the Candy model, a marked point process introduced by Stoica et al. (2000). We prove Ruelle and local stability, investigate its Markov properties, and discuss how the model may be sampled. Finally, we consider estimation of the model parameters and present a simulation study.

A RJMCMC Algorithm for Object Processes in Image Processing

Probabilistic approaches in image processing are usually based on a pixelwise modelling. Embedded in a Bayesian framework, Markov Random Fields play a leading role. However, they hardly ever take into account geometric constraints. Moreover, the likelihood computed on a pixel basis is sensitive to high level noise. In this paper, we consider the modelling of image features by the realisation of Markov Object Processes. A general interacting objects model, which includes a data term and some geometrical constraints, is proposed. We then derive a Reversible Jump Markov Chain Monte Carlo algorithm to optimise the proposed model. Some examples of this model are built to extract roads and buildings from high resolution remotely sensed images. KeywordsObject Process, Image feature extraction, Reversible Jump Markov Chain Monte Carlo.