Non-homogeneous polygonal Markov fields in the plane: graphical representations and geometry of higher order correlations

We consider polygonal Markov fields originally introduced by Arak and Surgailis (1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of features with the two-dimensional Ising model. We introduce non-homogeneous version of polygonal fields in anisotropic enviroment. For these fields we provide a class of new graphical constructions and random dynamics. These include a generalised dynamic representation, generalised and defective disagreement loop dynamics as well as a generalised contour birth and death dynamics. Next, we use these constructions as tools to obtain new exact results on the geometry of higher order correlations of polygonal Markov fields in their consistent regime.Comment: 54 page

Extracting Geometric Structures in Images with Delaunay Point Processes

International audienceWe introduce Delaunay Point Processes, a framework for the extraction of geometric structures from images. Our approach simultaneously locates and groups geometric primitives (line segments, triangles) to form extended structures (line networks, polygons) for a variety of image analysis tasks. Similarly to traditional point processes, our approach uses Markov Chain Monte Carlo to minimize an energy that balances fidelity to the input image data with geometric priors on the output structures. However, while existing point processes struggle to model structures composed of interconnected components, we propose to embed the point process into a Delaunay triangulation, which provides high-quality connectivity by construction. We further leverage key properties of the Delaunay triangulation to devise a fast Markov Chain Monte Carlo sampler. We demonstrate the flexibility of our approach on a variety of applications, including line network extraction, object contouring, and mesh-based image compression

Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Visual Perception of Garments for their Robotic Manipulation

Tématem předložené práce je strojové vnímání textilií založené na obrazové informaci a využité pro jejich robotickou manipulaci. Práce studuje několik reprezentativních textilií v běžných kognitivně-manipulačních úlohách, jako je například třídění neznámých oděvů podle typu nebo jejich skládání. Některé z těchto činností by v budoucnu mohly být vykonávány domácími robotickými pomocníky. Strojová manipulace s textiliemi je poptávaná také v průmyslu. Hlavní výzvou řešeného problému je měkkost a s tím související vysoká deformovatelnost textilií, které se tak mohou nacházet v bezpočtu vizuálně velmi odlišných stavů.The presented work addresses the visual perception of garments applied for their robotic manipulation. Various types of garments are considered in the typical perception and manipulation tasks, including their classification, folding or unfolding. Our work is motivated by the possibility of having humanoid household robots performing these tasks for us in the future, as well as by the industrial applications. The main challenge is the high deformability of garments, which can be posed in infinitely many configurations with a significantly varying appearance

Trends in Mathematical Imaging and Surface Processing

Motivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments

Regmentation: A New View of Image Segmentation and Registration

Image segmentation and registration have been the two major areas of research in the medical imaging community for decades and still are. In the context of radiation oncology, segmentation and registration methods are widely used for target structure definition such as prostate or head and neck lymph node areas. In the past two years, 45% of all articles published in the most important medical imaging journals and conferences have presented either segmentation or registration methods. In the literature, both categories are treated rather separately even though they have much in common. Registration techniques are used to solve segmentation tasks (e.g. atlas based methods) and vice versa (e.g. segmentation of structures used in a landmark based registration). This article reviews the literature on image segmentation methods by introducing a novel taxonomy based on the amount of shape knowledge being incorporated in the segmentation process. Based on that, we argue that all global shape prior segmentation methods are identical to image registration methods and that such methods thus cannot be characterized as either image segmentation or registration methods. Therefore we propose a new class of methods that are able solve both segmentation and registration tasks. We call it regmentation. Quantified on a survey of the current state of the art medical imaging literature, it turns out that 25% of the methods are pure registration methods, 46% are pure segmentation methods and 29% are regmentation methods. The new view on image segmentation and registration provides a consistent taxonomy in this context and emphasizes the importance of regmentation in current medical image processing research and radiation oncology image-guided applications