The segmentation of speckled images, as the synthetic aperture radar (SAR) images, is usually recognized as a very complex problem, because of the speckle, multiplicative noise, which produces granular images. In segmentation problems, based on level set method, the evolution of the curve is determined by a speed function, which is fundamental to achieve a good segmentation. In this paper we propose a study of the new speed function obtained by the linear combination of image average intensity and image gradient speed functions. Thus the aim is tuning the combined speed in the segmentation process. We segmented synthetic images by tuning parameters of the new speed function and we evaluated the best computed results. Then we applied this experimental setup to real SAR images, which are PRecision Images, acquired during European Remote Sensing mission, and a Cosmo-SkyMed image. In particular, we are interested in monitoring complex areas with low light covered by clouds, as coastlines and polar regions may be. In Earth Observation, the acquisition of SAR data becomes fundamental, since the SAR sensor can work in the night/day and in all weather conditions.

In document image analysis the task of segmenting images of ancient printed documents in distinct elements is known to be a very complex problem. In general, these documents are of low quality and can present skew and degradations because of old printing or ink stains. To face these problems we will show and discuss the validity of the Mumford and Shah variational method, based on the ? convergence theory, along with its numerical handling. In particular, we segment and extract the interest regions, constituted by textual and non-textual blocks, from page images of ancient books, combining the variational approach with morphological operations. Study case is the first edition of 'Scienza Nuova' (1725) of Giambattista Vico.

In areas of difficult access, such as the arctic ones, the extraction of inter- est zones (e.g. glaciers) from satellite images may be a valuable way to study and monitor their status . This work faces in particular the prob- lem of detecting different zones of glaciers from SAR (Synthetic Aperture Radar) images. In the polar regions the use of the SAR system is funda- mental because it works independently of weather and daylight. Segmentation is a process that allows an image to be divided into disjoint zones in such a way that each extracted area contains homogeneous char- acteristics. The numerical approach, here applied to detect glacier zones, is based on moving boundary modelling and is described by the eikonal equation. The upwind finite difference approximation of the eikonal equa- tion is solved by a fast marching technique, that starts from seed points in the region of interest and generates a front which evolves until the bound- ary of the region is identified. Results from segmentation of glacier images in the Svalbard archipelago acquired by ERS2 SAR (Synthetic Aperture Radar) and Envisat (ESA Environmental Satellite) ASAR (Advanced Synthetic Aperture Radar) are presented and discussed.

We present a work in progress about extracting words from images of historical printed documents by using fast marching method. Segmentation is a process that allows an image to be divided into disjoint zones, so that extracted areas contain homogeneous characteristics. The numerical method, we used to segment images, is based on the theory of interface evolution, described by the eikonal equation. We adopted the fast marching technique to solve the upwind finite difference approximation of the eikonal equation. Segmentation of ancient documents is generally acknowledged as a very complicated problem because this kind of documents can be low quality, presenting local skew and several degradations due to old printing or ink stains.

The aim of this work is to develop a prototype system, that is a software tool that contributes to monitor the coastline. In fact it, constituted by a set of techniques and methods for SAR (Synthetic Aperture Radar) image segmentation, can aid to investigate the state of conservation of the coastal environment. The proposed system, called ISC (Interactive System for Coastline detection) and written in JAVA language, is composed by a set of Java classes structured in packages and it is based on the level set method applied to SAR images. In this method, an initial curve defined on the image evolves according to a PDE (Partial Differential Equation) model by means of a velocity whose mathematical expression is related to the characteristics of the image to be segmented. This curve is deformed until it assumes a stable position at the boundary of the area to be extracted from the image. We used images SAR PRI (Precision Image Resolution) acquired during the ERS2 (European Remote Sensing Satellite) mission.

An innovative application focused on the segmentation of decay zones from images of stone materials is presented. The adopted numerical approach to extract decay regions from the color images of monuments provides a tool that helps experts analyze degraded regions by contouring them. In this way even if the results of the proposed procedure depend on the evaluation of experts, the approach can be a contribution to improving the efficiency of the boundary detection process. The segmentation is a process that allows an image to be divided into disjoint zones so that partitioned zones contain homogeneous characteristics. The numerical method, used to segment color images, is based on the theory of interface evolution, which is described by the eikonal equation. We adopted the fast marching technique to solve the upwind finite difference approximation of the eikonal equation. The fast marching starts from a seed point in the region of interest and generates a front which evolves according to a specific speed function until the boundary of the region is identified. We describe the segmentation results obtained with two speed functions, attained by the image gradient computation and color information about the object of interest. Moreover, we present the extension of the working modality of the method by introducing the possibility to extract the regions not only in a local way but also in a global way on the entire image. In this case, in order to improve the segmentation efficiency the application of the fast marching technique starts with more seed points defined as seed regions. The study case concerns the impressive remains of the Roman Theatre in the city of Aosta (Italy). In the image segmentation process the color space L^*a^*b^* is utilized.

In this paper we present an innovative and automatic procedure which is used to extract the coastline from SAR (Synthetic Aperture Radar) images by the level set model. This model consists in a PDE (Partial Differential Equation) equation governing the evolution of a curve corresponding to the zero level of a 3D function, called level set function, until the curve reaches the edge of the region to be segmented. A coastline is the boundary between land and sea masses. Detecting the coastline is of fundamental importance when monitoring various natural phenomena such as tides, coastal erosion and the dynamics of glaciers. In this case SAR images show problems which arise from the presence of the speckle noise and of the strong signal deriving from the rough or slight sea. In fact in the case of heavy sea the signal determines an intensity similar to the one of land, making it difficult to distinguish the coastline.