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.

In this paper we propose a numerical method for the simulation of acousticfields, in presence of an obstacle in the physical domain, by finite difference solution of a two-dimensional differential model on boundary-fittedgrids. The computational process gathers the elliptic grid generation, the linear Euler equations in curvilinear coordinates, the associated bicharacteristic equation and a fully explicit finite difference approximation. We detail the models, the algorithms and a series of both literature and new test problems. We present computed velocity and pressure fields by the help of figures. The method results to be able to reconstruct field evolutions and near obstacle perturbations caused by one or more, fixed or moving, pressure sources.

We present results of a numerical simulation of the thermal convection in the subsurface mushy ice layer of Europa, one of the Jupiter's moons. Beside fluid dynamics and heat transfer within such a layer, heat conduction in the solid crustal surface and heat exchange between the two phases - mushy ice and solid crust - are included in our model in order to follow also the evolution of the phase front. Since the images of Europa's crust taken by the spacecrafts Voyager and Galileo got to be known, planetary scientists stimulated this kind of investigations with the aim of studying the origin of such a topographic aspect. Actually the chaotic lineaments and splotches, clearly visible, solicited the conjecture of the existence of an internal ocean of water that is also supported by the most recent Galileo magnetic field data. The presence of water would make life possible on the jovian satellite. However, in the recent literature, just few numerical simulations describing the overall scenario and including either heat transfer and convection flow have been proposed. Here we adopt the stream-function/vorticity formulation of the Navier-Stokes equations for the flow of the mushy ice and a Stefan condition combined with a front-fixing technique for the front evolution. Our numerical discretization is based upon an ENO scheme. Mathematical model and numerical procedure have been thoroughly tested and have the advantage of yielding accurate numerical solutions via relatively coarse space discretization grids. For applications in this field the present one is the first attempt, at our knowledge, to solve a complete Stefan condition with convection flow, obtaining a good match with other numerical solutions in the literature.