Variational methods and its applications to computer vision

Many computer vision applications such as image segmentation can be formulated in a ''variational'' way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Open Acces

Convective regularization for optical flow

We argue that the time derivative in a fixed coordinate frame may not be the most appropriate measure of time regularity of an optical flow field. Instead, for a given velocity field $v$ we consider the convective acceleration $v_t + \nabla v v$ which describes the acceleration of objects moving according to $v$. Consequently we investigate the suitability of the nonconvex functional $\|v_t + \nabla v v\|^2_{L^2}$ as a regularization term for optical flow. We demonstrate that this term acts as both a spatial and a temporal regularizer and has an intrinsic edge-preserving property. We incorporate it into a contrast invariant and time-regularized variant of the Horn-Schunck functional, prove existence of minimizers and verify experimentally that it addresses some of the problems of basic quadratic models. For the minimization we use an iterative scheme that approximates the original nonlinear problem with a sequence of linear ones. We believe that the convective acceleration may be gainfully introduced in a variety of optical flow models

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls

Rock fractures analysis using Structure from Motion technology: new insight from Digital Outcrop Models

Fractures are one of the most important features of the rocks of the upper crust since they strongly influence their physical and chemical behavior and reflect their tectonic history. For this reason, fracture study plays a key role in different branches of the geosciences. Notwithstanding, the quantification of the features and parameters describing fractures could be unsatisfactory using the standard field techniques because they are mainly based on direct-contact methodologies that are affected by errors, as orientation bias and trace censoring, and scarce representativeness, due to the limited possibility of acquiring information of outcrops partially or totally inaccessible. Recently new remote sensing technologies, such as Terrestrial Laser Scanner (TLS) and Digital Photogrammetry (DP), can help to overcome these limitations. Whereas TLS could be very expensive and difficult to use in geological study, DP permits to obtain similar results in an easier way due to cheaper and lighter equipment and more straightforward procedures. Moreover, DP becomes even more useful when combined with Unmanned Aerial Vehicle (UAV) because permits to acquire digital images from positions inaccessible to humans, allowing to analyze geological objects from points of view previously unimaginable. The images acquired from the ground and/or by the UAV can be then processed using different digital algorithms, such as Structure from Motion (SfM), that permit to create 3D model of the studied outcrop. In geosciences, the 3D model representing the surface of the outcrop is often called Digital Outcrop Model (DOM). Despite DOMs can be really useful in different branches of geosciences, their applications are quite well limited because the procedures of their development and sampling/analysis are scarcely analyzed in literature. It is important to highlight that whereas the UAV-based SfM approach is fairly discussed in literature for simple flat areas, is scarcely treated for application to near vertical and not-planar slopes. Moreover, the validity of some procedures of fracture sampling on 3D model, with special regards to the automatic ones, that have been recently presented in literature, is not well treated for real cases of study. The scarce knowledge about these approaches could cause different troubles to the scientific-users: from the application of avoidable time-consuming routine, to the acquisition and interpretation of erroneous data. This research aims to contribute to the scientific knowledge of the use of digital photogrammetry for fractured rock mass analysis, creating and defining new approaches and procedures for the development, analysis and application of DOMs. Here, a workflow for the fracture analysis of steep rocky outcrops and slopes using the 3D DOM is presented. In particular, the following steps are discussed: (i) image acquisition; (ii) development of 3D model; (iii) sampling of DOM; (iv) quantification and parametrization of the 3D measures; (v) application of the 3D quantitative data and parameters to different case of study. Four different cases of study were selected to validate the proposed method: the upper Staffora Valley and Ponte Organasco (Northern Apennines, Italy), Ormea (Ligurian Alps, Italy), and Gallivaggio (Western Alps, Italy) cases of study. However, this methodology could not completely replace the 'direct-contact' field activity, because some information as roughness, infilling and aperture of fractures cannot be measured satisfactory, and because, where possible, field control measures to validate the 3D data are necessary. However, this methodology could be considered as a new necessary procedure for rock-fracture studies because it allows to overcome the inevitable errors of the ground-based traditional methodology and because the DOMs are always available for the analysis, promoting data sharing and comparison, two fundamental principles on which science have and will have to be basedFractures are one of the most important features of the rocks of the upper crust since they strongly influence their physical and chemical behavior and reflect their tectonic history. For this reason, fracture study plays a key role in different branches of the geosciences. Notwithstanding, the quantification of the features and parameters describing fractures could be unsatisfactory using the standard field techniques because they are mainly based on direct-contact methodologies that are affected by errors, as orientation bias and trace censoring, and scarce representativeness, due to the limited possibility of acquiring information of outcrops partially or totally inaccessible. Recently new remote sensing technologies, such as Terrestrial Laser Scanner (TLS) and Digital Photogrammetry (DP), can help to overcome these limitations. Whereas TLS could be very expensive and difficult to use in geological study, DP permits to obtain similar results in an easier way due to cheaper and lighter equipment and more straightforward procedures. Moreover, DP becomes even more useful when combined with Unmanned Aerial Vehicle (UAV) because permits to acquire digital images from positions inaccessible to humans, allowing to analyze geological objects from points of view previously unimaginable. The images acquired from the ground and/or by the UAV can be then processed using different digital algorithms, such as Structure from Motion (SfM), that permit to create 3D model of the studied outcrop. In geosciences, the 3D model representing the surface of the outcrop is often called Digital Outcrop Model (DOM). Despite DOMs can be really useful in different branches of geosciences, their applications are quite well limited because the procedures of their development and sampling/analysis are scarcely analyzed in literature. It is important to highlight that whereas the UAV-based SfM approach is fairly discussed in literature for simple flat areas, is scarcely treated for application to near vertical and not-planar slopes. Moreover, the validity of some procedures of fracture sampling on 3D model, with special regards to the automatic ones, that have been recently presented in literature, is not well treated for real cases of study. The scarce knowledge about these approaches could cause different troubles to the scientific-users: from the application of avoidable time-consuming routine, to the acquisition and interpretation of erroneous data. This research aims to contribute to the scientific knowledge of the use of digital photogrammetry for fractured rock mass analysis, creating and defining new approaches and procedures for the development, analysis and application of DOMs. Here, a workflow for the fracture analysis of steep rocky outcrops and slopes using the 3D DOM is presented. In particular, the following steps are discussed: (i) image acquisition; (ii) development of 3D model; (iii) sampling of DOM; (iv) quantification and parametrization of the 3D measures; (v) application of the 3D quantitative data and parameters to different case of study. Four different cases of study were selected to validate the proposed method: the upper Staffora Valley and Ponte Organasco (Northern Apennines, Italy), Ormea (Ligurian Alps, Italy), and Gallivaggio (Western Alps, Italy) cases of study. However, this methodology could not completely replace the 'direct-contact' field activity, because some information as roughness, infilling and aperture of fractures cannot be measured satisfactory, and because, where possible, field control measures to validate the 3D data are necessary. However, this methodology could be considered as a new necessary procedure for rock-fracture studies because it allows to overcome the inevitable errors of the ground-based traditional methodology and because the DOMs are always available for the analysis, promoting data sharing and comparison, two fundamental principles on which science have and will have to be base

Moving and adaptive grid methods for compressible flows

This paper describes adaptive grid methods developed specifically for compressible flow computations. The basic flow solver is a finite-volume implementation of Roe's flux difference splitting scheme or arbitrarily moving unstructured triangular meshes. The grid adaptation is performed according to geometric and flow requirements. Some results are included to illustrate the potential of the methodology

Part decomposition of 3D surfaces

This dissertation describes a general algorithm that automatically decomposes realworld scenes and objects into visual parts. The input to the algorithm is a 3 D triangle mesh that approximates the surfaces of a scene or object. This geometric mesh completely specifies the shape of interest. The output of the algorithm is a set of boundary contours that dissect the mesh into parts where these parts agree with human perception. In this algorithm, shape alone defines the location of a bom1dary contour for a part. The algorithm leverages a human vision theory known as the minima rule that states that human visual perception tends to decompose shapes into parts along lines of negative curvature minima. Specifically, the minima rule governs the location of part boundaries, and as a result the algorithm is known as the Minima Rule Algorithm. Previous computer vision methods have attempted to implement this rule but have used pseudo measures of surface curvature. Thus, these prior methods are not true implementations of the rule. The Minima Rule Algorithm is a three step process that consists of curvature estimation, mesh segmentation, and quality evaluation. These steps have led to three novel algorithms known as Normal Vector Voting, Fast Marching Watersheds, and Part Saliency Metric, respectively. For each algorithm, this dissertation presents both the supporting theory and experimental results. The results demonstrate the effectiveness of the algorithm using both synthetic and real data and include comparisons with previous methods from the research literature. Finally, the dissertation concludes with a summary of the contributions to the state of the art