The volume collects several contributions to the INDAM workshop Mathematical Methods for Objects Reconstruction: from 3D Vision to 3D Printing held in Rome, February, 2021.  The goal of the workshop was to discuss new methods and conceptual structures for managing these challenging problems. The chapters reflect this goal and the authors are academic researchers and some experts from industry working in the areas of 3D modeling, computer vision, 3D printing and/or developing new mathematical methods for these problems. The contributions present methodologies and challenges raised by the emergence of large-scale 3D reconstruction applications and low-cost 3D printers. The volume collects complementary knowledges from different areas of mathematics, computer science and engineering on research topics related to 3D printing, which are, so far, widely unexplored.  Young researchers and future scientific leaders in the field of 3D data acquisition, 3D scene reconstruction, and 3D printing software development will find an excellent introduction to these problems and to the mathematical techniques necessary to solve them.

This book presents the latest advances in photometric 3D reconstruction. It provides the reader with an overview of the state of the art in the field, and of the latest research into both the theoretical foundations of photometric 3D reconstruction and its practical application in several fields (including security, medicine, cultural heritage and archiving, and engineering). These techniques play a crucial role within such emerging technologies as 3D printing, since they permit the direct conversion of an image into a solid object. The book covers both theoretical analysis and real-world applications, highlighting the importance of deepening interdisciplinary skills, and as such will be of interest to both academic researchers and practitioners from the computer vision and mathematical 3D modeling communities, as well as engineers involved in 3D printing. No prior background is required beyond a general knowledge of classical computer vision models, numerical methods for optimization, and partial differential equations.

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

This book presents the latest advances in photometric 3D reconstruction. It provides the reader with an overview of the state of the art in the field, and of the latest research into both the theoretical foundations of photometric 3D reconstruction and its practical application in several fields (including security, medicine, cultural heritage and archiving, and engineering). These techniques play a crucial role within such emerging technologies as 3D printing, since they permit the direct conversion of an image into a solid object. The book covers both theoretical analysis and real-world applications, highlighting the importance of deepening interdisciplinary skills, and as such will be of interest to both academic researchers and practitioners from the computer vision and mathematical 3D modeling communities, as well as engineers involved in 3D printing. No prior background is required beyond a general knowledge of classical computer vision models, numerical methods for optimization, and partial differential equations.

This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.