Mathematical Methods for Objects Reconstruction

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, 3Dscene reconstruction, and 3D printing software development will find an excellent introduction to these problems and to the mathematical techniques necessary to solve them.

Presents several mathematical problems for 3D and 3D printing plus a survey that gives the links between the two areas Contains contributions from highly reputed academic and industrial researchers with a long experience Shows several techniques, applications and benchmarks that can be useful for young researchers approaching the field

Autorentext

Emiliano Cristiani, born in 1977, is Senior Researcher at National Research Council of Italy. He graduated in 2004 in Mathematics and got a Ph.D. in Applied Mathematics from Sapienza Università di Roma. His research interests include models for simulation of self-organization in collective behaviour (vehicles, pedestrians, animals), Hamilton-Jacobi equations with application to optimal control theory, image processing, and 3D printing. He is author of about 40 papers on international journals. Maurizio Falcone, born in 1954, is Full Professor of Numerical Analysis at Dipartimento di Matematica, Sapienza Università di Roma. He received a Master Degree in Mathematics, cum laude, from the same university in 1978. Main research areas are numerical analysis, partial differential equations, control theory and differential games, image processing. He is author of about 80 papers on international journals and he was coordinator of International Research Projects (Galileo,INTAS, Marie Curie).

Silvia Tozza, born in 1985, is Senior Assistant Professor (tenure-track) in Numerical Analysis at Department of Mathematics, ALMA MATER STUDIORUM Università di Bologna. She obtained her B.Sc. in Mathematics at Università degli Studi di Salerno in 2008, M.Sc. and Ph.D. in Applied Mathematics at Sapienza Università di Roma in 2011 and January 2015, respectively. Her research activity focuses mainly on analysis and approximation of Hamilton-Jacobi equations with applications in Image Processing.

Klappentext

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, 3Dscene reconstruction, and 3D printing software development will find an excellent introduction to these problems and to the mathematical techniques necessary to solve them.

Inhalt
1 Emiliano Cristiani, Maurizio Falcone, and Silvia Tozza, An Overview of Some Mathematical Techniques and Problems Linking 3D Vision to 3D Printing.- 2 Georg Radow, Giuseppe Rodriguez, Ashkan Mansouri Yarahmadi, and Michael Breuß, Photometric Stereo with Non-Lambertian Preprocessing and Hayakawa Lighting Estimation for Highly Detailed Shape Reconstruction.- 3 Toby Collins and Adrien Bartoli, Shape-from-Template with Camera Focal Length Estimation.- 4 J. Andreas Bærentzen, Ida Bukh Villesen, Ebba Dellwik, Reconstruction of a Botanical Tree from a 3D Point Cloud.- 5 Jesse Beisegel, Johannes Buhl, Rameez Israr, Johannes Schmidt, Markus Bambach, and Armin Fügenschuh, Mixed-Integer Programming Models for Two Metal Additive Manufacturing Methods.- 6 Ashkan Mansouri Yarahmadi, Michael Breuss, Carsten Hartmann, Toni Schneidereit, Unsupervised Optimization of Laser Beam Trajectories for Powder Bed Fusion Printing and Extension to Multiphase Nucleation Models. <p