Mathematical Methods for Objects Reconstruction: From 3D Vision to 3D Printing

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.

本書收錄了幾篇關於「數學方法應用於物體重建：從3D視覺到3D打印」的INDAM研討會的貢獻，該研討會於2021年2月在羅馬舉行。研討會的目標是討論管理這些具有挑戰性問題的新方法和概念結構。這些章節反映了這一目標，作者包括學術研究人員和一些來自工業界的專家，他們在3D建模、計算機視覺、3D打印和/或開發這些問題的新數學方法的領域工作。這些貢獻介紹了大規模3D重建應用和低成本3D打印機的出現所帶來的方法和挑戰。本書匯集了來自數學、計算機科學和工程學不同領域的互補知識，探討了迄今為止尚未廣泛探索的與3D打印相關的研究主題。對於3D數據收集、3D場景重建和3D打印軟件開發等領域的年輕研究人員和未來的科學領袖來說，本書提供了解決這些問題所需的優秀介紹和數學技術。

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.

Emiliano Cristiani，1977年出生，是意大利國家研究委員會的高級研究員。他於2004年畢業於羅馬大學Sapienza的數學專業，並獲得應用數學博士學位。他的研究興趣包括集體行為（車輛、行人、動物）自組織模型的模擬、應用於最優控制理論的Hamilton-Jacobi方程、圖像處理和3D打印。他是國際期刊上約40篇論文的作者。

Maurizio Falcone，1954年出生，是羅馬大學Sapienza數學系的數值分析全職教授。他於1978年在同一所大學獲得數學碩士學位（優等榮譽）。他的主要研究領域包括數值分析、偏微分方程、控制理論和微分博弈、圖像處理。他是國際期刊上約80篇論文的作者，並曾擔任國際研究項目（Galileo、INTAS、Marie Curie）的協調人。

Silvia Tozza，1985年出生，是博洛尼亞大學數學系的高級助理教授（tenure-track）。她於2008年在薩萊諾大學獲得數學學士學位，並於2011年和2015年分別在羅馬大學Sapienza獲得應用數學碩士學位和博士學位。她的研究主要集中在Hamilton-Jacobi方程的分析和逼近，並應用於圖像處理。