Название: Mathematical Methods for Objects Reconstruction: From 3D Vision to 3D PrintingАвтор: Emiliano Cristiani, Maurizio Falcone, Silvia Tozza
Издательство: Springer
Год: 2023
Страниц: 185
Язык: английский
Формат: pdf (true), epub
Размер: 36.0 MB
Three-dimensional (3D) reconstruction of the shape of objects is an issue that has been investigated largely by the computer vision and applied mathematics communities since the last century. The class of problems related to that issue is the so-called Shape-from-X class, where the X specifies the kind of data used for the reconstruction (e.g., shading, texture, template, polarization).
One of the most interesting problems that fully relates 3D vision to 3D printing is probably the appearance replication. This problem, only partially explored, consists in replicating (multi-material) real objects with complex reflectance features using a single, cheaper printing material, possibly with the simple diffuse Lambertian reflectance. To trick the eye, the surface of the object is rippled with tiny facets that regulate the reflection of light, analogous to what is done, for example, in the Oren-Nayar reflectance model for recovering the 3D shape of the object in the context of the Shape-from-Shading problem.
This volume is devoted to mathematical and numerical methods for object reconstruction, and it aims at creating a bridge between 3D vision and 3D printing, moving from the 3D data acquisition and 3D reconstruction to the 3D printing of the reconstructed object, with software development and/or new mathematical methods to get closer and closer to real-world applications. Some contributions focus on 3D vision, dedicated to photometric- or geometric-based Shape-from-X problems. Other contributions address specific issues related to 3D printing, further widening the research topics of this newly investigated area.
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 is useful for both academic researchers and experts from industry working in these areas who want to focus on complementary knowledge in 3D vision and 3D printing fields. Also practitioners and graduate students working on partial differential equations, optimization methods, and related numerical analysis will find this volume interesting as an approach to the field.
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