An overview of some mathematical techniques and problems linking 3D vision to 3D printing

TL;DR

This paper reviews mathematical techniques linking 3D vision and 3D printing, focusing on shape-from-shading and PDE-based optimization, and explores potential integrated workflows for object manufacturing from images.

Contribution

It provides an overview of mathematical methods connecting 3D vision and printing, highlighting PDE and optimization approaches and proposing integrated processes.

Findings

PDE and optimization techniques are key in shape-from-shading.

Coupling vision and printing processes can enable automated object manufacturing.

Practical examples demonstrate the feasibility of integrated workflows.

Abstract

Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an overview of some techniques for Shape-from-Shading problems as well as for 3D printing with an emphasis on the approaches based on nonlinear partial differential equations and optimization. We also sketch possible couplings to complete the process of object manufacturing starting from one or more images of the object and ending with its final 3D print. We will give some practical examples of this procedure.