An overview of some mathematical techniques and problems linking 3D vision to 3D printing
This work addresses the gap between computer vision and 3D printing for researchers and practitioners, but it is incremental as it primarily reviews and connects existing techniques.
The paper tackles the limited interaction between computer vision and 3D printing by providing an overview of mathematical techniques, such as nonlinear partial differential equations and optimization, to link shape-from-shading problems with 3D printing, and sketches a procedure for manufacturing objects from images to prints with practical examples.
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.