3D-Dithered Ortho-Pictures: 3D Models from Independent 2D Images

Gershon Elber
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 207–214


This work portrays a scheme to simultaneously 3D-dither two (or more) 2D gray-level images in ℝ3, in orthogonal orthographic views, into one 3D model embedded in a cube, so that the different input images are seen from the different faces of the cube. From one axis-parallel orthographic view of the cube model, the first image is seen, and from a second, orthogonal, orthographic view, the second image is seen. We show that the dithering problem of more than one image does not have an exact solution as one image cannot be completely decoupled from the other; however, for images with rich enough gray-levels, the result will be a highly precise 3D-dithering of both images. Moreover, error correction methods common in classical dithering, such as the well known Floyd-Steinberg [8] algorithm, can be exploited in this 3D-dithering scheme. We then present some tangible examples, etched in glass (See Figure 1).