Recognising Algebraic Surfaces from Two Outlines

Photographic outlines of 3 dimensional solids are robust and rich in information useful for surface reconstruction. This paper studies algebraic surfaces viewed from 2 cameras with known intrinsic and extrinsic parameters. It has been known for some time that for a degree d = 2 (quadric) algebraic surface there is a 1-parameter family of surfaces that reproduce the outlines. When the algebraic surface has degree d > 2, we prove a new result: that with known camera geometry it is possible to completely reconstruct an algebraic surface from 2 outlines i.e. the coefficients of its defining polynomial can be determined in a known coordinate frame. The proof exploits the existence of frontier points, which are calculable from the outlines. Examples and experiments are presented to demonstrate the theory.

• Type: Journal
• Year: 2008
• Where: JMIV
• Authors: Simon Collings, Ryszard Kozera, Lyle Noakes
• Keywords: Algebraic Surface, JMIV 2008, Photographic Outlines, Surface Reconstruction