Rank Conditions in Multiple View Geometry

			Jana Kosecka
		   George Mason University
		Department of Computer Science

			   Abstract

Geometric relationships governing multiple images of 3D features
(points, lines and planes) and associated algorithms for motion and
structure recovery have been studied to a large extent separately in
multiple view geometry.

We will show that *all* the known constraints among multiple images of
3D features can be captured concisely through certain rank conditions
on the so-called multiple view matrix M.  These rank conditions
capture all the known multilinear constraints and enables us to carry
out global geometric analysis for multiple views, as well as
systematically characterize all degenerate configurations, without
breaking image sequence into two or three views at the time.

I will discuss various applications of the presented formulation to
problems in computer vision, graphics and robotic control. In
particular the rank conditions give rise to a set of natural linear
algorithms for structure and motion recovery from multiple views,
enable us to formulate multiview feature matching criteria and image
transfer to a novel view.

This is joint work with Yi Ma (UIUC), Rene Vidal (UCB), Kung Huang (UIUC).