This paper presents an application of some recent results in computer
vision, in particular the use of geometric properties. The problem we
examine here is the accurate positioning of an object with respect to
another, say a tool. Such applications could be used in complex and ha
zardous environments like nuclear plants. Because high accuracy in pos
itioning is our goal here, we suppose that the objects have planar fac
es on which targets can be put. Without loss of generality, we have us
ed only two objects in our experiments. Throughout this paper, we have
called them the reference object and the unknown object respectively.
The positions of the targets of the reference object with their assoc
iated projective invariants are computed in an off-line stage. Hence,
given at least two images of the two objects, we can automatically ide
ntify the reference object points in the images and reconstruct the po
ints of the unknown object relative to the reference object. The exper
iments show that a precision of 0.1 mm in relative positioning can be
reached for an object observed at a distance of 2 m. (C) 1998 Elsevier
Science B.V.