Presents an ellipsoidal calculus based solely on two basic operations: propagation and fusion. Propagation refers to the problem of obtaining an ellipsoid that must satisfy an affine relation with another ellipsoid, and fusion to that of computing the ellipsoid that tightly bounds the intersection of two given ellipsoids. These two operations supersede the Minkowski sum and difference, affine transformation and intersection tight bounding of ellipsoids on which other ellipsoidal calculi are based. Actually, a Minkowski operation can be seen as a fusion followed by a propagation and an affine transformation as a particular case of propagation. Moreover, the presented formulation is numerically stable in the sense that it is immune to degeneracies of the involved ellipsoids and/or affine relations. Examples arising when manipulating uncertain geometric information in the context of the spatial interpretation of line drawings are extensively used as a testbed for the presented calculus.

An alternative approach for the propagation of uncertain geometric information, based on the ideas presented by J.R. Deller (IEEE ASSP Magazine, vol.6, p.4-20, Oct. 1989) and extended to deal with graphs of geometric constraints, is presented. This method avoids the independency assumption of the probabilistic approach. In this approach, when new sensory data are acquired, a set of strips is obtained, propagated, and fused to obtain the updated ellipsoids associated with each feature, Then, the hypothesis about the location of the involved geometric features can be easily updated. Inconsistencies are easily detected, resulting in fast rejection of erroneous data.>