Publication

An ellipsoidal calculus based on propagation and fusion

Journal Article (2002)

Journal

IEEE Transactions on Systems, Man and Cybernetics: Part B

Pages

430-442

Volume

32

Number

4

Doc link

http://dx.doi.org/10.1109/TSMCB.2002.1018763

File

Download the digital copy of the doc pdf document

Abstract

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.

Categories

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Author keywords

ellipsoidal bounds, ellipsoidal calculus, set-membership uncertainty description

Scientific reference

L. Ros, M.A. Sabater and F. Thomas. An ellipsoidal calculus based on propagation and fusion. IEEE Transactions on Systems, Man and Cybernetics: Part B, 32(4): 430-442, 2002.