Minimal decomposition of model-based invariants

Model-based invariants are relations between model parameters and image mea surements, which are independent of the imaging parameters. Such relations are true for all images of the model. Here we describe an algorithm which, given L independent model-based polynomial invariants describing some shape , will provide a linear re-parameterization of the invariants. This re-para meterization has the properties that: (i) it includes the minimal number of terms, and (ii) the shape terms are the same in all the model-based invari ants. This final representation has 2 main applications: (1) it gives new r epresentations of shape in terms of hyperplanes, which are convenient for o bject recognition; (2) it allows the design of new linear shape from motion algorithms. In addition, we use this representation to identify object cla sses that have universal invariants.