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“Machine Perception of Partially Specified Planar Shapes”
by Paul Frank Singer
May 1985
A new set of global shape descriptions is defined which is useful in the machine perception of planar shapes from their partially specified boundaries. These shape descriptors are estimated from the observed portions of the boundary, thus obviating the need for boundary reconstruction. The boundary is modeled as a circular auto-regressive (CAR) process. The CAR descriptors preserve class shape information and are shown to be insensitive to within class variations. The maximum likelihood (ML) estimator of the CAR descriptors is derived from the CAR model. Obscured boundaries are modeled as the product of the complete boundary and a binary valued obscuring process. This model of obscuration is general enough to include both occlusion and segmentation errors. The ML estimator is extended to include obscured boundaries by retaining the form of the original ML estimator and rederiving its component parts. This derivation is dependent upon the asymptotic stationarity of the obscured boundary process. The asymptotic properties of the extended ML estimator and its estimates are established. These properties are used to derive the tight analytic upper bound on classification performance. A classifier is designed from theasymptotic distribution of the estimates and two classification experiments are performed using partially obscured boundaries. The first experiment uses four synthetic shape classes and establishes the dependence of classification accuracy upon the stationarity of the boundary process. The extended ML estimates are shown to perform better than the least squares (LS) estimates computed from the reconstructed boundary. The second experiment uses real aircraft boundaries and all model parameters are estimated from the observed boundary. An experimental classification accuracy of 91% is achieved using the extended ML estimator on boundaries which are 30% obscured.