This paper considers the problem of detecting the local similarity between templates in a given class and a given image using a hierarchically ordered sequential decision rule. When the given set consists of a large number of templates and the number of locations in the image matching any of the templates is small, it is wasteful to examine each of the templates at every location in the image for a match. Instead, it is proposed that the set of templates be partitioned and a ``representative template'' be defined for each of the partitions. Several levels of partitioning are defined. Elimination of mismatching locations and termination of computation can take place at each, level of detection. Each level of testing is over a more restrictive subset of the template class than the previous level. The paper presents a general formulation of this approach and gives criteria for selecting representative templates, the ordering of components of a template vector for error evaluation, and the threshold sequences to be used in deciding about a ``match.'' Suboptimal solutions are given satisfying these criteria. Illustrative examples are provided showing recognition of linear features in test patterns and photographs obtained by aerial and spaceborne sensors.

This paper considers the problem of asymptotic stability in the large of an autonomous system containing a single nonlinearity. The nonlinear function is assumed to belong to several subclasses of monotonically increasing functions in the sector(0, K), and the stability criterion is shown to be of the formRe Z(j\omega) [G(j\omega) +\frac{1}{K}] -\frac{\delta'}{K} \geq 0where the constant\delta'is equal toZ(\infty) - Z_{p}(\infty)andZ_{p}(s)is a Popov multiplier. The multiplierZ(s)can, in general, have complex conjugate poles and zeros and is thus more general than the type of multipliers obtained in previous results. The nonlinear functions considered are odd monotonic functions, functions with a power law restriction, and a new class of functions with restricted asymmetry having the property|\frac{f{\theta}{f{\-theta}|\leq cfor all\theta. Unlike in certain earlier publications, no upper bound is placed on the derivative of the nonlinearity here. The results obtained can be used to establish stability in some cases even when the Nyquist plot of the linear part transfer function lies in all four quadrants and the nonlinearity is not necessarily odd. Furthermore, it is shown that the conditions on the multiplier and, consequently, those on the linear part can be relaxed as the feedback function approaches linearity.