We address here the problem of scale and rotation invariant object recognition, making use of a correspondence-based mechanism, in which the identity of an object represented by sensory signals is determined by matching it to a representation stored in memory. The sensory representation is in general affected by various transformations, notably scale and rotation, thus giving rise to the fundamental problem of invariant object recognition. We focus here on a neurally plausible mechanism that deals simultaneously with identification of the object and detection of the transformation, both types of information being important for visual processing. Our mechanism is based on macrocolumnar units. These evaluate identity- and transformation-specific feature similarities, performing competitive selection of the alternatives of their own subtask, and cooperate to make a coherent global decision for the identity, scale and rotation of the object.
The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.