In this paper, we describe a novel approach to scale-orientation- and shift-invariant object recognition. The modulo of locally computed Fourier-Mellin Descriptors serve as features that describe local image-patches scale-and orientation-invariant. Those features can be efficiently computed w. r. t. each image location, thus enabling positional invariance as well. Based on those features, we use a two-step procedure for locating and subsequently identifying previously learnt objects. First, all known objects are searched for in parallel in the Principle Components Domain using a probabilistic similarity measure. Hereafter, possible object locations are further examined using Fisher's Discriminant Analysis, thus enabling multi-object identification in one step. A spin-off from the Principle Components Analysis enables for representation-based feature selection, which in turn reduces the computational burden of feature generation.