In: Neural Networks, 17(8-9):1311-1326, 2004. Maplets for Correspondence-Based Object Recognition Junmei Zhu ∗ Computer Science Department University of Southern California Christoph von der Malsburg Institut f¨ ur Neuroinformatik Ruhr-Universit¨at Bochum Abstract We present a correspondence-based system for visual object recognition with invari- ance to position, orientation, scale and deformation. The system is intermediate between high-dimensional and low-dimensional representations of correspondences. The essence of the approach is based on higher-order links, called here maplets, which are specific to narrow ranges of mapping parameters (position, scale and orientation), which interact cooperatively with each other, and which are assumed to be formed by learning. While being based on dynamic links, the system overcomes previous problems with that for- mulation in terms of speed of convergence and range of allowed variation. We perform face recognition experiments, comparing ours to other published systems. We see our work as a step towards a reformulation of neural dynamics that includes rapid network self-organization as essential aspect of brain state organization. Keywords: Object recognition, correspondence, dynamic link, map formation, self- organization, maplet. 1 Introduction The classical way to model the data structure of the brain is based on a vector of neural activity values V i (t),i =1, ..., N . It has been argued previously that this data structure is deficient in leaving open the binding problem (Leg´ endy, 1970; von der Malsburg, 1981; Hummel and Biederman, 1992; Ajjanagadde and Shastri, 1991; von der Malsburg, 1999). In (von der Malsburg, 1981) it is proposed that a better interpretation of dynamic brain states must contain the equivalent of dynamic links between neural units. These could be binary, involving pairs of elements, (i, j ), i, j =1, .., N , or links could be of higher order, e.g., involving triplets (i, j, k), i, j, k =1, ..., N , and would have weights changing on the psychological time scale of 100 msec or less. In this paper, we present a concrete application of those general ideas, using invariant object recognition as example. We see this as an important paradigm for brain state organization in general. We place particular emphasis here, first, on the efficiency of the process, efficiency measured in terms of the number of iterations necessary in a fully parallel implementation, and, second, on the enlargement of the useful search space, permitting invariance to scale and orientation in addition to translation. Although we pay attention to neural constraints (especially such as locality of ∗ Current address: Computer Science, University of Memphis, Dunn Hall 373, Memphis, TN 38152. Email: jzhu@memphis.edu. Phone: 901-678-1539. Fax: 901-678-2480. 1