Invariant template matching in systems with spatiotemporal coding: a vote for instability

We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition. 1 Notational preliminaries We define an image as a mapping S0(x, y) from a class of locally bounded mappings S ⊆ L∞(Ωx × Ωy), where Ωx ⊆ R, Ωy ⊆ R, and L∞(Ωx × Ωy) is the space of all functions f : Ωx × Ωy → R such that ‖f‖∞ = ess sup{‖f(x, y)‖, x ∈ Ωx, y ∈ Ωy} < ∞. Symbols x, y denote variables on different spatial axes. The value of S0(x, y) depends on the characteristic value of interest (e.g. brightness, contrast, color, etc.). We assume that an image can be described within the system as a set of a-priory specified templates, Si(x, y) ∈ S, i ∈ I ⊂ N, Laboratory for Perceptual Dynamics, RIKEN (Institute for Physical and Chemical Research) Brain Science Institute, 2-1, Hirosawa, Wako-shi, Saitama, 351-0198, Japan, e-mail: {tyukinivan}@brain.riken.jp Laboratory for Perceptual Dynamics, RIKEN (Institute for Physical and Chemical Research) Brain Science Institute, 2-1, Hirosawa, Wako-shi, Saitama, 351-0198, Japan, e-mail: {tatianat}@brain.riken.jp Corresponding author. Laboratory for Perceptual Dynamics, RIKEN (Institute for Physical and Chemical Research) Brain Science Institute, 2-1, Hirosawa, Wako-shi, Saitama, 351-0198, Japan, e-mail: {ceesvl}@brain.riken.jp