## Introduction

This chapter examines some theoretical mathematical models for visual feature extraction in visual systems. The vertebrate retina and compound eye/optic lobe systems operate as spatiotemporal filters. That is, object contrast, size, and shape (its spatial frequency content) and its motion relative to the sensory array are both factors in determining the responses of an output neuron.

First examined is the Boolean logic model for visual spatiotemporal filtering described by Zorkoczy (1966). To respond to spatiotemporal properties of simple objects, Zorkoczy's filters use unit delay elements, as well as conventional AND and OR gates, etc. Zorkoczy sensor arrays have unit spacing, S degrees, between receptors. The unit velocity is defined as v = S/T, °/s (T is the unit delay). An object must be moving at v for the filter to produce an output.

Next examined is an analog, directional correlation model for moving object detection described by Reichardt (1964). Reichardt's directional correlator was proposed to describe optomotor behavior in insects; that is, the tendency of the insect to turn and follow an object of moving stripes. The correlator only requires two adjacent receptors, each of whose outputs is delayed and then multiplied by the direct output of the other receptor. The two multiplier outputs are subtracted, and then low-pass-filtered.

A third feature extraction model based more closely on retinal anatomy and neurophysiology devised by Fukushima (1969; 1970) is next considered. Fukush-ima's model is basically a continuous, linear, spatial filtering model whose analog outputs are non-negative, continuous variables proportional to instantaneous spike frequency. Fukushima's models are static models; they can "recognize" (detect is a better word) stationary shapes, such as spots, edges, lines at an angle, etc.

The concept of a neural spatial matched filter that can detect specific static object shapes is considered in Section 7.2. The matched filter is usually thought of as an engineering communications tool operating in the time domain. The basic matched filter architecture has also been extended into coherent optical signal processing. Its application in neural systems as a prototype model for a static pattern recognizer is considered. 