Receptive Fields and the Specificity of Neuronal Firing

Neuronal firing does not occur at random. In the sensory parts of the brain, firing is triggered by properties of various input stimuli, such as the position of a light stimulus in the visual field, the pitch of a tone, or the appearance of a familiar face. In “associative” areas of the brain, specificities for more abstract concepts have been found including cells representing place (e.g., in rodent hippocampus), or numerosity (e.g., in primate prefrontal cortex). In the motor parts of the brain, neurons have been found that fire preferably prior to pointing movements of the arm into a certain direction. That is to say, these neurons are specific for particular motor actions. In the sensory domain, specificities are quantified in terms of the receptive field, which can be defined as the totality of all stimuli driving a given neuron. The receptive field is measured by correlating the activity of a single neuron with externally measurable parameters of the stimulus. This approach is known as reverse correlation, since stimuli will always preceed the neuronal activity. The concept of correlation between neuronal activity and external measurables, however, generalizes easily to the motor system, leading to the concept of the motor field of a neuron. In this sense, visual receptive fields can be considered as an example for neuronal specificity at large. In this chapter, we discuss the basic theory of visual receptive fields which can be extended to similar concepts in other sensory, motor, or associative areas. The theory is closely related to linear systems theory applied to spatio-temporal signals, i.e. image sequences.Mathematically, it rests on integral equations of the convolution type which will be introduced in due course.