Field Computation in Motor Control

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Abstract

Field computation deals with information processing in terms of fields, continuous distributions of data. Many neural phenomena are conveniently described as fields, including neuron activity from large (brain area) to small (dendritic) scales. Further, it is often useful to describe motor control and sensorimotor coordination in terms of external fields such as force fields and sensory images. We survey the basic concepts of field computation, including both feed-forward field operations and field dynamics resulting from recurrent connections. Adaptive and learning mechanisms axe discussed briefly. The application of field computation to motor control is illustrated by several examples: external force fields associated with spinal neurons (Bizzi & Mussa-Ivaldi 1995), population coding of direction in motor cortex (Georgopoulos 1995), continuous transformation of direction fields (Droulez & Berthoz 1991a), and linear gain fields and coordinate transformations in posterior parietal cortex (Andersen 1995). Next we survey some field-based representations of motion, including direct, Fourier, Gabor and wavelet or multiresolution representations. Finally we consider briefly the application of these representations to constraint satisfaction, which has many applications in motor control.

Section snippets

Motivation

My purpose in this chapter is to introduce the general concepts of field computation and to describe some possible applications of it to motor control. Field computation deals with continuous distributions of activity such as are found in the topographic maps and other functional areas of the brain (Knudsen et al. 1987), but also with external distributions of quantity, such as force fields. In field computation we are generally concerned with the topology of the space over which a quantity is

Definition

For the purposes of field computation, a field is defined to be a spatially continuous distribution of quantity. Field computation is then a computational process that operates on an entire field in parallel. Often we treat the field as varying continuously in time, although this is not necessary.

It is sometimes objected that distributions of quantity in the brain are not in fact continuous, since neurons and even synapses are discrete. However, this objection is irrelevant. For the purposes of

Definition

The primary defining feature of field computation is that it operates on an entire field in parallel. For example, operations that process a retinal image in parallel, or which generate a spatial or motor map in parallel, are clear examples of field computation. On the other hand, a process that generates one or a few scalar signals sequentially in time is not considered field computation (except in a degenerate or trivial sense). The point is not to have a clear and. absolutely precise

Field Dynamics

The field operations considered above are examples of nonrecurrent operations, typically implemented by feed-forward connections between neural areas. In this section we will consider recurrent operations, which are typically implemented by feed-back or reciprocal connections. Thus there are dynamical relations between several areas that govern the variation in time of one or more fields; these processes are especially important in motor control, since time-varying motor fields in the central

Learning

Representations of motion patterns can be quickly learned and adapted by a variety of field computational methods; many involve the extraction of frequency-domain information from example motions (by application of inner-product or filtering techniques). Invariances in sensorimotor coordination can emerge similarly from simple correlational adaptive algorithms. Since an adequate treatment of field-computational approaches to learning is beyond the scope of this paper, I will give just two

External Force Fields and Motor Basis Fields

Bizzi & Mussa-Ivaldi (1995) survey experiments showing that regions in the spinal chord of the frog define associated force fields in the vicinity of the leg; that it; microstimulation of that spinal region causes the leg to exert a consistent force, which depends on the position of the leg, thus defining a force field over its range of motion. They further show that microstimulation of multiple spinal regions create a force field that is the linear superposition (sum) of the individual force

Direct (Spatial) Representation

One of the simplest ways to represent a trajectory ϕ(t) is by direct spatial encoding of the time dimension; then the trajectory can be read sequentially from the fixed field. (This process is like playing an audio tape.) More precisely, suppose ϕu(t) is a time-varying field defined

Concluding Remarks

We have seen that field computation deals with information processing in terms of fields, which may be described as continuous distributions of data. Many neural phenomena are conveniently described as fields, including neuron activity from large (brain area) to small (dendritic) scales, and it is often useful to describe motor control and sensorimotor coordination in terms of external fields such as force fields and sensory images. We have surveyed the basic concepts of field computation,

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