saccadic exploration and perceptual-motor learning

Acta Psychologica 63 (1986) 263-280 North-Holland

263

SACCADIC EXPLORATION AND PERCEPTUAL-MOTOR LEARNING *

Peter WOLFF hvemty of Bielefeld, FRG

Accepted May 1986

A cognitive model of perceptual-motor learning by saccadic exploration is outlined. The model proceeds from the assumption that saccades are guided by anticipating their specific retinal change (intentional control of saccades). Perceptual-motor learning by saccadic exploration is described as the process of detecting the invariance which determines the relationship between efference and reafference.

Introduction

Perceptual learning

There is ample empirical evidence that geometrical optical illusions are reduced when the figure is inspected over a prolonged period of time (overview in Coren and Girgus 1978). Yet the illusions hardly diminish during steady fixation (e.g., Day 1962; Festinger et al. 1968; Coren and Hoenig 1972), or when saccades are prevented by other methods (e.g., Lewis 1908; Burnham 1968). Thus, illusion decrement appears to be a result of exploration by saccadic eye movements, and can be considered a case of perceptual learning by saccades, since the decrement depends on classical learning variables, e.g., spacing of trials (e.g., Mountjoy 1958), and accumulates over days and even weeks of practice (Girgus et al. 1975; Judd 1902).

Perceptual learning by saccades also occurs when a prism contact lens, which causes straight lines to appear curved, is attached to the

* I thank Dr. D.A. Owens, Dr. D. Graham, and Dr. W. Epstein for very valuable suggestions and comments.

Mailing address: P. Wolff, ZiF, Universitlt Bielefeld, Wellenberg 1, D-4800 Bielefeld 1, FRG.

OOOl-6918/86/$3.50 0 1986, Elsevier Science Publishers B.V. (North-Holland)

264 P. Wolff / Saccadic exploration

eye. As a result of saccadic exploration, the initially perceived distortion is reduced (Festinger et al. 1967; Slotnick 1969; Taylor 1962/1975; short summary in Wolff 1985, in press).

Motor learning

The magnitude of the geometrical optical illusions correlates with eye movement behavior: with the Mueller-Lyer illusion, e.g., perceptual overestimation of the ‘wing-out’ part corresponds to overshoots, perceptual underestimation of the ‘wing-in’ part corresponds to under- shoots (Festinger et al. 1968; Stratton 1906; Yarbus 1967), and the erroneous main saccades are followed by appropriate corrective movements (Festinger et al. 1968). When the illusion diminishes as a result of saccadic exploration, the saccades, too, come to match more pre- cisely the true spatial relationship within the figure (Festinger et al. 1968). Thus, illusion decrement is correlated with oculomotor adaptation.

With the contact lens paradigm, saccades will initially miss their targets, too, because the contact lens modifies not only the exafference, but (in contrast to prism glasses) also the saccadic reafference (Howard and Templeton 1966: 400 ff.; Taylor 1962/1975: 220 ff.; Wolff, in press). Unfortunately, eye’ movements have not been measured during exploration with the contact lens. Whether or not the saccades became progressively more accurate during perceptual adaptation, therefore, have not been studied. However, since perceptual adaptation typically seems to go with motor adaptation (Welch 1978), one might speculate that with ongoing practice in the contact lens paradigm oculomotor learning will also occur.

There are three alternative possibilities to explain why perceptual learning is accompanied by motor learning: either, perceptual learning results from motor learning (alternative a), or, motor learning results from perceptual learning (alternative b), or, both perceptual learning and motor learning are two aspects of one and the same process (alternative c).

In the present paper I argue that perceptual learning and motor learning reflect two sides of one and the same process of adaptation (alternative c) which fulfills the function of enabling the perceiver to control saccades by their perceptual outcome. Subsequently, a cognitive model of perceptual-motor learning by saccades is outlined. According

P. Wolff / Succadic exploration 265

to the model which is a modification of an earlier version (Wolff 1985, in press), perception is based on invariant properties of the efference-reafferene relationship.

Perceptual-motor learning

Motor theory

The view that perceptual learning results from motor learning (alternative a) has been presented historically in a variety of motor theories (overview in Scheerer 1984; Weimer 1977). According to this approach, the amplitude and direction of saccades which are needed to fixate objects and to explore the environment can be considered to constitute the perceptual space (e.g., Burnham 1968; Coren 1981; Festinger et al. 1968; 1967). However, there is clear evidence (summary in Wolff 1985, in press) that oculomotor learning can also occur without perceptual learning.

A particularly incisive refutation of motor theory was reported by Kohler (1951), although he did not study adaptation by saccadic exploration. Kohler tested the aftereffect of a subject who was fully adapted to half-prism glasses. Such glasses contain prisms in the upper half of each lens, but normal glass in the lower half. Through the half-prisms, the upper and lower parts of a vertical line, for example, appear to be shifted relative to another, In the post-test session after the adaptation period, the subject tracked a vertically moving luminous point in the dark. The lower half of the point’s path could be shifted relative to the upper one. The aftereffect was measured by the shift at which the subject perceived the point’s movement to be continuous. When the subject, whose head was fixed, tracked the point with the naked eye, the path’s lower half had to be shifted in the opposite direction to the prismatic shift which had been produced by the half-prisms in the upper part of the visual field during adaptation. Consequently, the subject, while tracking the point, executed a horizontal saccade at the center of the path. Nevertheless, the subject perceived the path’s lower part as continuation of the upper one, clear evidence that the motor properties of saccades are not equivalent to perceptual properties, as motor theory assumes.


Environment-specific invariances

If motor learning results from perceptual learning (alternative b), the latter must have a purely visual basis, i.e., saccadic exploration must reveal optical information which specifies the external display unequivocally (cf. G ibson 1966, 1968, 1979), and, thus, corrects misperception. Clearly, with the contact lens as well as with illusions, the retinal variation which is produced during saccadic exploration is systematic inasmuch as there are structural limitations which are not altered by saccades, and which correspond to the stable features of the display: a line in the retinal image, for example, always remains a line, however it is deformed during saccadic exploration, and is never transformed into a square. There are, however, several arguments against the view that perceptual learning is based on strictly sensory detection of such invariances (Wolff 1985). O f particular interest in the present context are the following two arguments:

First, if the retinal image is moved independently of the eye movements, i.e., if saccades and retinal change are experimentally decorre- lated, forms begin to disappear (Coren 1971; Coren and Porac 1974; Sharpe 1972), although invariant structures within the moving (e.g., rotating) retinal image are preserved. If one considers this dramatic change of perception as a special case of perceptual learning, it follows that perceptual learning does not result from the invariants of retinal change alone, but rather from the invariants of the relationship between saccades and retinal change.

Second, if the principle of detecting environment-specific information applies to the exploration during a prolonged period of time, it must also hold for a single saccade. O therwise, how can perceptual learning be initiated and proceed? It is well known, however, that the reafference of a single saccade does not necessarily reveal environment-specific information (cf. MacKay 1973): if the eye is prevented from moving, while the subject intends a saccade, a motion is perceived in the direction of the intended saccade, and, further, when the eye is mechanically rotated, while the subject intends fixating a target, the subject perceives a motion in the opposite direction to the passive eye movement (Brindley and Merton 1960; Helmholtz 1867; Skavenski et al. 1972). Thus, perception is strongly influenced by

P. Wolff / Saccadic exploration 261

efferent processes which control the extraocular muscles (Gibson 1950: 147; Mackay 1973; MacKay and Mittelstaedt 1974). It is hard to see, therefore, how perceptual learning can result from retinal information alone.

Function of perceptual-motor learning

According to the conclusions from the previous two sections, perceptual learning and motor learning are two aspects of one and the same process of adaptation (alternative c) which quite obviously is initiated because saccades are in error. The failures of saccades are not experienced on the basis of motor information, because in the above men- tioned experiments in perceptual learning (including the decorrelation studies) oculomotor processes were not impeded. From a motor point of view, saccades were successful, because the efferent commands to the extraocular muscles were actually realized. Consequently, de- termination of whether or not the saccades are successful is dependent exclusively on the saccades’ retinal effects.

Retinal feedback presupposes that the saccade’s retinal change had been determined in advance. Following the general principle that voluntary movements are guided by anticipating their intended result (e.g., Bernstein 1967; Greenwald 1970) the present view proceeds from the assumption that saccades are programmed by anticipating their retinal change, a fact which I call ‘intentional control’ (Wolff, in press). According to this view, saccades are utilized as a tool for producing the intended retinal change which was predetermined in the course of target selection. Adaptation starts when the eye movement misses the target, and thus intentional control is disrupted. Consequently, the function of perceptual-motor learning is to re-establish intentional control of saccades, i.e., to re-enable the perceiver to select a peripheral or parafoveal target, and to produce the retinal change necessary to fixate the target by the appropriate eye movement. Accordingly, saccadic exploration provides information about how the retinal stimulation can be varied by saccades.

A cognitive model

According to the findings cited above which show a strong influence of efferent processes on perception, retinal information is processed as


if the eye always behaved according to the efferent command, independently of the eye’s actual behavior. Thus, at every moment during saccadic exploration, there can be experienced no more and no less than the coincidence of efference and retinal change. Consequently, by saccadic exploration, the perceiver learns to manipulate retinal stimulation by efferent commands, i.e., the perceiver detects the law which determines the relationship between efference and retinal change. In order to see why such learning is reflected not only in motor adaptation, but also in perceptual adaptation, a simplified model is used. The simplification consists in the fact that both position and identity of environmental features or objects are characterized by one-dimensional continua. The same holds for position and identity of the retinal images of features or objects. Finally, saccades are illustrated as one-dimensional movements.

The model starts with a situation in which no perceptual world exists. Such condition may hold for congenitally blind people, when they begin to see after an operation (Von Senden 1931), or when they explore their surroundings with a sensory substitute (Bach-Y-Ma 1984).

Description of the model

Fig. 1 shows a frame over a line, the original line, which is shown in fig. 2. The frame contains a screen on which the line is projected by an optical device which deforms the vertical dimension of the original line, according to a projection algorithm. i The projected line is called the screen-line. The center row of the screen is in line with the optical axis, i.e., the point which becomes projected onto the screen’s center row coincides with the optical axis.

i In the present model, the projection algorithm is:

P=D’

D is the screen-centric distance of a point of the original line, i.e., the point’s vertical distance from the optical axis. P is the screen-position of a point on the projected line, i.e., the projected point’s vertical distance from the center row (which is in line with the optical axis). The type of projection algorithm is not essential for the model. The model would also work with an asymmetrical projection and/or with the optical axis not corresponding to the position of the center row. The only condition is that the projection algorithm remains stable.


Fig. 1. Movable screen in a frame over a line (the original line) whose projection on the screen (the screen-line) is shown in the figure. When the stick is tilt to the left or the right, the frame moves back and forth, and the screen-line deforms.

Fig. 2. Original line. (Concerning the marked locations A, B, and C, see figs. 3 and 4.)


-

- 5OOL

- ;

c3

Fig. 3. Screen-lines for different frame positions. A, B, and C represent the cases where the locations A, B, and C of the original line (see fig. 2) are projected on the center row.

The frame (with the screen and the optical device) can be moved vertically across the line by a motor. When the frame is moved, the screen-line deforms. Fig. 3 shows three different screen-lines, created when the frame takes three different positions (cf. fig. 2).

On the screen lives Perceptor who is sensitive to screen-line changes. Perceptor handles the steering stick (fig. 1) which is connected to the motor via servo-control. As soon as Perceptor tilts the stick to the left or the right, the motor guides the frame up or down across the original line. The amplitude of the frame’s movement depends on the duration with which Perceptor holds the stick tilt. Although Perceptor par- ticipates in the trip, he is unaware of the screen’s movement, because his sensory world consists only of what happens on the screen, when he handles the stick.

In the present model the frame represents the eye and the motor represents the extraocular muscles. The movement of the frame represents a saccade, and the original line represents the environment. The horizontal dimension of the original line stands for the identity of

P. Wolff / Succadic exploration 211

environmental features (or objects), and the vertical dimension for their spatial relations. Thus, each point of the original line characterizes an environmental feature at a certain relative location. That point of the original line which is projected onto the center row represents the fixation point, and the distance (D) of every point from the point projected on the center row represents their oculocentric direction.

The screen represents the retina and the center row the fovea. The projected screen-line characterizes the retinal image. The vertical positions of the screen-line points correspond to the retinal positions. The horizontal point positions correspond to the identity of retinal features. Thus, each point of the screen-line illustrates a certain stimulation at a certain retinal position. Different horizontal point positions within the center row, for example, stand for different stimulations at the fovea, created when different objects of the environment are fixated.

Perceptor represents the visual system whose efferences are sym- bolized by his steering-stick manipulations: the direction of the stick- operation (S) symbolizes the efferent component which determines the direction of the saccade, while the duration of the stick-operation (S) symbolizes the efferent component which determines the amplitude of the saccade. 2

Registering retinal change

The description of the law which determines the relationship between stick-operation and screen-line change depends upon how the screen-line changes are registered. In principle, the changes of the screen-line can be described in two ways, namely, either as vertical shifts of the screen-line points (between the screen-rows), or as horizontal shifts of the screen-line points (within the screen-rows). Described as vertical shifts, the screen-line changes are considered as positional shifts of features with constant identity. Described as horizontal shifts, the screen-line changes are considered as changes of features at constant positions.

The systematics between stick-operation and vertical shifts of the

’ The model simulates the fact that the amplitude of a saccade is determined by the duration of neural activity in a set of neurons, while the direction is presumably coded by which set is activated (Carpenter 1977).


screen-line points can be formalized. 3 Since the vertical shifts of the points are independent of their horizontal positions, the relationship between stick-operation and vertical shifts depends on the projection algorithm and does not depend on the frame’s relation to the original line. In contrast to this, the relationship between stick-operation and horizontal shifts cannot be formalized, since the horizontal shifts are independent of the vertical positions, and, therefore, independent of the projection algorithm. Rather, the horizontal shifts depend on the frame’s movement relative to the original line.

Applied to retinal stimulation, the reafference can be described either as positional shifts of retinal features which do not change identity (corresponds to the vertical shifts in the Perceptor model), or as variation of stimulation at constant retinal positions (corresponds to the horizontal shifts in the Perceptor model). On which of the two alternative descriptions must the model of perceptual-motor learning be based?

. In an ecological environment, and in most laboratory situations, environmental features (often objects) are repeated at different positions. Thus, different environmental sections do not necessarily differ in identity. Consequently, retinal features are repeated at different retinal positions. The Perceptor model illustrates that ecological condition by the fact that, with the original line as well as with the screen-line, several points share the same horizontal position. Vertical shifts of such screen-line points, however, which can be discriminated by nothing else than their vertical position, cannot be registered. Perceptor, therefore, cannot detect an invariance behind the screen-stick relationship, until he registers the screen-state changes as horizontal shifts at constant positions. Registering horizontal shifts is possible, because each screen-line point can be discriminated from each other by its screen-row.

Applied to retinal stimulation, saccadic reafference is not registered as positional shifts of retinal features or images whose identity remain

3 If the distance (D’) covered by the frame is a square function of the stick-operation’s duration (S), i.e., D’ = S’s (where s is either - 1 or + 1, depending on the stick-operation’s direction), the vertical-shifts systematics follows the function:

P:= (‘Ji;T-s’s)3-Pl.

P: is the vertical shift of a point at the initial screen position P,.


constant, i.e., as spatial deformation of the retinal image, but rather as changes of stimulation at constant retinal positions, i.e., as a change of the identity of retinal stimulation. The reason is that, typically, several retinal features are repeated at different retinal positions, and positional shifts of repeated retinal features cannot be registered.

Since the retinal positions are given by the receptive units, i.e., the receptors or the receptive fields, and since, further, from the visual system’s viewpoint, the possible changes of stimulation at each receptive unit are absolutely unrelated to the units’ spatial distances from another, i.e., unrelated to what is expressed by the term ‘retinal position’, I use the term ‘receptive unit’ instead of retinal position, henceforth. For, according to the present view, the retinal arrangement of the receptive units is not needed in perceptual-motor learning. The only condition is that the retinal arrangement of .the receptive units remains stable.

While the unity of each receptive unit preserves the temporal relations between changes which are produced at different moments, the difference between the receptive units allows for registering different changes simultaneously. In the Perceptor model the receptive units are illustrated by the screen-rows.

Relationship between efference and change of stimulation

Intentional control exists when the change of stimulation at every receptive unit can be controlled consistently by efferent commands. However, the method of changing stimulation by way of efferences differs for different receptive units, and, further, alters with every efferent command. The Perceptor model demonstrates that point as follows: the method of shifting a point horizontally by the stick at a certain row and at a given moment can be illustrated as a two-dimensional line (the ‘rule ‘) with the entries ‘horizontal point-position’ and ‘stick-operation’ (fig. 4). The rules depend, first, on how the frame can be moved by the stick, i.e., on the relationship between stick-operation and frame-movement. Second, the rules depend on which point of the original line is projected onto the corresponding screen-row, momentarily. Fig. 4 shows the rules when the original points A and C (marked in fig. 2) are projected on a reference screen-row, and when the distance (D’) covered by the frame is a square function of the stick-operation’s duration (S), i.e., D’ = S2s, where s is either - 1 or + 1 depending on the stick-operation’s direction (cf. fn. 3).

274 P. Wolff / Succadic exploration

T PCSITIO~ bt a reference screen row]

Fig. 4. Rule-lines at a given screen-row. A and C represent the cases where the locations A and C of the original line (see fig. 2) are projected on the reference screen-row.

Since, at a given moment, different rows represent different original points, and since further, at a given row, each stick-operation changes the projected original point, the rule, i.e., the method of shifting the point by the stick differs between the screen-rows, given a certain moment, and changes with every stick-operation at each screen-row.

Of course, all possible rules are related: how they differ between the screen-rows at a given moment and how they change at each screen-row, given a certain stick-operation, is determined by the same factors which determine the rules themselves, i.e., the original line and the relationship between stick-operation and frame-movement, in short, by how the frame can be moved with the stick relative to the original line. But how can the law of the relationship between stick-operation and screen-line changes be described from the cognitive viewpoint of Per- ceptor who does not know anything about the frame’s movement and the original line?


Invariance

The horizontal shifts, which coincide with a particular stick-operation are neither determined by their rows, nor by the initial horizontal point positions, nor by the combination of rows and initial point positions. In spite of this, each single coinciding shift is unequivocally determined, since each coincidence of stick-operation and shift (at each row) is reversible, and, therefore, can be repeated at different moments. The shift which coincides at a row does not change with time, and is very specific for each particular stick-operation.

Reversibility means that the single stick-shift coincidences which can be realized at different moments at each row, are determined by their mutual temporal relations: each coincidence depends on its temporal relations to all coincidences which are possible at that certain row.

However, it is not only the temporal relations of coincidences within the rows which are invariantly determined, but also the temporal relations between the rows. For, how the point at a given row can be shifted by the stick, depends upon how the points at all other rows can be shifted at the same time. In fact, Perceptor cannot avoid shifting all momentary points simultaneously by the same stick-operation. Gener- ally speaking, the temporal relations of coincidences between rows are invariantly determined, as well. Thus, from Perceptor’s point of view, each single coinciding shift is determined by its temporal relations to all shifts which can actually be produced by the stick. Thus, the entirety of all possible coincidences of stick-operation and horizontal shift, within the rows and between the rows, is invariantly determined by their temporal relations to one another.

From Perceptor’s point of view, the systematics behind the stick-shift relationship can only be described by the invariant temporal relations between all possible coincidences of stick-operation and horizontal shift. That means, at the same time, that all possible coincidences are qualitatively arranged in such a way that their arrangement describes each coinciding shift at each row every time. Fig. 5 illustrates that invariance, i.e., it represents all possible coincidences by their temporal relations to another.

The structure in fig. 5 represents Perceptor’s perceptual world, and describes completely all possible events on the screen and how to produce them with the stick. The relations between all possible coinci-


Fig. 5. Invariant distribution of all possible stick-point coincidences. The two-sided arrow shows how Perceptor moves through the structure, when he tilts the stick.

-1000

3- 500 0 05 z ~-100 g -50

w E

&

6 7 5; 2 +50 1 +I00 z r E >+500

+I000

Fig. 6. Correspondence between perceptual locations and screen-row positions.


dences must be described by related point locations which define a space through which Perceptor moves when he handles the stick. The same reality which in the reference system of the screen has to be described as stick-produced screen-line deformations is described in Perceptor’s perceptual world as free movements through a stable structure, which is the qualitative lay-out of all possible coincidences.

To detect that invariance, Perceptor does not need the vertical screen-row positions, although, of course, they are related to the locations within the invariant structure. From an external viewpoint from which the screen-state changes are described as spatial deformations (vertical shifts) in a resting reference-system (the screen), Percep- tor’s perceptual world might be described by the movement of a deformed reference-system. (fig. 6). However, that is not Perceptor’s point of view. He does not know anything about the vertical position. He merely detects the relations between all possible coincidences, i.e., he detects an invariant structure through which he moves freely.

As soon as Perceptor has acknowledged his screen-universe’s relativ- istic nature, he is able to control the screen-state by the stick, since every screen-line change which is possible momentarily is represented, together with the necessary stick-operation, as a perceptual location. Therefore, in order to change the screen-state in a specific way, Perceptor has merely to move to the appropriate location within his perceptual world, since moving within the perceptual world and changing the screen by the stick is one and the same event described from different cognitive positions (Wolff 1985, in press).

Concluding remarks

Applied to retinal stimulation, perceptual-motor learning means, recognizing how the relations between all possible coincidences of efference and retinal change at each receptive unit determine each other. The invariant lay-out of all possible coincidences defines the perceptual world 4 which, in turn, offers how the retinal state can be changed by efferent commands every time. The perceptual world is not a construction, inasmuch as it contains not more than what actually

’ Concerning the application of the present account to such cases of oculomotor learning which seem not to be accompanied by perceptual adaptation, see Wolff (in press).


occurs on the retinal surface during saccadic exploration (cf. Wolff 1985, in press). The perceptual world describes the invariantly arranged relations of all possible coincidences as they really are.

Although perceptual locations correspond to retinal positions, perceptual space is not produced by rectifying the retinal image. Retinal position is not needed at all. According to the present view, saccades can be controlled by intention if the saccades’ retinal changes which are offered as possibilities by the perceptual world can actually be produced. If so, perception is veridical, i.e., the perceptual world tallies with the environment (Wolff 1985, in press).

To the extent’ that the saccade’s retinal change can be determined in advance, saccades do not introduce new information. However, the coinciding change of the microstructure which is analyzed at the fovea1 area cannot be anticipated completely, since merely the global change at the fovea1 area is governed by the invariance to be detected (cf. Wolff 1984). The reason is that the retinal periphery analyzes the retinal image merely in terms of global features, so that only the relations between coincidences of efference and change of global retinal features can be recognized. From the viewpoint of’ the visual system, therefore, only the invariance which governs the reafferent change of global retinal features at every receptive unit (including the fovea1 area), can be detected. Saccades support local information. According to the present view, perceptual-motor learning enables selection of local information about an environmental section by using the section’s relative location as criterion, i.e., basis of selection (cf. Neumann, in press; Wolff 1977). For, since the relative locations of all environmental sections (or objects) to another are virtually ‘measured’ during saccadic exploration by the operations needed to change fixation from one section (or object) to another, the invariant lay-out of all possible coincidences will be identical with the actual lay-out of all possible fixation-points, i.e., with the relative locations of all possible environmental sections.

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saccadic exploration and perceptual-motor learning

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