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J Neurophysiol 97: 1068-1077, 2007. First published November 22, 2006; doi:10.1152/jn.00515.2006
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"Motor Oblique Effect": Perceptual Direction Discrimination and Pointing to Memorized Visual Targets Share the Same Preference for Cardinal Orientations

Nikolaos Smyrnis1,2, Asimakis Mantas1 and Ioannis Evdokimidis1

1Cognition and Action Group, Neurology Department and 2Psychiatry Department, National and Kapodistrian University of Athens, Eginition Hospital, Athens, Greece

Submitted 15 May 2006; accepted in final form 17 November 2006


 ABSTRACT
 
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
In previous studies we observed a pattern of systematic directional errors when humans pointed to memorized visual target locations in two-dimensional (2-D) space. This directional error was also observed in the initial direction of slow movements toward visual targets or movements to kinesthetically defined targets in 2-D space. In this study we used a perceptual experiment where subjects decide whether an arrow points in the direction of a visual target in 2-D space and observed a systematic distortion in direction discrimination known as the "oblique effect." More specifically, direction discrimination was better for cardinal directions than for oblique. We then used an equivalent measure of direction discrimination in a task where subjects pointed to memorized visual target locations and showed the presence of a motor oblique effect. We finally modeled the oblique effect in the perceptual and motor task using a quadratic function. The model successfully predicted the observed direction discrimination differences in both tasks and, furthermore, the parameter of the model that was related to the shape of the function was not different between the motor and the perceptual tasks. We conclude that a similarly distorted representation of target direction is present for memorized pointing movements and perceptual direction discrimination.


 INTRODUCTION
 
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
In previous studies we investigated the directional accuracy of planar pointing movements to visually presented targets using a memory-delay paradigm (Gourtzelidis et al. 2001Go; Smyrnis et al. 2000Go). We showed that when subjects pointed to the location of previously seen targets, a systematic directional error was observed that varied with target direction. This systematic directional error reflected a bias for movement endpoints to cluster toward the oblique directions between the cardinal axes. After excluding more trivial explanations for this error, relating to the mechanical properties of the arm (Smyrnis et al. 2000Go) we sought to explain this phenomenon as an effect of spatial working memory (Gourtzelidis et al. 2001Go). More specifically, we found that the same pattern of systematic directional errors was previously observed in a series of studies of spatial working memory where subjects had to memorize the location of a dot within a circle and then use a pen to draw the dot in an empty circle (Huttenlocher et al. 1991Go). A model provided to account for the pattern of errors in both direction and amplitude stated that these errors emerged from a strategy of subjects to categorize space, to help them memorize the spatial location of the targets. In a subsequent study (Theleritis et al. 2004Go) we investigated the space categorization hypothesis, using a modified version of the memory-pointing task. In this task subjects had to remember a series of target locations presented sequentially and then respond to a cue target, by moving to the next target in the previously presented series. Our hypothesis was that the increase in memory load in this task, as the number of targets to remember increased from two to four, would result in a more prominent space categorization effect and thus a larger systematic directional error. Surprisingly, however, we observed that the systematic directional error was the same for all memory loads. This result thus suggested that the space categorization strategy does not explain this phenomenon.

In another study de Graaf et al. (1991)Go instructed subjects to draw with a pen a line toward a visually presented target and proceed to do this very slowly. It was found that the initial movement direction, measured at the beginning of these slow pointing movements, consistently deviated from the target direction and the pattern of systematic directional errors that emerged was surprisingly identical to the one we observed in fast pointing movements performed in memory conditions. It was also found that the same systematic directional errors were observed when subjects used a pointer to point in the direction of a target in two-dimensional (2-D) space, suggesting that these errors might not be restricted to the execution of a movement. In a follow-up study de Graaf et al. (1994)Go showed that the same systematic directional errors were observed when targets were presented using kinesthetic instead of visual input. In a recent study of pointing movements, where the movement endpoints were defined by a passive positioning of the arm, in a location in 2-D space by a robot arm, Baud-Bovy and Viviani (2004)Go observed the same pattern of systematic directional errors. A similar systematic directional error pattern was observed when subjects used an isometric force manipulandum to produce force pulses to the direction of visually presented targets without feedback (Massey et al. 1991Go).

A common theme in all these studies is that the individual has to specify the direction of a target in 2-D space without the presence of feedback. In all these cases then, the same qualitatively systematic directional anisotropy emerges: a trend of subjects to direct their movements away from the cardinal and toward the oblique directions in 2-D space. What is the origin then of this systematic directional error observed in such diverse tasks both in terms of input (visual, kinesthetic), output (fast or slow movements, isometric forces, pointing with a pointer), and cognitive demands (memory movements, movements toward a visual target)?

In perception research there is a well-described phenomenon of direction anisotropy called the "oblique effect." This term has been used to codify the observed superiority in visual discrimination of the cardinal orientations as opposed to the oblique (Appelle 1972Go). The oblique effect was first demonstrated psychophysically by Jastrow in 1893. In these experiments subjects had to reproduce visually presented lines or had to set lines to predefined orientations. It was found that subjects performed better (were faster and more accurate) with horizontal and vertical as opposed to oblique lines. This effect in visual discrimination was observed not only for lines but for a series of visual stimuli that could be oriented. It was also not a particular characteristic of humans but it was observed in other mammals and even in much more primitive animals such as the octopus (see review by Appelle 1972Go). It was also shown that this effect in visual discrimination is already present in 6-wk-old infants (Leehey et al. 1975Go).

With respect to the origin of the oblique effect in visual discrimination, more trivial explanations such as eye movements, optical disorders, and various dioptric characteristics, as well as the composition of the retinal mosaic, were found to be inadequate (Appelle 1972Go). On the other hand, neurophysiological evidence suggested that at least some part of this perceptual phenomenon might rely on cortical mechanisms. Maffei and Campbell (1970)Go showed that the amplitude of the evoked potential for visually presented vertical and horizontal gratings was larger than that for oblique gratings. In a recent functional magnetic resonance imaging study it was also observed that the magnitude of the blood oxygenation level–dependent response in area V1 for horizontal and vertical lines was larger than that for oblique lines (Furmanski and Engel 2000Go). These findings led to the hypothesis that the oblique effect is related to low-level visual processing in primary visual cortex. In yet other studies that used haptically defined stimuli an oblique effect was also observed, in the sense that gravitationally defined horizontal and vertical axes were more accurately discriminated than oblique axes in blindfolded and blind adults and in blindfolded children (Gentaz and Hatwell 1995Go, 1998Go). In yet another study Gentaz and Streri (2004)Go found a haptic oblique effect in 5-mo-old infants. A theoretical framework (Essock 1980Go) to consider the wealth of these findings proposes the existence of two classes of oblique effect: a purely visual one (class 1) related to low-level visual processing in the primary visual cortex and a higher-level oblique effect relying on extraretinal cues (vestibular, kinesthetic, haptic) that extends to cognitive and memory processes (class 2). In a recent study Krukowski and Stone (2005)Go found an oblique effect in smooth eye pursuit.

In this study we will strive to establish a connection of the directional error pattern, observed in the pointing tasks described above, to the oblique effect in perception. We will first demonstrate theoretically how these two phenomena could be related. Let us assume that movements are made to neighboring targets and an observer has to use the distributions of endpoint directions to decide whether a particular endpoint is aimed at one target or its neighbor. In Fig. 1A we present the case where the observer would have to discriminate between a target T1 located at a cardinal direction (90°) and a neighbor target T2, as well as between T2 and a target T3 located at an oblique direction (45°). The light shaded areas around T1, T2, and T3 represent the spread of the distributions of movement endpoints around these targets, respectively (S1, S2, and S3), and the overlapping dark shaded area represents the part of the endpoint direction distributions where the observer would not be able to tell whether the movement would be toward T1 or T2. The pattern of systematic directional errors that we previously described would correspond to a shift of T2 to T2a as shown in Fig. 1B. The effect of this shift would be a smaller overlapping dark shaded area between T1 and T2. Thus the observer would be more certain in discriminating T1 from T2. At the same time though this shift of T2 would result in T2a being closer to target T3. Target T2 now shares a shaded area (dark) with target T3 and the observer would be less certain in discriminating T2 from T3. The end result then of the systematic directional error for a target T2 presented between a cardinal and an oblique direction would be better direction discrimination from the cardinal and worse direction discrimination from the oblique direction, which is the definition of an oblique effect. A similar pattern of anisotropy in direction discrimination for the observer would be produced if, instead of a shift in T2, the spread of movement endpoints would increase with increasing directional deviance from the cardinal direction and toward the oblique as shown in Fig. 1C. It is noted here that the two phenomena described in Fig. 1, B and C could theoretically be independent, canceling or adding to each other. In conclusion our theoretical analysis shows that the systematic directional error could indeed be related to differences in direction discrimination between cardinal and oblique directions, thus reflecting an oblique effect in pointing.


Figure 1
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FIG. 1. Graphic representation of origin of the motor oblique effect as described in the INTRODUCTION. Target T1 is presented at a cardinal direction (90°) and the spread of directions of movement endpoints around it is shown as S1 with a light shaded area target. Same presentation was used for targets T2, which is in between a cardinal and an oblique direction, and T3, which is at an oblique direction (45°) with corresponding spreads S2 and S3. Shaded areas in the 3 parts of the figure show the overlapping spread of movement endpoints, representing ambiguity in discrimination between neighboring targets. B: result on ambiguity of a shift in T2 direction (to location T2a). C: result of an increase in the spread of the distributions on ambiguity.

 
In what follows we use a perceptual task of direction discrimination, where subjects have to decide whether an arrow is pointing in the direction of a visually presented target, to demonstrate a perceptual oblique effect. We will then use a memory-pointing task to the same target locations, to provide evidence of a motor oblique effect with properties similar to those of the perceptual one. We will finally show that the motor oblique effect is the result of the systematic directional error pattern that we previously described for these movements.


 METHODS
 
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Subjects

Five healthy adults (age span: 28–38 yr, two men) participated in the memory-pointing (MP) experiment. Three of these subjects plus two new subjects (age span: 28–40 yr, two men) performed the arrow-pointing (AP) experiment. All participants were naïve to the purposes of this study and gave written informed consent for participation in the study after a detailed explanation of the experimental procedures. The experimental protocol was approved by the Eginitio Hospital Scientific and Ethics Committee. All participants were right handed and performed the tasks using their preferred right hand.

Setup and procedure for the AP experiment

Subjects sat comfortably in front of a computer monitor (CM630ET, 32.8 cm horizontal x 24.5 cm vertical; Hitachi) at a distance of about 60 cm. The amplitude of the target stimuli was 6 cm from the center target and thus the degrees of visual angle for all stimuli were 5.7°. The subjects used two fingers of their right hand to press the left or right arrow key on the computer keyboard. Each trial started when a filled red disk (diameter: 5 mm) appeared at the center of the screen (center target). After a variable period of 1–2 s, a second white filled disk (diameter: 5 mm), the peripheral target, appeared at the circumference of an imaginary circle of 6-cm radius in one of 32 directions (11.25° intervals) and a yellow arrow appeared, originating at the center target that was either aligned with the target (50% of cases) or deviating 2.5° away from the target either clockwise (25% of cases) or counterclockwise (25% of cases). The subject was instructed to use the right or left arrow key of the keyboard to respond either "yes" if the arrow and the target had the same direction or "no" if the arrow direction deviated from the target direction. The arrow length varied among four values (15, 30, 45, and 60 mm).

Each subject performed one experimental session every day for 6 days. In each session the subject performed four repetitions for every arrow length, for every target direction in a randomized sequence, for a total of 512 trials (4 repetitions x 4 arrow lengths x 32 target directions). The total number of trials for each subject was 6 x 512 = 3,072.

Data processing for AP

We excluded trials where the latency of the arrow key press was <80 or >5,000 ms. After application of these exclusion criteria we retained 15,335 of the 15,360 trials for all subjects (99.8%).

We then computed a d-prime score for each target direction, each arrow length, and each subject as follows. The total numbers of responses for one subject, one arrow length, and one target direction were grouped in four categories as indicated in Table 1. The correct detection of the same direction of arrow and target was defined as a hit. The probability of a hit was then

Formula 1(1)
The false detection of the same direction of arrow and target was defined as a false alarm. The probability of a false alarm was thus

Formula 2(2)
The P(Hit) and P(FalseAlarm) were then transformed to z-scores and finally the d-prime, denoted as dap throughout, was computed

Formula 3(3)
According to the arrow length we computed dap15 (arrow length = 15 mm), dap30 (arrow length = 30 mm), dap45 (arrow length = 45 mm), and dap60 (arrow length = 60 mm).


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TABLE 1. Grouping of responses in the AP task

 
Setup and procedure for the MP experiment

Subjects sat in a darkened room and faced a wooden rectangular board covered with black paper. A digitizer tablet (Calcomp 2000) was laying beneath this wooden board and a mouse device that the subject grasped, using the right arm. The tablet height was adjusted at waist level for each subject. A liquid crystal display projector (TDP-140, Toshiba) was fixed on the room ceiling facing down at the wooden board. Visual stimuli and a cursor indicating the mouse position were produced by a PC computer program (using Delphi 7.0) and projected onto the black paper surface on the board (40 cm horizontally x 30 cm), while the subject moved the mouse on the digitizer tablet below. Although the subject's head was not fixed the distance of the subject's eyes from the board was about 60 cm and the amplitude of the stimuli was 6 cm from the center target; thus the degrees of visual angle were 5.7, as in the AP experiment. The mouse position was sampled at 100 Hz and was displayed on the board surface as a 2.5-mm-diameter round white cursor. The ratio of arm movement to the cursor movement was 1.0.

Each subject performed trials of two tasks: a visual-pointing and a memory-pointing (MP) task. Each trial started when a filled red disk (diameter: 5 mm) appeared at the center of the screen (center target) and the subject moved the cursor in the center target. After a variable period of 1–2 s, a second white filled disk (diameter: 5 mm), the peripheral target, appeared at the circumference of an imaginary circle of 60-mm radius in one of 32 directions (11.25° intervals). In the visual-pointing task the center target was turned off simultaneously, indicating to the subject to move the mouse-controlled cursor as accurately as possible to the peripheral target. In the MP task the peripheral target remained lit for 300 ms and, after a delay period of 3 s, the center target was turned off. This was the signal for the subject to move to the position of the previously shown peripheral target, by performing a single pointing movement. Herein we discuss the results from the analysis of the directional error, at the end of the movement trajectory, for the MP task only. In the visual-pointing task the error at the end of the movement trajectory was zero by definition because the subject was required to place the cursor on the visible target. The directional error at various points in the trajectory for the two tasks, before the end of the movement, will be discussed in a companion paper. The subject in both tasks was instructed to hold the cursor at the target position for 2 s. Then the center target was turned on again, to signal to the subject to move to the center for the beginning of the next trial. Subjects were instructed to maintain head and trunk in an upright position during task execution and to use only shoulder and elbow movements to move the mouse (no wrist or finger movements). No special equipment was used for stabilizing the trunk or head, although one of the authors was standing behind a participant giving instructions whenever the subject tended to change posture or use wrist or finger movements to perform the task.

Each subject performed one experimental session every day for 6 days (except from one subject who did not complete the first-day session, missing seven trials in the visual pointing task and 22 trials in the MP task). Within each session four repetitions were performed for every target direction for every task; thus in all 256 trials were performed in a randomized sequence (4 repetitions x 32 directions x 2 tasks). Every subject (except the one mentioned above) therefore performed a total of 256 x 6 = 1,536 trials of which 768 were of the MP task.

Data processing for MP

The sampled X–Y position data from the digitizer were transformed to the location of the feedback cursor on the screen. Although the digitizer had a spatial resolution of 0.01 mm the smallest movement that could be visualized as a cursor movement on the screen was 0.3 mm (one pixel). We chose to use X–Y movement data of the cursor at the screen (lowest movement detected 0.3 mm) to calculate the direction and amplitude of the movement. The same X–Y data were also used to calculate the instantaneous speed of the cursor by numeric differentiation. This speed was literally zero when the subject was waiting at the center target because very small movements of the arm that were <0.3 mm did not result in cursor movement. An interactive program (programmed in Delphi 7.0) was used to compute and visualize the instantaneous speed trace, to compute the movement onset (rise of instantaneous speed >0 for three consecutive measurements = 30 ms), and the end of the first movement (return of instantaneous speed to zero and remaining zero for ≥100 ms).

The cursor X–Y position at each point within each trial trajectory was transformed to conventional polar coordinates (direction and amplitude) with the origin at the center target. The directional error (DE) was the polar angular difference (in degrees) of a particular point in the movement trajectory minus the peripheral target. A counterclockwise deviation from the peripheral target was defined as positive DE. The amplitude error (AE) was a measure of the difference (in millimeters) of the amplitude at a particular point in the movement trajectory minus the amplitude of the peripheral target that was set to 60 mm. Thus a negative AE corresponded to target undershoot and a positive AE corresponded to a target overshoot. The DE was computed at five points along the movement trajectory: when the amplitude was 15, 30, and 45 mm from the center target and at the end of the first movement. Herein we will discuss only the results for the DE of the first-movement endpoint. The AE was measured at the end of the first movement.

We excluded from further analysis trials where the subject moved before the go signal and trials where the movement started earlier than 80 ms (anticipations) or later than 1,500 ms, after turning off the center target (late onset of movement). We also excluded trials in which the DE was >22.5° or < –22.5° at any one of the five points in the trajectory where it was measured. Finally, we excluded trials where the AE for the first movement was < –15 or >15 mm. After application of these exclusion criteria we retained 3,036 of the 3,818 trials for all subjects (86.6%).

The direction of the first-movement endpoint in the MP experiment was used to measure the following variables for each subject and each target direction:

  1. )Gain (g)
    Gain is a measure of the rate with which the direction of movement varies for different target directions and shows whether the directional space for movement endpoint direction is expanded or contracted with respect to the target directional space (see also Krukowski and Stone 2005Go). Figure 2 presents how this measure is derived. The figure plots the mean direction of movement endpoints on the Y-axis (output) versus the direction of the target on the X-axis (input). We called gain for target direction n, the slope of the best fitting regression line for movement endpoints at the two neighbor targets n – 1, n + 1, and target n. This line is given by the equation

    Formula 4(4)
    In the hypothetical case of no anisotropy between target and movement direction (black filled squares in Fig. 2), the gain for target n is 1 (black solid line). Thus in this case the movement directional space in the vicinity of target direction n is neither expanded nor contracted. In the case where the movement endpoints for neighbor target directions are shifted away from target n (open circles in Fig. 2), the gain will be >1 (dotted line in Fig. 2). Thus the directional space for movement endpoints in the vicinity of target n is expanded (larger output difference for the same input difference). Finally, in the case where the movement endpoints for the neighbor target directions are shifted toward n (filled triangles in Fig. 2), the gain will be <1 (dashed line). Thus the directional space for movement endpoints in the vicinity of target n will be contracted. Note that if directional space is expanded in one region (gain >1) then it is obligatory that directional space will be contracted in another neighboring region (gain <1); thus the mean gain for all directions around the total directional space of 360° must be equal to 1. One value of gain was computed for each target direction for each subject.

  2. )SD of DE (s)
    To measure the spread of the distribution of DE for each target direction we calculated the SD of the mean DE for movement endpoints, for each target direction, for each subject.
  3. )d-prime (dmp)
    In Fig. 1 we showed that the differences in mean direction and the SD of direction for movement endpoints around a specific direction define how well another target direction, in the vicinity of this target, would be discriminated.
    If a target would be set to 2.5° away from a particular target direction used in our experiment (i.e., the directional offset of the arrow in the AP experiment described above), then we can compute a z-score representing how many SDs away is this angular difference of 2.5° from the target direction. This score is equivalent to the d-prime computed for the same directional difference of 2.5° in the AP experiment. We will denote this d-prime for the MP experiment as dmps throughout. Thus

    Formula 5(5)
    where dmps is the z-score for discriminating a target at a 2.5° deviation from the mean direction of movement endpoints for the particular target direction and s is the SD of DE for this target direction.
    As we explained in the previous section in our definition of the gain measure, the discrimination of a target at 2.5° deviation from the mean direction of movement for this target will also be affected by the gain in the vicinity of the target. A gain >1 would result in a shift of this hypothetical target away from the mean that would be equal to gain x 2.5, thus resulting in a better discrimination. If we take into account the gain in the vicinity of each target direction then

    Formula 6(6)
    The discrimination then of a hypothetical target at 2.5° away from a target direction will increase with increasing gain and decrease with decreasing variability of movement endpoint directions.
    If the variance of movement endpoints remains the same independent of target direction and there are only mean endpoint shifts as shown in Fig. 1B then the differences in discrimination will depend only on the differences in gain for different target directions. To derive a d-prime measure that is independent of differences in s for different target directions we computed the mean s for all target directions pooled together that was 3.5°. We then derive the following d-prime

    Formula 7(7)
    Note that this last measure of discrimination is actually the gain multiplied by a constant thus one could directly use the gain for statistical analysis, although we sought to have equivalent measures of d-prime in our AP and MP tasks to directly compare them in our modeling.


Figure 2
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FIG. 2. Determination of gain for target direction n using the mean direction of movement endpoints at n, n – 1, and n + 1. Three cases are shown. In the first case (filled squares and solid line) the mean direction of movement endpoints for n, n – 1, and n + 1 equals n, n – 1, and n + 1, respectively; thus the gain is 1. In the second case (open circles and dotted line) the mean direction of movement endpoints for n – 1 is smaller than n – 1 and for n + 1 is larger than n + 1; thus the gain is >1. Finally, in the last case (open triangles and dashed line) the mean direction of movement endpoints for n – 1 is greater than n – 1 and for n + 1 is smaller than n + 1; thus the gain is <1.

 
Data analysis

For the analysis of each variable of interest in the AP and MP tasks the data for each target direction were regrouped to correspond to a particular directional deviance from a cardinal direction within each one of eight hemiquadrants as shown in Fig. 3. Every target direction corresponds to one of five directional deviances away from the cardinal direction within each hemiquadrant: 0° (corresponding to the cardinal direction), 11.25, 22.5, 37.75, and 45° (corresponding to the oblique direction). Notice that in this regrouping of data, the values corresponding to 0° (cardinal) and 45° (oblique) direction of each quadrant are represented twice (Fig. 3).


Figure 3
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FIG. 3. Regrouping of data for each target direction to the corresponding directional deviance from a cardinal direction. Each target direction (line) corresponds to one of 8 hemiquadrants depicted with the Latin number that the line points to. Arabic number corresponds to the directional deviance (in degrees) of this target direction from the cardinal direction for this hemiquadrant. In the case of a target direction that corresponds to a cardinal (0°) or oblique (45°) direction, 2 Latin numbers are shown corresponding to the 2 hemiquadrants that share this cardinal or oblique direction.

 
The directional deviance and arrow length were introduced as within-subject repeated-measure factors in repeated-measures ANOVA. A separate repeated-measures ANOVA with directional deviance as the only within-subject factor was then used to test the effect of directional deviance separately on dap15, dap30, and dap45 in the AP task. The same repeated-measures ANOVA model was used to test the effects of directional deviance on g, s, dmp, dmpg, and dmps in the MP task.

In another analysis a second-degree polynomial was used to model the effects of directional deviance on each of the following variables: dmp, dmps, dmpg, dap15, dap30, and dap45. We used the nonlinear estimation module of the STATISTICA 6.0 software (StatSoft 1994–2001) to fit the polynomial to our data and estimate the linear and quadratic parameters of the model and their significance. The module uses the Gauss–Newton method for solving the nonlinear least-squares problem. In general, this method makes use of the Jacobian matrix J of first-order derivatives of a function F to find the vector of parameter values x that minimizes the residual sums of squares (sum of squared deviations of predicted values from observed values).

For all statistical analyses we used the STATISTICA 6.0 software.


 RESULTS
 
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
AP task

Figure 4, AC shows the modulation of dap15, dap30, and dap45, respectively, with target direction. It can be seen that d-prime increases for cardinal directions and decreases for the oblique—a phenomenon that is present for all subjects. Thus all subjects were more accurate at discriminating a 2.5° deviation of the arrow from a cardinal direction and less accurate at discriminating this deviation from an oblique direction reproducing an oblique effect. A comparison of the figures also shows that discrimination efficiency (higher d-prime scores) increases with increasing arrow length, as expected (e.g., the values of dap45 are generally higher than those for dap30 and in turn the values for dap30 are higher than those for dap15).


Figure 4
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FIG. 4. A: plot of d-prime scores for each target direction for arrow length of 15 mm in the arrow-pointing (AP) experiment (dap15). Large solid circles represent the mean score for each target direction for the 5 subjects; small open circles represent the scores of individual subjects. B and C: d-prime scores for each target direction are plotted for arrow lengths of 30 (dap30) and 45 mm (dap45), respectively.

 
A repeated-measures ANOVA confirmed a significant effect of directional deviance [F(4,140) = 48.613, P < 10–5] and arrow length [F(3,105) = 16.3, P < 10–5] on dap. The directional deviance by arrow length interaction was highly significant [F(12,420) = 252.3, P < 10–5]. The subject x directional deviance interaction was not significant [F(16,140) = 1.53, P = 0.09] and the subject x arrow length interaction was also not significant [F(12,105) = 0.55, P = 0.87]. Finally, the three-way interaction subject x directional deviance x arrow length was also not significant [F(48,420) = 1.13, P = 0.26].

We then analyzed separately the effect of direction deviance on dap for each arrow length. A repeated-measures ANOVA confirmed a significant effect of directional deviance on dap15 [F(4,140) = 52.8, P < 10–5], dap30 [F(4,140) = 42.28, P < 10–5], and dap45 [F(4,140) = 18.24, P < 10–5], whereas the subject x directional deviance interaction was not significant in all cases. Finally, there was no significant directional deviance effect for dap60, as expected. In Fig. 6A the effect of directional deviance on dap15, dap30, and dap45 is presented. A clear oblique effect is present for the small arrows (15 and 30 mm), whereas for the 45 mm arrow it is less clear.


Figure 6
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FIG. 6. A: plot of the d-prime variation with directional deviance in AP. Squares, circles, and triangles represent mean d-prime for arrow lengths of 15 mm (dap15), 30 mm (dap30), and 45 mm (dap45), respectively (error bars: SE). Solid dashed and dotted lines represent the model fit for d-prime for arrow lengths of 15, 30, and 45 mm, respectively. B: plot of the d-prime variation with directional deviance in MP. Squares represent the mean d-prime (dmp), the circles represent the gain component of d-prime (dmpg), and the triangles represent the variance component (dmps) in the MP task, respectively (error bars: SE). Solid, dashed, and dotted lines represent the model fit for dmp, dmpg, and dmps, respectively.

 
In conclusion this analysis showed the existence of a perceptual oblique effect in the AP task for all subjects that is modulated by arrow length.

MP task

Figure 5A shows the modulation of mean DE for each subject and the mean for all subjects for each target direction. The variation of mean DE produced a pattern similar to that described in our previous work (Gourtzelidis et al. 2002; Smyrnis et al. 2001). Figure 5B shows the modulation of gain for each subject and the mean for all subjects for each target direction. It can be seen that the gain is generally higher in the cardinal target directions (0, 90, 180, and 270°) compared with the oblique. The repeated-measures ANOVA showed a significant effect of directional deviance [F(4,140) = 54.1, P < 10–5] and a nonsignificant subject x directional deviance interaction [F(16,140) = 1.1, P = 0.35].


Figure 5
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FIG. 5. A: plot of mean directional error for each target direction in the memory-pointing (MP) experiment. Large solid circles represent the mean directional error (DE) for each target direction for the 5 subjects; small open circles represent the mean DE of individual subjects. B, C, and D: the gain, SD of directional error (s), and d-prime (dmp) for each target direction in the MP experiment.

 
Figure 5C shows the modulation of s for each subject and the mean for all subjects for each target direction. There is a difference in s with target direction but the expected decrease of s for cardinal directions compared with the oblique is not present in all directional space. The repeated-measures ANOVA showed a significant effect of directional deviance [F(4,140) = 3.8, P < 0.006] and a nonsignificant subject x directional deviance interaction [F(16,140) = 1.4, P = 0.14].

Figure 5D shows the modulation of dmp for each subject and the mean for all subjects for each target direction. A pattern similar to that for the d-prime in the AP task can be observed: that dmp was larger in the cardinal directions and smaller in the oblique, representing an oblique effect. Figure 6B shows the modulation of dmp with direction deviance and again the oblique effect is evident. The repeated-measures ANOVA of dmp showed a significant effect of directional deviance [F(4,140) = 13.8, P < 10–5] and a nonsignificant subject x directional deviance interaction [F(16,140) = 1, P = 0.46].

In conclusion this analysis showed a significant effect of directional deviance from the cardinal directions for gain, directional variance, and the d-prime in the MP task. An oblique effect was evident in the case of d-prime for the MP task.

Modeling of the oblique effect in AP and MP

Figure 6A shows the effect of directional deviance on the d-prime measures in the AP task and Fig. 6B shows the effect of directional deviance on the d-prime measures for the MP task. A steep decrease of d-prime close to the cardinal direction and then a plateau close to the oblique direction can be observed in most cases. A function that describes this decrease is a second-order polynomial of the form

Formula 8(8)
Coefficient a is related to the mean level of direction discrimination (d-prime). Coefficient b is related to the magnitude of the oblique effect, that is, how large is the decrease in d-prime between the cardinal and the oblique direction. The third coefficient c is related to the changes in the rate with which the d-prime decreases with deviance away from the cardinal direction. From Fig. 6, A and B it is obvious that not only the mean level of direction discrimination but also the magnitude of the oblique effect differ between the AP and MP tasks, although the rate of decrease of the d-prime is rather constant such that the d-prime decrease reaches a plateau at roughly halfway between the cardinal and oblique directions (at 22.5° of direction deviance). This observation indicated to us that maybe what is very similar in both tasks is the relation between the linear component b and the quadratic component c in Eq. 8. That is, the larger the difference in d-prime between cardinal and oblique directions, the steeper the decrease in d-prime away from the cardinal, so that the shape of the oblique effect function will scale with the magnitude of the oblique effect. Thus we hypothesized that the ratio of c to b is constant

Formula 9(9)
By substituting c in Eq. 8 we attain the final model that we tested

Formula 10(10)
The data for all subjects for each one of the d-prime measures were pooled for this analysis because the ANOVA analysis showed no differences among subjects of the directional deviance effect (nonsignificant interaction of directional deviance with the subject). The results are shown in Table 2 and the resulting model fits are shown for AP in Fig. 6A and for MP in Fig. 6B. It can be seen from Table 2 that for both dap15 and dap30 all model coefficients were significant, whereas for dap45 only coefficient a was significant, indicating that in this case the coefficients b and r were not significantly different from zero and the model in Eq. 10 could be reduced to

Formula 11(11)


View this table:
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TABLE 2. Modeling of the oblique effect in AP and MP tasks

 
In the case of the MP task we tested the model on dmp, dmps, and dmpg (see METHODS). Table 2 shows that for dmp and dmpg all model coefficients were significant, whereas for dmps the model could again be reduced to Eq. 11.

Figure 7, A, B, C shows a comparison of the constant a, linear b, and ratio r coefficients for dmp, dmpg, dap15, dap30, and dap45. The bars denote 95% confidence intervals for these coefficients. It can be seen in Fig. 7A that the constant a differed in all tasks and the 95% confidence intervals did not overlap. The linear coefficient b (Fig. 7B) differed between the AP and MP tasks, whereas it was similar for the two small arrow lengths in the AP task (dap15 and dap30) where the 95% confidence intervals overlapped. There was no linear coefficient for dap45 because the model in that case was reduced to Eq. 11 as previously described. Finally the ratio coefficient r (Fig. 7C) was very similar for dap15, dap30, and dmpg and smaller for dmp but with overlapping 95% confidence intervals. There was no ratio coefficient for dap45.


Figure 7
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FIG. 7. Histograms comparing the model coefficients for the d-prime of the MP task (dmp), the gain component of d-prime of the MP task (dmpg), the d-prime for the arrow length of 15 mm of the AP task (dap15), the d-prime for the arrow length of 30 mm of the AP task (dap30), and the d-prime for the arrow length of 45 mm of the AP task (dap45). A: comparison for the model constant a. B: comparison for the linear component b (absolute value). C: comparison for the ratio factor r (absolute value).

 
We thus conclude that a quadratic function can be used to describe the oblique effect in both the AP and MP tasks. Furthermore, in the MP task the predicted oblique effect by the model was not present when the d-prime computation did not take into account the effect of gain (dmps) but was present when the computation of d-prime was based solely on the variations of gain (dmpg). The oblique effect was smaller in magnitude in the MP task than that in the AP task. Finally, we showed that the shape of the oblique effect function normalized for the overall magnitude of the oblique effect (coefficient r in the model) was similar for the AP and MP tasks; that is, the oblique effect diminished as the deviance from cardinal direction increased to reach a plateau halfway between the cardinal and oblique direction.


 DISCUSSION
 
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
We argued in the INTRODUCTION that the pattern of systematic directional errors that we observed in this and previous studies is theoretically equivalent to a better directional discrimination for targets presented around the cardinal directions as opposed to targets presented around the oblique direction, a phenomenon known in perception research as the oblique effect. To provide evidence for this argument we first used a task that required a perceptual discrimination of direction and observed a perceptual oblique effect that was very robust and did not vary significantly among subjects. We then used a memory-pointing task and demonstrated the presence of a motor oblique effect that was also very robust and did not vary significantly among subjects. We successfully modeled the oblique effect using a quadratic function in both tasks. We also showed that, although the perceptual oblique effect was larger in magnitude than the motor one, the shape of the oblique effect function, normalized for its overall magnitude, was similar for the AP and MP tasks. More specifically, the oblique effect in both tasks diminished as the deviance from cardinal direction increased, to reach a plateau halfway between the cardinal and oblique directions.

We could argue that an oblique effect in the memorized motor representation of target direction could be the result of a shared reference frame between visual perception and memory movement. The existence of the motor oblique effect could be explained using two alternative hypotheses that are not mutually excusive. The first hypothesis is that the direction representation in the motor system itself produces an oblique effect. This would imply—in analogy with the visual system—more neurons coding for cardinal directions than for oblique. This hypothesis does not seem to fit with current knowledge on direction specificity in the motor areas. Georgopoulos and colleagues (1988)Go showed in the monkey primary motor cortex that directionally tuned neurons are homogeneously distributed with no underrepresented areas of directional space. There is the possibility, though, that other motor areas that are more related to visual processing would have a larger neural representation for cardinal directions compared with the oblique. Such an area, for example, could be the ventral premotor cortex where Schwartz et al. (2004)Go showed that neurons respond to the perceived and not the actual trajectory of an arm movement. Still we believe that the oblique effect in memory movements is not the result of an anisotropic neural representation of direction in the motor system. The main argument against this hypothesis is that we do not find a significant oblique effect in the variance of directional error in memory movements. If more neurons would be encoding the cardinal directions compared with the oblique then we would expect that the coding for these directions would be less noisy, thus resulting in less variable directional error. Still this hypothesis needs to be rigorously tested in future neurophysiological experiments.

The alternative hypothesis is that the oblique effect in the motor system originates in the perceptual system. An anisotropic perceptual representation of directional space is thus transferred to the motor system. In a recent study Krukowski and Stone (2005)Go measured how well subjects discriminated the direction of a moving target when this deviated from a cardinal direction compared with an oblique direction while subjects followed the moving target with smooth eye pursuit movements. The authors, by transforming the direction of smooth eye pursuit into a binary decision to match the perceptual decision, showed that both the perceptual discrimination of target motion and the discrimination based on smooth eye pursuit shared the same qualitatively oblique effect, that is, a better discrimination for cardinal than for oblique directions. This result is very similar to our finding of a shared oblique effect in a memory-pointing task and a perceptual decision task (the arrow-pointing task). Krukowski and Stone (2005)Go furthermore decomposed the oblique effect in smooth eye pursuit in two components: one related to changes in the variance of pursuit direction between cardinal and oblique directions of target motion and one related to changes in the gain. In striking resemblance to our results they observed that the oblique effect in smooth eye pursuit was the result of a modulation in gain and not variance. We also observed that our model of the oblique effect in the AP and MP tasks was successful when the d-prime in the MP task was computed based only on the gain variations with direction but was not successful when the d-prime was computed based only on the variance variations with direction. It is interesting to note here the very close similarity of the shape factor of the model for the oblique effect based on gain variations (dmpg) and the perceptual oblique effect (see Fig. 7C). In their study Krukowski and Stone (2005)Go postulate that an anisotropic visual representation of direction is transferred to motion processing areas in the brain. Our findings suggest that this representation might also be transferred to arm-movement–related areas of the brain.

We could further refine the hypothesis of a similar representation of directional space between perceptual and motor systems and ask whether the perceptual oblique effect that is transferred to the motor representation in memory movements is a class 1 or class 2 effect. A class 1 oblique effect suggests a distorted representation of visual space produced in primary visual cortex that is reflected later on in all visuomotor transformations. However, this hypothesis cannot explain the findings of Baud-Baudry and Viviani (2004)Go, that is, the presence of the same pattern of directional errors, suggesting the presence of the same motor oblique effect, in a motor task where subjects had to move their arm to a position that was instructed by a prior passive movement of the arm. In fact the presence of the same oblique effect in smooth eye pursuit, memory pointing with visual input, and pointing with kinesthetic input suggests that a class 2 oblique effect contaminates eye and arm movement in all these conditions.

A prominent theory on the dissociation of ventral and dorsal streams proposes an anatomical and functional segregation between vision for perception and vision for action (Goodale and Milner 1992Go). In this view the representation of visual space in the dorsal stream involves accurate representations of spatial locations based on egocentric frames of reference that are used to guide movements of the eye and arm. On the other hand, the representation of visual space in the ventral stream involves relative representations of spatial locations that are prone to the effects of visual illusions—and are thus inaccurate—and use allocentric reference frames. These representations are used to detect objects in the visual world, categorize them, and attribute abstract properties to them such as a name. This theory would then predict that perceptual phenomena would not contaminate the space representation for visuomotor processing. In this study we have evidence for such a contamination by the oblique effect in specification of the direction of memory-pointing movements. Is this result against the theory? In a refinement of the action–perception dissociation Goodale and Westwood (2004)Go propose that this dissociation is present only when reaching and grasping of objects is performed in real time. When delays are introduced in reaching and grasping the memory trace of the object that is used is more related to the ventral perceptual stream. This memory representation then is prone to perceptual phenomena such as visual illusions, whereas the representation for reaching and grasping under visual guidance is not (Goodale and Westwood 2004Go; Goodale et al. 2003Go; Hu and Goodale 2000Go). In accordance with this theory we observed that the memory representation of target direction is affected by a perceptual distortion—the oblique effect. The prediction of this theory then would be that this oblique effect would not be present in the programming and execution of direct pointing movements to a visual target. We will fully investigate this hypothesis in a later study.

In conclusion we showed that memory-pointing movements and visual perception share an oblique effect in direction discrimination that is reflected in a distorted representation of directional space, implying similarity in the processing of directional information in these conditions.


 GRANTS
 
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
This work was partly supported by the "Kapodistrias 2004–2005" program of research support from the National and Kapodistrian University of Athens.


 FOOTNOTES
 
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Address for reprint requests and other correspondence: N. Smyrnis, Psychiatry Dept., National University of Athens, Eginition Hospital, 72 Vas. Sofias Ave., Athens, GR-11528, Greece (E-mail: smyrnis{at}med.uoa.gr)


 REFERENCES
 
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Appelle S. Perception and discrimination as a function of stimulus orientation: the "oblique effect" in man and animals. Psychol Bull 78: 266–278, 1972.[CrossRef][Web of Science][Medline]

Baud-Bovy G, Viviani P. Amplitude and direction errors in kinesthetic pointing. Exp Brain Res 157: 197–214, 2004.[CrossRef][Web of Science][Medline]

de Graaf G, JB, Sitting AC, Denier van der Gon JJ. Misdirections in slow goal-directed arm movements and pointer-setting tasks. Exp Brain Res 84: 434–438, 1991.[Web of Science][Medline]

de Graaf G, JB, Sitting AC, Denier van der Gon JJ. Misdirections in slow, goal-directed arm movements are not primarily visually based. Exp Brain Res 99: 464–472, 1994.[Web of Science][Medline]

Essock EA. The oblique effect of stimulus identification considered with respect to two classes of oblique effects. Perception 9: 37–46, 1980.[Web of Science][Medline]

Furmanski CS, Engel SA. An oblique effect in human primary visual cortex. Nat Neurosci 3: 535–536, 2000.[CrossRef][Web of Science][Medline]

Gentaz E, Hatwell Y. The haptic "oblique effect" in children's and adults' perception of orientation. Perception 24: 631–646, 1995.[Web of Science][Medline]

Gentaz E, Hatwell Y. The haptic oblique effect in the perception of rod orientation by blind adults. Percept Psychophys 60: 157–160, 1998.[Web of Science][Medline]

Gentaz E, Streri A. An "oblique effect" in infant's haptic representation of spatial orientations. J Cogn Neurosci 16: 1–7, 2004.[CrossRef][Web of Science][Medline]

Georgopoulos AP, Kettner RE, Schwartz AB. Primate motor cortex and free arm movements to visual targets in three-dimensional space. II. Coding of the direction of movement by a neuronal population. J Neurosci 8: 2928–2937, 1988.[Abstract]

Goodale MA, Milner AD. Separate visual pathways for perception and action. Trends Neurosci 15: 20–25, 1992.[CrossRef][Web of Science][Medline]

Goodale MA, Westwood DA. An evolving view of duplex vision: separate but interacting cortical pathways for perception and action. Curr Opin Neurobiol 14: 203–211, 2004.[CrossRef][Web of Science][Medline]

Goodale MA, Westwood DA, Milner AD. Two distinct modes of control for object-directed action. Prog Brain Res 144: 131–144, 2003.[Web of Science]

Gourtzelidis P, Smyrnis N, Evdokimidis I, Balogh A. Systematic errors of planar arm movements provide evidence for space categorization of multiple frames of reference. Exp Brain Res 139: 59–69, 2001.[CrossRef][Web of Science][Medline]

Hu Y, Goodale MA. Grasping after a delay shifts size-scaling from absolute to relative metrics. J Cogn Neurosci 12: 856–868, 2000.[CrossRef][Web of Science][Medline]

Huttenlocher J, Hedges LV, Duncan S. Categories and particulars: prototype effects in estimating spatial location. Psychol Rev 98: 352–376, 1991.[CrossRef][Web of Science][Medline]

Jastrow J. On the judgment of angles and positions of lines. Am J Psychol 5: 214–248, 1893.[CrossRef]

Krukowski AE, Stone LS. Expansion of direction space around the cardinal axes revealed by smooth pursuit eye movements. Neuron 45: 315–323, 2005.[CrossRef][Web of Science][Medline]

Leehey S, Moskowitz-Cook A, Brill S, Held R. Orientational anisotropy in infant vision. Science 190: 900–902, 1975.[Abstract/Free Full Text]

Maffei L, Campbell FW. Neurophysiological localization of the vertical and horizontal visual coordinates in man. Science 167: 386–387, 1970.[Abstract/Free Full Text]

Massey JT, Drake RA, Georgopoulos AP. Cognitive spatial-motor processes. 5. Specification of the direction of visually guided isometric forces in two-dimensional space: time course of information transmitted and effect of constant force bias. Exp Brain Res 83: 446–452, 1991.[Web of Science][Medline]

Schwartz AB, Moran DW, Reina GA. Differential representation of perception and action in the frontal cortex. Science 303: 380–383, 2004.[Abstract/Free Full Text]

Smyrnis N, Gourtzelidis P, Evdokimidis I. Systematic directional error in 2-D arm movements increases with increasing delay between visual target presentation and movement execution. Exp Brain Res 131: 111–120, 2000.[CrossRef][Web of Science][Medline]

Theleritis C, Smyrnis N, Mantas A, Evdokimidis I. The effects of increasing memory load on the directional accuracy of pointing movements to remembered targets. Exp Brain Res 157: 518–525, 2004.[CrossRef][Web of Science][Medline]




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