330 Motor Control
object can be described in terms of a vector. The length
of the vector corresponds to the distance from the reference to
the object; for egocentric location the reference is a point be-
tween the eyes (thecyclopean eye), and for allocentric location
it is another object in the visual field. The direction is usually
specified by angles both in a reference plane and orthogonal to
it, but for the following its specification is of little importance.
The available data suggest that both egocentric and allocentric
localizations are used in the visual specification of targets.
Which one dominates seems to depend on task characteristics.
Figure 12.10 shows a well-known optical illusion, the
Müller-Lyer illusion. Although the length of the shaft is the
same in both figures, it appears longer in the figure with out-
going fins than in the figure with ingoing fins. Elliott and Lee
(1995) used one of the intersections as the start position and
the other intersection as the target position for aimed move-
ments. Corresponding to the difference in perceived distance
between the intersections in the two figures, movement am-
plitudes were longer with outgoing fins than with ingoing
fins (cf. Gentilucci, Chiefi, Daprati, Saetti, & Toni, 1996). In
contrast to this result, Mack, Heuer, Villardi, and Chambers
(1985) found no effect or only a very small effect of the
illusion on pointing responses.
Perhaps the critical difference to the study of Elliott and
Lee (1995) was that the participants in the study of Mack
et al. (1985) pointed not from one intersection to the other,
but from a start position in their lap to one or the other of the
two intersections. The difference between the two tasks sug-
gests that the movements were based on allocentric (visual
distance) and egocentric (visual location) information, re-
spectively. In fact, when psychophysical judgments of the
length of the shaft are replaced by judgments of the positions
of the intersections, the illusion also disappears (Gillam &
Chambers, 1985). Thus, although physically a distance is
the difference between two positions on a line, this is not
necessarily true for perceived distances and positions. This
distinction between perception of location and perception of
distance matches a distinction between different types of pa-
rameters for motor control structures, namely target positions
versus distances (cf. Bock & Arnold, 1993; Nougier et al.,
1996; Vindras & Viviani, 1998).
Specification of spatial targets in terms of distances
implies a kind of relative reference system for a single
movement: Wherever it starts, this position constitutes the
origin. A visually registered distance (and direction) is then
used to specify a movement in terms of distance (and direc-
tion) from the start position. This way of specifying move-
ment characteristics has a straightforward consequence:
Spatial errors should propagate across a sequence of move-
ments. In contrast, with a fixed reference system as implied
by the specification of target locations in terms of (egocen-
tric) positions, spatial errors should not propagate. In studies
based on this principle, Bock and Eckmiller (1986) and Bock
and Arnold (1993) provided evidence for relative reference
systems, that is, for amplitude specifications. The movements
they studied were pointing movements with the invisible
hand to a series of visual targets. However, Bock and Arnold
also noted that error propagation was less than perfect. Heuer
and Sangals (1998) used different analytical procedures, but
these were based on the same principle of error propagation
or the lack thereof. As would be expected, when only ampli-
tudes and directions were indicated to the subjects, only a rel-
ative reference system was used. However, when sequences
of target positions were shown, there was some influence of a
fixed reference system, although the movements were per-
formed on a digitizer and thus displaced from the target
presentation in a manner similar to the way a computer
mouse is used.
Gordon, Ghilardi, and Ghez (1994) provided evidence for
a reference system with the origin in the start position based
on a different rationale, again with a task in which targets
were presented on a monitor and movements were performed
on a digitizer. Targets were located on circles around the start
position. The distribution of end-positions of movements to a
single target typically has an elliptical shape. Under the as-
sumption that the target position is specified in terms of di-
rection and distance from the origin of the reference system,
the axes of the elliptical error distributions, determined by
principal component analysis, should be oriented in a partic-
ular way: The axes (one from each endpoint distribution)
should cross in the origin. It turned out that the long axes of
the error ellipses all pointed to the start position, as shown
in Figure 12.11. Corresponding findings were reported by
Vindras and Viviani (1998), who kept the target position con-
stant but varied the start position.
Amplitude specifications allow accurate movements even
when visual space and proprioceptive-motor space are not
precisely aligned. Specifically, they do not require absolute
calibration, but only relative calibration: It must be possible
to map distances correctly from one space to another, but not
positions. Of course, without absolute calibration, move-
ments may drift away from that region of space where the
targets are, as is typical with the use of a computer mouse.
Without proprioception it seems that absolute calibration is
essentially missing. In the case of the deafferented patientFigure 12.10 The Müller-Lyer illusion.