The purpose of this study was to determine whether the Muller-Lyer ill
usion is produced by a mechanism which uses information defined in the
retinal coordinates, or by a mechanism taking into account the three-
dimensional (3-D) shape of the illusion figure. The classical Muller-L
yer figure could not be used to address this question since it is two-
dimensional. Three-dimensional Muller-Lyer figures were created to see
if the illusion they produce is correlated with the shape of the proj
ected retinal image, or with the shape of these figures defined in a 3
-D coordinate frame. In the experiments retinal image shape was juxtap
osed against the 3-D shape of the illusion displays. For some displays
the direction in which the fins pointed, relative to the shafts, in t
he 3-D frame was the 'opposite' of the direction in which they pointed
in the retinal images. For such displays, the illusion predicted on t
he basis of the 3-D structure was the opposite of that predicted on th
e basis of retinal image shapes. For another 3-D display the fins were
oriented such that each projected a single straight line in the retin
al image, thus the typical retinal image (< >, > <) was replaced by st
raight lines (\ \, \ \). For all the displays the observed illusion wa
s consistent with how the fins were oriented relative to the shaft in
the 3-D coordinate frame, ie with the 3-D shape of the illusion displa
ys. The retinal image shape appeared to play little, if any, role. One
conclusion that emerges is that the specific retinal image shape proj
ected by the classical line-drawn pattern is neither necessary nor suf
ficient for producing the illusion. The present findings are inconsist
ent with two well known theories of the Muller-Lyer illusion: inapprop
riate constancy scaling and selective filtering.