 
Summary: 1 Introduction
An ellipse rotating rigidly in the image plane may be perceived in at least three different
ways (Musatti 1924; Wallach et al 1956; Vallortigara et al 1988). Sometimes, the veridi
cal rigid rotation is perceived but two other `illusory' motions can be seen as well. The
ellipse may be perceived as deforming nonrigidly in the image plane, as if it were made of
rubber. Alternatively, the ellipse may be perceived as executing a rigid motion in depth,
as if it were a coin twisting in 3D.
Wallach et al (1956) and Hildreth (1983) have pointed out that these additional
percepts should not really be called `illusions'öthey are interpretations that are fully
consistent with the retinal input. Since the ellipse is bounded by a smooth contour, there
exists an infinite number of velocity fields that would generate the same retinal sequence.
In accordance with the wellknown aperture problem (Wallach 1935; Marr and Ullman
1981; Hildreth 1983), at any point along the contour the local motion information is
consistent with an infinite number of possible motions (figure 1a). Graphically, this
ambiguity corresponds to a `constraint line' in velocity space (Adelson and Movshon
1982; Nakayama and Silverman 1988a) (see figure 1b). To illustrate this ambiguity,
figure 2 shows velocity fields that have been computed analytically such that they are
consistent with the local constraint lines of a rotating ellipse. Figures 2a and 2c show the
rotational velocity fields for ellipses of two aspect ratio, and figures 2b and 2d show
the deforming normal flow; at every location the flow is perpendicular to the contour
