Nonrigid illusory motion in depth induced by translational motion of static images.

A new nonrigid motion illusion is presented based on patterns of aligned nonparallel line segments undergoing apparent motion. The illusory effect can be explained by the mismatch in local orientation segments that signals local rotational motion contradictory to the global translational motion.

We report a new nonrigid motion illusion elicited by the translational motion of a static stimulus that may be based on the misperception of the trajectories of converging lines. One of the best examples is shown in figure 1.

Figure 1.

The central building appears to move nonrigidly when the entire figure is scrolled up and down.

When observers gaze at points on the near corner of the central building (indicated by an arrow) during an up-and-down translation of the image[(1)] up and down on a computer screen. To get the strongest impression of this illusion we recommend readers to drag the vertical scroll bar slider up and down with a mouse, rather than scrolling via the mouse wheel. The animations are also available online (see text for details). they perceive a nonrigid transformation of the central building, unlike other parts of the scene. An animated version of figure 1 can be viewed in movie 1 (or see http://rci.rutgers.edu/sungho4/movie1.mov). When the whole scene is moving up the near corner of the central building wiggles down, and vice versa. The novelty in this illusion is that the nonrigid transformation is experienced in 3-dimensional (3D) depth, rather than on the picture plane, making the 3D percept that is generated in the static image by the perspective projection even stronger. The illusion is persistent despite the knowledge of the physical implausibility of a nonrigidly moving building.

Apparently, the lines of the building floors joining at the near corner—and converging at vanishing points on the horizon—seem to be related to the illusory nonrigid motion, because the rightmost small five-story building with nearly parallel floor lines appears to be rigidly translated up and down. One can argue that this illusory nonrigid 3D motion might be attributed to perspective projection. Some retinal projections of 3D objects introduce shape distortions that result in illusory percepts of false 3D shape (eg Griffiths and Zaidi 1998, 2000). Let us imagine that an observer is right in front of the near corner of the central building in a real scene during an earthquake that shakes the Earth up and down. The physical vertical displacement would be the same for all points in the scene; but, because of motion parallax, the retinal displacement of points on the near corner would be larger than far parts of the central building. By contrast, for an up-and-down translation of the 2-dimensional (2D) image in this illusion the retinal vertical displacements of all points are the same. Thus, when the whole 2D scene moves upward, points on the near corner move at the same retinal speed as points away from the corner, whereas they would move faster for a 3D scene; this difference might cause the near corner to appear to wiggle down, as confirmed by viewers of the illusion.

Figure 2a is a line drawing version of the building projected in two-point perspective. Figure 2b is a control variant where corner angles are made invisible by a gap, and figure 2c presents a version where line segments form a concave angle in 3D depth. An animated version of figure 2 can be viewed in http://i-perception.perceptionweb.com/misc/i02/i0434_s2.mov movie 2 (or see http://rci.rutgers.edu/sungho4/movie2.mov). The perspective projection explanation seems unlikely because nonrigid 3D motion is shown not only in figure 2a but also in figures 2b and 2c where the line pattern loses the 3D shape of convex corner angles. One difference among these figures is that nonrigid motion is likely to be perceived in 3D depth in figures 2a and 2c but not as strongly in figure 2b. To examine whether the nonrigid motion contributes to an enhanced 3D percept we asked sixteen naive observers to judge the strength of their 3D percept for both static and dynamic versions of each stimulus in figure 1 and figure 2. As shown in figure 3, translational motion increased significantly the appearance of a 3D percept as compared with a static image (p < 0.05 for each paired t-test), except for the stimulus in which the corner angles were deleted by a gap (p > 0.1).

Figure 2.

(a) Line drawing version of the central building in figure 1 where perspective projection induces illusory percept of a convex 3-dimensional (3D) corner; (b) control version of line arrays where a 3D interpretation is less likely due to the deletion of corner angles by a gap; (c) same as in (a) but for a concave 3D corner.

Figure 3.

Three-dimensional (3D) percept rating (range 1–7) by sixteen naive observers for both static and moving displays of a convex angle (figure 2a), hidden convex angle (figure 2b), concave angle (figure 2c), and real scene (figure 1). The rating of 1 (minimum 3D percept) was illustrated by simple parallel horizontal lines moving up and down; the rating 7 (strongest 3D percept) was illustrated by an animation sequence of a smoothly rotating 3D cube that gave a strong impression of a solid 3D object. Error bars represent ± one standard error. n.s. = nonsignificant; * statistically significant differences, p < 0.05.

These demonstrations suggest that the nonrigid illusory motion is related to a low-level motion correspondence process, rather than to the 3D interpretation of 2D pictures, similar to the aliasing experienced in the classical wagon-wheel effect. In complex shapes or patterns the mismatch between the global and local motion signals leads to an apparent loss of shape rigidity and deformation of the global pattern (Anstis 2003; Cohen et al 2010; Fantoni and Pinna 2008; Gori et al 2010). In the present illusion there are mismatches between line segments of different orientations across frames, which result in local rotational motion even though the physical trajectory of each line segment is purely translational. In figures 1, 2a, and 2c, because two columns of line segments are connected and form corners, their simultaneous rotation is more likely to be perceived in 3D depth than on a 2D plane, which results in a nonrigid deformation of the 3D surface.

Figure 4.

(a) As the image is translated up and down, it appears that two gears, coupled by a chain, rotate in opposite directions; (b) rainbow-colored version of figure 4a (see text for details).

If the nonrigid motion is based on illusory rotational apparent motion of line segments, it should be stronger for an image comprising a radial pattern of line segments; this is precisely the case shown in figure 4a and http://i-perception.perceptionweb.com/misc/i02/i0434_s3.mov movie 3 (or see http://rci.rutgers.edu/sungho4/movie3.mov). When the image in figure 4 moves up and down spoke line segments rotate in the opposite direction to the global motion, giving the impression that two gears, coupled by a chain, rotate in opposite directions (clockwise and counterclockwise); it must be pointed out that this figure does not produce a 3D percept. Figure 4b (see http://i-perception.perceptionweb.com/misc/i02/i0434_s4.mov movie 4 or http://rci.rutgers.edu/sungho4/movie4.mov) was suggested by Stuart Anstis, and it is a variant of figure 4a; each line segment (spoke) is painted with the same rainbow color in each frame of the animation sequence, yet the animation elicits the percept of moving spokes that are accompanied by color changes. This suggests that the visual system does not track each line segment correctly but solves the motion correspondence problem by pairing “nearest neighbors” (Ullman 1979), producing featural (orientation and color) mismatches.

The illusions presented here provide an interesting case of illusory nonrigid motion induced by patterns of converging line segments undergoing translational apparent motion, where the mismatch between global and local motion signals results in illusory rotation of the microstructure of line orientations.