# Pinna illusion

Curator and Contributors

1.00 - Baingio Pinna

## Pinna illusion

Figure 1: The Pinna Illusion

Pinna illusion is the first visual illusion showing a rotating motion effect. In Figure 1 the squares, delineated by two white and two black edges each, are grouped by proximity in two concentric rings. All the squares have the same width, length, and orientation in relation to the center of their circular arrangements. The two rings differ only in the relative position of their narrow black and white edges forming the vertexes. More precisely, the two rings show reversal of the vertex orientation and, consequently, opposite inclination of the virtual or implicit diagonal orientation polarity obtained by joining the two vertexes where black and white lines meet (Pinna, 1990; Pinna & Brelstaff, 2000).

When the observer’s head is slowly moved towards the figure with the gaze fixed in the center, the inner ring of the squares appears to rotate counter-clockwise and the outer ring clockwise. The direction of rotation is reversed when the observer moves away from the figure, the same squares of the inner ring appear to rotate clockwise, while those of the outer ring rotate counter-clockwise. The apparent motion is perceived instantaneously and in a direction perpendicular to the true motion. The speed of the resultant illusory motion appears to be proportional to that of the motion imparted by the observer. Figure 2 simulates the action of moving towards and away from the figure by physically expanding and contracting the pattern shown in Figure 1. The two concentric rings of squares now appear to counter-rotate when the gaze is fixed on the center and the observer is stationary. When the same figure is physically rotated clockwise, the inner ring appears to contract and the outer one appears to expand (Figure 3). The opposite effects are perceived when the figure is rotated counter-clockwise.

 Figure 2: When the two concentric rings of squares physically expand and contract, they appear to counter-rotate when the gaze is fixed on the center.
 Figure 3: When the two concentric rings of squares physically rotate clockwise, the inner ring appears to contract and the outer one appears to expand.

## Phenomenology of the Pinna illusion

### The role of peripheral vision

The apparent rotation is typically perceived in peripheral vision. The looming in and out of Figure 1, with the gaze fixed not on the center but on any square, destroys the counter-rotation effect and the fixed square appears motionless. This is because motion detectors in the fovea are not sensitive to this type of stimulus pattern. Furthermore, with peripheral viewing the precise spatial square form of the pattern elements ought to be blurred and the dominant motion cues ought to derive, not from the constituent line sections, but from the entire elements (see Figure 10).

### Reversing implicit diagonals

By reversing the implicit diagonal polarity, rendered by the internal organization of luminance, the perceived rotation reverses accordingly (Figure 4). This result demonstrates that it is the difference in slant of the implicit diagonals of the squares that provides the directional cues for biasing the global motion vector thus affecting the perceived motion direction.

Figure 4: When the polarity of the elements is reversed, the direction of apparent rotation reverses.

### Misaligning implicit diagonals

The apparent rotation does not require that the stimulus components be accurately aligned. When the squares are randomly shuffled and arranged approximately in concentric circles the apparent rotation persists (Figure 5). Therefore, the organization of the squares does not imply oriented Fourier components that may serve as a secondary feature to the motion system.

Figure 5: When the elements are misaligned, the illusion persists.

This result suggests that apparent motion is individually assigned to each square, depending on the relative location of the black and white edges. Afterwards, the perceptual segregation of the counter-rotation components into a central circular cluster within an irregular circular surround, not present in the stationary stimulus, requires perceptual grouping of the two populations of squares according to the Gestalt principle of common fate. (Through the paper, the Gestalt principles are not considered as explanations of the reported illusions but as directions of the neural integration processes occurring among local motion vectors. The neural questions underlying these principles, are “how are single-neuron signals transformed and elaborated by successive levels of processing?” and “how are different processing levels and areas represented in large-scale patterns of neural activity?”)

### Alternating implicit diagonals

In the previous figures, the principle of common fate is synergistic with other principles like good continuation or relative position (inside vs. outside). In fact, the two implicit orientation polarities are organized circularly at different radii and then placed in different locations of the stimulus: one inside and the other outside. As a consequence, the squares with the same implicit orientation polarity are grouped in the smoothest continuation. By alternating the orientation polarity of the squares within each ring and, therefore by breaking the direction and the good continuation of the individual assignment of motion, the illusory counter-rotation is nulled Figure 6a. A similar result is obtained by alternating the orientation polarity of two squares, one included in the other and arranged in two rings (Figure 6b; to find this figure, click on the blue right-pointing triangle below Figure 6a).

These nulling effects demonstrate the action of mutual inhibition of opposite orientation polarities and imply long-range interactions of motion vectors and of the grouping of input signals that belong to the same global direction. In Figure 6c, while the single squares maintain their alternated orientation polarities from the outside to the inside of the figure as in Figure 1, the grouping of the squares by proximity is not concentrically (as in Figure 1) but radially oriented (Pinna & Gregory, 2009). Due to the radial grouping, the counter rotating effect is reduced, and a waving or twisting global motion through the radial grouping now appears.

### Implicit vs. explicit diagonals

Two kinds of orientation cues, instilling “polarity” to the basic square elements, can be distinguished in the previous figures: (i) The orientation of the squares themselves – explicit orientation; and (ii) the orientation of the invisible base of the vertex – implicit orientation. In Figure 7, the explicit orientation (tilt) of the squares can be either synergistically summed (Figure 7a) or pitted against (subtracted to) the implicit orientation (Figure 7b). By moving the eye towards or away from the figure with the gaze fixed in the center, the effect of counter-rotation of Figure 1 can be either increased or decreased as in Figure 7a and Figure 7b, respectively.

 Figure 6: (a) When the orientation polarity of the squares within each ring alternates, the illusion is destroyed. (b) (to find this and other versions of this figure, click on the blue right-pointing triangle) When each square is surrounded by an opposite-polarity square, the illusion is destroyed. (c) When the elements are arranged more radially than concentrically, the counter rotating effect is reduced, and a waving or twisting global motion through the radial grouping appears.
 Figure 7

### Apparent motion from asymmetric luminance profile

Another directional cue for biasing motion vectors is the asymmetric luminance profile. In Figure 8a, when the eye is moved towards the figure with the gaze fixed in the center, the inner ring of squares appears to rotate counter-clockwise and the outer ring rotates in a clockwise direction. However, when the eye is moved away from the figure, the squares of the inner and outer rings appear to rotate barely (or not at all) clockwise and counter-clockwise, respectively, as expected from Figure 1 (Pinna & Spillmann, 2002a). There is a clear asymmetry in the strength of the apparent rotation in moving toward or away from the figure. This result depends on the asymmetric luminance profile (the black bars, the dark grey within each square, the white bars and the light grey background) that represents a strong directional bias and a different kind of explicit polarity in the direction of the minimum luminance intensity change (i.e., in the direction of the white bars). This cue is the basis of the staircase illusion (Fraser & Wilcox, 1979) and of the peripheral drift illusion (Faubert & Herbert, 1999; see also Kitaoka & Ashida, 2003). In the same way as the explicit orientation of the squares, shown in Figure 7, can be synergistically summed or subtracted to the implicit orientation, the result of Figure 8a depends on the summation (when the eye is moved toward the stimulus) and the subtraction (when the eye is moved away) of the asymmetric luminance profile from the implicit orientation. In Figure 8b, the summation/subtraction effect produces the effect of counter-clockwise rotation and expansion alternated in a loop with clockwise rotation and contraction.

### Alternating implicit diagonals in rows and columns

In Figure 1, the illusion is elicited by an optical flow field corresponding to radial expansion or contraction. However, it can also be produced by a translation of the stimulus, i.e., by a parallel vector field. In Figure 9a-b, apparent sliding motion arises in a pattern of square elements arranged in rows and columns on a grey background (cf. Pinna 1990). In Figure 9a, by alternating the black and white edges of the squares from one column to the other and from the bottom-half to the top-half of the pattern and by keeping the gaze fixed on the horizontally moving dot, sliding motion is perceived in the perpendicular direction: the columns of squares appear to move up and down alternately (vertical inter-column shearing motion). (In order to perceive consistent sliding motion effects it is necessary to track the black target carefully. Once the gaze strays off the target, the sliding effect is lost.) Apparent dynamic convergence and divergence of the columns is also perceived. The loss of parallelism occurs in a direction opposite to the Zöllner illusion (1860). In Figure 9b, as one follows the vertically moving dot with one’s gaze, the columns of squares appear to alternately move left and right (inter-column expansion and contraction) and to converge and diverge. In Figure 9c, by keeping the gaze fixed on the diagonally moving dot, the apparent motion is strongly reduced or nulled. The role of the Gestalt factor of common fate is demonstrated in Figure 9d where, by examining the figure without fixating a particular point, a central cluster immediately segregates from the irregular surround and appears as floating before the background. When tracking the moving target, a cluster of squares sliding together in the same plane as the other squares are perceived. These results demonstrate that the difference in slant of the implicit diagonals provides the directional cues for biasing the global motion vector (Gurnsey et al., 2002; Morgan, 2002; Pinna & Brelstaff, 2000; Pinna & Spillmann, 2005).

 Figure 8
 Figure 9

## Neural mechanisms underlying the Pinna illusion

The important points useful to explain this illusion are the following: (i) the micropatterns have oriented low-frequency components, (ii) these engage low-level direction selective mechanisms, which (iii) are subject to the aperture problem. The implicit orientation polarity in the micropatterns (i.e., the low frequency luminance gradients) and not the black and white edges (i.e., the high-frequency components), is the basic attribute underlying this illusion. The notion of implicit orientation suggests that the illusion can be explained in terms of orthogonal biases (Grossberg, Mingolla & Viswanathan, 2001; Gurnsey & Pagé, 2006; Gurnsey et al., 2002; Mather, 2000; Pinna & Brelstaff, 2000; Pinna & Spillmann, 2005), on the basis of which the visual system produces an interpretation of image flow biased towards the strongest velocities perpendicular to the two-dimensional contours in the image. In Figure 10-left, the two bottom micropatterns show a blurred version of the two above. Under these conditions the high frequencies have been removed from the micropatterns. By translating the micropatterns to the right, they will most strongly stimulate neurons selective for the directions indicated by the white arrows. This bias can be considered to occur when the process of optical flow estimation is contaminated by spatiotemporal noise (Fermüler & Malm, 2004; Fermüller, Pless & Aloimonos, 2000; Weiss & Fleet, 2002; Weiss, Simoncelli & Adelson, 2002). More precisely, the interpretation of the motion effect depends on a step where image features such as lines, intersections of lines, black and white edges like those of Figure 1 and local image movement are derived.

Figure 10: Modified from Gurnsey & Pagé, 2006

These features contain many sources of noise or uncertainty that can cause bias. As a result, the locations of features are perceived erroneously and the appearance of the patterns is altered. Thus, the estimated flow vectors of Figure 1 are biased in the clockwise and in the counterclockwise directions as can be perceived in the outer and inner ring. The role of low-frequency luminance gradients is demonstrated by replacing the micropatterns with Gabor patches (Bayerl & Neumann, 2002; Gurnsey & Pagé, 2006; Gurnsey et al., 2002; Morgan, 2002). In this case, the strength of the illusion persists or is even enhanced (see Figure 10-right). Gurnsey et al. (2002) demonstrated that the strength of the illusion depends on the number of Gabor patches in the display, their wavelengths, and the orientation diﬀerence between adjacent micropatterns in the inner and outer rings. The illusion can be explained by the response of direction-selective neurons at the earliest cortical stage of visual processing, i.e., area V1. These neurons can signal the speed with which a line of its preferred orientation moves through its receptive field. This constraint may be considered as akin to the aperture effect (cf. Nakayama & Silverman, 1988) by which a moving straight line seen through an aperture can be perceived to move only along the direction of its normal. While this seems to explain how individual square elements receive a local illusory motion signal, the illusory rotational motion can be thought to be sensed by the higher cortical area such as MT (medium scale motion analysis, inhibition of opponent directions) and dorsal MST (MSTd – large scale motion analysis, directional decomposition) which collates all the signals provided by the local motion micropatterns. An FMRI study of the illusion showed activation of the motion specific complex hMT+ in addition to the V1/V2 areas to be involved in the perception of the illusion (Budnik et al., 2006).

## New phenomena related to the Pinna illusion and originated by implicit orientations

### The illusory tilted squares

In Figure 11a, when viewed peripherally, alternating implicit diagonals, organized in columns, produce tilt distortions in the same direction as the implicit diagonal of each square; the squares appear distorted like rhombic shapes. The illusory tilt can also be perceived by slowly moving the gaze along the columns. In Figure 11b, the rhombic distortion can be seen in the two global concentric square shapes made up of small squares with black and white edges.

### Illusory intertwining and spiral effect

Consequences of the illusory convergence and divergence (loss of parallelism) of Figure 9a-b are manifest in the two effects illustrated in Figure 12a-b, where the concentric circles, made up of squares, appear (a) intertwined when the implicit diagonals are alternated among the circles or (b) like a spiral when all the implicit polarities have the same orientation. The two effects rotate in opposite (clockwise vs. counter-clockwise) directions when the orientation polarities are explicit as illustrated in Figure 12c-d (Pinna & Gregory, 2002).

 Figure 11
 Figure 12

## From the Pinna illusion to new effects of apparent motion: On the complex role of directional biases

### Sliding motion from local and global explicit orientations: the Ouchi illusion and variations

The previous figures demonstrate the role of implicit orientations and, then, of directional biases in eliciting apparent motion and other illusory effects. Explicit orientations produce motion as demonstrated in the well known Ouchi illusion (1977, first shown by Spillmann et al., 1993), where a disk-shaped inner region and an annular surround, made up from black and white rectangles oriented at right angles, produce an apparent sliding motion of the disk when the stimulus is moved or shaken. Pinna (1990) described independently a variation of the Ouchi illusion (Figure 13a) in which a disk and an annulus are comprised of horizontally and vertically parallel zigzag lines instead of rectangular checks. It is worthwhile noticing that the zigzagging lines in the disk and the annulus have the same line segments within each wiggle with local orientations of 45 and 135 deg, respectively. The only difference is in the global orientation. Figure 13b shows that apparent sliding can be elicited when the rectangles in the two inset and surrounding regions of the Ouchi pattern are replaced by rectangles with the same orientation but phase-shifted (Pinna & Spillmann, 2002a, 2002b). By keeping the gaze fixed on the upwards moving dot, the inner disk appears to move up although the offset terminators move down and vice versa when the dot moves down. Some deformation of the circumference of the disk is also perceived during the apparent translation. This effect is different from the previous ones and may require an explanation involving motion biases from offset discontinuities and whole shapes that represent new classes of directional bias.

 Figure 13

### The accordion illusion

Explicit orientations can produce motion even if they are not at right angles as in the Ouchi illusion and, differently from all the previous conditions, even if there is only one specific explicit orientation not phase-shifted. In Figure 14a, when the eye is moved towards the figure and away from it with the gaze fixed on the central dot, the checkerboard, made up of alternating black and white rectangles, appears distorting and folding like an accordion: the rectangles within two regions above and below the dot appear alternately shrinking and expanding (Pinna, 2008; Pinna & Fantoni, 2004; Pinna & Spillmann, 2002a). While distorting the two regions changes their appearance, they emerge as regions with a clear shape subjected to apparent dynamic distortions. The illusory distortion creates horizontally elongated ellipses or rhombic shapes as approximately represented by the blue ellipses of Figure 14b. The strength of the effect increases by increasing the size of the stimulus.

It is worthwhile noticing that the checkerboards of the regions that appear distorted shrink while the observer moves closer and expand when the observer moves away. In other words, when the stimulus expands on the retina the micropatterns shrink and, vice versa. This result is the opposite of what is expected on the basis of size-distance constancy. When the checkerboards are replaced by parallel strips, expansion and contraction effects are perceived but following the size-distance constancy and similarly to the bulging grid and pincushion illusions (not illustrated). The accordion effect also occurs by simulating the action of moving towards and away from the figure as shown in Figure 14c. In Figure 14d, by keeping the gaze fixed on the diagonally moving dot, the rectangles of the checkerboard and the vertical stripes made up of aligned rectangles appear to move horizontally left or right following the main horizontal direction of the dot. This result is unexpected on the basis of an aperture-type effect.

The accordion illusion disappears when the rectangles of the checkerboard are replaced with squares, which nulls the directional bias. Under these conditions the well known bulging grid and pincushion illusions are perceived (Foster & Altschuler, 2001; Helmholtz, 1867/1962): a spherical bulge protrudes from the grid. Unlike the bulging grid and pincushion effects, the accordion illusion (i) shows a different kind of dynamic distortion, (ii) it is not an illusion of depth but implies apparent motion and dynamic distortion, (iii) it is clearly perceived under an equiluminous colored grid, and (iv) its strength does not change with monocular or binocular viewing. The accordion illusion depends on directional bias and may represent a good test to understand the retinal/cortical magnification as a function of visual field location.

 Figure 14

### Sliding motion from continuous vs. segmented lines

In the following figures, apparent sliding motion can be obtained without perpendicular directional cues and through a new class of directional bias. In Figure 15a-c, a clear sliding motion in depth is perceived when the eye follows the moving dot (Pinna, 2008). The sliding motion is mostly perceived in the inset regions of Figure 15a-b even if both regions can appear to move. In Figure 15c, the sliding motion separates the two kinds of lines, continuous and segmented in black and white components, that appear to belong to different depth planes while moving in opposite directions. In Figure 15a the inner region made up of continuous lines appears as a window or as a hole through which the lines, placed behind in depth, slide in the right direction when the dot moves down. In Figure 15b the inner region, composed of lines made up of alternating black and white segments, appears in front of the background of continuous lines and slide in a direction opposite to the one of the continuous lines of Figure 15a (i.e. in the left direction when the dot moves down). This opposite result is related to the inverse figure-ground organization of the inset vs. outer regions of Figure 15a-b. Finally, although the inset region appears to slide against the outer one in opposite direction, the continuation of the continuous lines in the segmented ones is not broken but it remains unchanged.

While in Figure 15a-b the local and global orientation of the two kinds of lines is the same, the directional bias along the lines of their element components is the opposite. In fact, when the eye follows the tip of a pen moving up and down along a segmented line, the black and white elements clearly flow in the opposite direction (i.e. down and up). This effect can be perceived in Figure 15d, where, by following the moving dot, the segmented circumferences and the single discontinuities appear respectively to rotate and flow in the opposite direction. When the eye moves along a continuous line, because the information about motion is ambiguous, then the line can appear to flow in the same or in the opposite direction of the real motion. However, the juxtaposition of segmented lines strengthens, by contrast, the motion information of the continuous line in the same direction. As a consequence, in Figure 15a-c there are indeed two opposite directional cues that elicit sliding motion as previously described. These effects can shed light on other related motion effects like the boogie-woogie illusion (Cavanagh & Anstis, 2002).

### Sliding motion from edge contrast

There is a further kind of directional bias that can induce apparent sliding motion: edge contrast. In Figure 16, by following the moving dot, the central region appears to move up when the dot moves in the left direction and down when the dot moves to the right (Pinna & Fantoni, 2004). The pattern is made up of parallel zigzag oblique lines reversing their edge contrast in the central region; each zigzag line changes from black/white to white/black and then to black/white again. The strength of the motion effect increases by increasing the size of the stimulus.

 Figure 15
 Figure 16

### Sliding motion in depth without directional bias

There is another class of stimuli in which the elements have no oriented edges at all and yet elicit vivid apparent sliding motion. These stimuli suggest a motion bias based on motion sensors that respond to other stimulus features such as boundary contour differences, contrast polarity, edge blur, demarcation by a frame, and shape. Such features are also responsible for surface and depth segmentation (Pinna & Spillmann, 2002b, 2005). In Figure 17a, a central array of filled black squares, each surrounded by a thin narrow grey annulus, is presented within a larger surround of similarly arranged, but empty circles. A thin black frame separates center and surround. Under these conditions, the black filled squares are perceived as lying behind the plane of the empty circles. If the stimulus configuration is slowly moved about there is a strong sliding motion of the filled squares relative to the surround of empty circles. In Figure 17b, as the fixation dot moves diagonally, the inset matrix is perceived to move diagonally alternately in counter-phase to the dot motion.

When the location of filled and empty elements is reversed Figure 17c, the depth percept reverses accordingly. The central array of empty squares is now clearly seen as hovering in front of the surrounding filled squares. However, while in the first case the sliding motion is in the opposite direction to the dot motion, in the second it is in the same direction (this can be obtained by moving the mouse arrow on Figure 17c. When the thin narrow grey annulus of each element is replaced by a bluish one, the resulting sliding motion is the strongest we have seen so far, showing a complete in-depth dissociation between the inner and outer regions (Figure 17d-e). The sliding motion can also be perceived, even if it is diminished, in the limiting conditions illustrated by Figure 17f-g.

For an explanation of these effects, differences in spatio-temporal frequency between the two stimulus regions may be invoked. Such differences are known to elicit different speed signals (Thompson, 1982) and could originate from the juxtaposition of empty and filled elements (high and low spatial frequency components) in conjunction with a grey or bluish edge. Next to spatial frequency differences, we suggest different speed signals resulting from figural properties that enhance figure-ground segregation and apparent depth.

### Apparent motion from luminance modulation: The role of explicit orientations

Luminance contrast modulation elicits apparent motion under certain conditions. In the two frames of Figure 18a, while the green edges get brighter, the purple ones get darker and vice versa. Phenomenally, by keeping the gaze on the center of the stimulus, the modulation appears as a pulsation of contrast. Some motion can be also perceived although it is weak. By adding to each square two parallel segments tangent to the virtual annuli created by the squares (Figure 18b), the two annuli appear now to emit two ticks, like those of a clock, going counter-clockwise and clockwise. Some apparent expansion and contraction can also be perceived but they are secondary with respect to the rotation. By replacing the tangent segments with perpendicular ones, a clear alternating expansion and contraction is perceived Figure 18c, i.e., while one annulus expands the other contracts and vice versa (Pinna & Spillmann, 2002a).

These movies demonstrate the role of explicit orientations in polarizing the field of motion biases induced by the contrast modulation. The synergistic organization of both components is also demonstrated in Figure 18d-e, where the black edges induce the ticking. In Figure 18f, tiny modulating dots, which are under threshold in peripheral viewing (with the gaze kept on the central dot), are sufficient to instill motion in the black edges and in their main orientation. The contrast modulation instills motion not only in the direction of explicit orientations but also in the direction of the asymmetric luminance profile shown in Figure 17. This is demonstrated in Figure 18g-h (Pinna & Spillmann, 2002a). It is worthwhile noticing that the spatial and dynamic organization of lines and grey annuli of Figure 18h can be perceived as a continuous counter-clockwise ticking even if, on the basis of the contrast modulation of the juxtaposed edges, the ticking is expected to appear going back and forth. Related to these last effects are the so-called “phenomenal phenomena” described by Gregory and Heard (1972), the reverse phi and four-stroke motion (Anstis & Rogers, 1975, 1986) and the visual illusions based on single-field contrast asynchronies (Shapiro, Charles & Shear-Heyman, 2005).

 Figure 17
 Figure 18

### The windmill illusion

Contrast modulation can instill motion also under the following new conditions (Figure 19a-c). By alternately gradually increasing and suddenly reducing the degree of transparency of the grey annulus superimposed on a radial arrangement of black and white radial sectors, the fine-grained matter or the paste of the annulus and the annulus itself appear to rapidly rotate (Pinna & Dasara, 2005, 2006).

 Figure 19

The apparent rotation of the fluid or of the ethereal paste appears to flow within and along the annulus area ambiguously in both clockwise and counter-clockwise directions. Some apparent expansion and contraction of the annuli can also be seen. The intentional motion of the gaze in one direction (e.g., clockwise) disambiguates the illusory rotation that follows the gaze direction. The loss of transparency strongly reduces or nulls the apparent rotation implying that the figural organization plays an important role (Figure 19d). The apparent rotation is clearly perceived when alternating dark and bright sectors are circularly arranged (Figure 19e). The physical rotation of the figure disambiguates the direction of the apparent rotation that clearly appears opposite to the physical one (Figure 19f), which is constant, slow and whose speed and amplitude is proportional to the ramp of the contrast modulation. The physical rotation of the annulus, when the transparency organization is lost, shows a very weak if any apparent rotation (compare Figure 19g-h). All else being equal, if the disk is smaller than the sectors, the apparent rotation belongs to the disk; if it has the same size as the sectors, both rotate. If it is larger than the sectors, the rotation belongs to them (Figure 19i). This result demonstrates again the important role played by the figural organization. It is worthwhile noticing that, under the conditions illustrated in Figure 19j, what appears to rotate is an ethereal light comprising both the dark and the bright sectors, whose boundaries appear instead to rotate constantly and uniformly.

The windmill illusion shows the role played by the figural organizations (grouping of luminance contrast components, transparency, rotation of the whole shape or of the paste substance, spatial ratio between surrounding and surrounded components). The basic neural substrate may be found in the motion-sensitive neurons in visual area MT (Thiele et al., 2000). This illusion can shed light on the grouping rules operating at a higher cortical stage that organize the responses of motion-sensitive neurons.

## Conclusions

In this work we showed the Pinna illusion and the complexity of the notion of directional bias and its limits in explaining motion illusions. Different classes of directional biases in eliciting the motion illusions are presented. Although the described phenomena are similar in appearance, they constitute different classes of apparent motion likely requiring different explanations. This is particularly evident if one considers the difference in stimulus cues eliciting these phenomena. Further experiments and computational modeling are needed to account for these differences.

The Pinna illusion and the related effects represent an opportunity within the context of vision science and cognitive neuroscience (Gazzaniga, 2004; Purves & Lotto, 2003). If the task of a sensory system is to provide a faithful representation of biologically relevant events in the external world, the previous phenomena show that visual perception contrives, through complex neural computations, to create informative and efficient representations of the external environment. These representations are at the same time simpler and richer than the raw signals transduced by receptors. They are simpler because they simplify the enormous quantity of raw measurement information submitted to the central nervous system (see Section 2). They are richer because they contain properties of events and objects abstracted from the primitive sensory signals (see Sections 3 and 4). Therefore, the first opportunity suggested by the previous effects concerns the basic encoding of the features of the stimuli, i.e. the nature and meanings of the signals carried by single neurons, the maps and areas where they operate (see Section 2) and the pattern of motion of objects, surfaces, and edges in a visual scene due to the relative motion between an observer and the scene (optical flow, Gibson, 1979). Furthermore, they are good tests to understand the perceptual context within which a specific element is perceived, namely “what is ‘figure and what is ‘background”, “how separated elements of a visual event are combined and organized in a sensory representation” (see Section 4).

Within modern visual and cognitive neuroscience, the Pinna illusion reveals two issues that challenge scientists and that deserve to be further investigated. The first issue is related to the basic role of the observer’s motion of the head towards and away from the stimulus. In Figure , the perception of motion depends on this action that on the contrary should cancel the effect as it is predicted by analyses of observer’s head motion in natural scenes. In fact, the pattern of motion of objects, surfaces, and edges in a visual scene, due to the optical flow, is not perceived as illusory motion of the objects but only as motion of the observer. Therefore, if normally in natural scene the final motion outcome of the objects is modulated by messages from other sensory systems (e.g. proprioception), on the contrary in the Pinna illusion it is just the observer’s head movement that instills the illusory motion. The second issue follows the first one and is related to at least two different perceptual levels emerging from the Pinna illusion: the illusion of motion and the illusoriness (Pinna, 2008) of the apparent motion clearly perceived in a pattern that, at the same time, appear as static (likely due to proprioception). If in recent neuroscience all visual percepts are considered equally illusory, the Pinna illusion shows that not all the illusions appear illusoriness. The study of the illusoriness is a further challenge for neuroscientists. Both issues raised by the Pinna illusion can shed a new light in the scientific land between “sensory” and “cognitive” processes not fully explored yet.

## References

• Anstis, S. M., & Rogers, B. J. (1975). Illusory reversal of visual depth and movement during changes of contrast. Vision Research, 15(8-9), 957-961.
• Anstis, S. M., & Rogers, B. J. (1986). Illusory continuous motion from oscillating positive-negative patterns: Implications for motion perception. Perception, 15(5), 627-640.
• Bayerl, P., & Neumann, H. (2002). Cortical mechanisms of processing visual flow - Insights from the Pinna-Brelstaff illusion. Proceedings of 4th Workshop Dynamische Perzeption, Bochum.
• Budnik U., Bayerl P., Attar C.H., Pinna B., Hennig J., & Speck O. (2006). The contribution of human brain areas for visual illusory effects. An fMRI-study on the illusory motion effect in the Pinna-Figure. ECVP2006 Perception.
• Cavanagh, P., & Anstis, S. (2002). The boogie woogie illusion. Perception, 31, 1005-1011.
• Faubert, J., & Herbert, A. M. (1999). The peripheral drift illusion: A motion illusion in the visual periphery. Perception, 28, 617–621.
• Fermüller, C., & Malm, H. (2004). Uncertainty in visual processes predicts geometrical optical illusions. Vision Research, 44, 727-749.
• Fermüller, C., Pless, R., & Aloimonos, Y. (2000). The Ouchi illusion as an artifact of biased flow estimation. Vision Research, 40, 77-96.
• Foster, C., & Altschuler, E. L. (2001). The bulging grid. Perception, 30(3), 393–395.
• Fraser, A., & Wilcox, K. J. (1979). Perception of illusory movement. Nature, 281, 565–566.
• Gazzaniga, M.S. (2004). The Cognitive Neurosciences III. MIT Press, Cambridge, MA.
• Gibson, J.J. (1979). The Ecological Approach to Visual Perception. Boston: Houghton Mifflin.
• Gregory, R. L., & Heard P. (1972). Visual dissociations of movement, position, and stereo depth: Some phenomenal phenomena. Quarterly Journal of Experimental Psychology, 35A, 217-237.
• Grossberg, S., Mingolla, E., & Viswanathan, L. (2001). Neural dynamics of motion integration and segmentation within and across apertures. Vision Research, 41, 2521-2553.
• Gurnsey, R., & Pagé, G.. (2006). Effects of local and global factors in the Pinna illusion. Vision Research, 46, 1823-1837.
• Gurnsey, R., Sally, S., Potechin, C., & Mancini, S. (2002). Optimising the Pinna - Brelstaff illusion. Perception, 31, 1275-1280.
• Helmholtz H von (1867/1962). Treatise on Physiological Optics, volume 3, New York, Dover, 1962); English translation by J P C Southall for the Optical Society of America (1925) from the 3rd German edition of Handbuch der physiologischen Optik (Hamburg: Voss, 1910; first published in 1867, Leipzig, Voss).
• Kitaoka, A., & Ashida, H. (2003). Phenomenal Characteristics of the Peripheral Drift Illusion. Vision, 15(4), 261-262.
• Mather, G. (2000). Integration biases in the Ouchi and other visual illusions. Perception, 29, 721-727.
• Morgan, M. (2002). Running rings around the brain. The Guardian Thursday, 24 January 2002.
• Nakayama, K., & Silverman, G. (1988). The aperture problem – II. Spatial integration of velocity information along contours. Vision Research, 28, 747-753.
• Ouchi H. (1977). Japanese Optical and Geometrical Art. New York, Dover.
• Pinna, B. (1990). Il Dubbio sull’Apparire. Padua, Upsel Editore.
• Pinna, B. (2008). The illusion of art. Pinna, B. (Eds) (2008). Art and Perception: Towards a visual science of art. Brill, Leiden, The Netherlands.
• Pinna, B., & Brelstaff, G. J. (2000). A new visual illusion of relative motion. Vision Research, 40, 2091-2096.
• Pinna, B., & Dasara, M. (2005). The Windmill Illusion. Fifth Annual Meeting of the Vision Sciences Society, Journal of Vision, Sarasota.
• Pinna, B., & Dasara M. (2006). Figural organizations in the windmill illusion. The Fourth Asian Conference on Vision, Matsue, Japan
• Pinna, B., & Fantoni, C. (2004). Local and global motion by edge discontinuities. Fourth Annual Meeting of the Vision Sciences Society, Journal of Vision, Sarasota.
• Pinna, B., & Gregory, R.L. (2002). Shifts of Edges and Deformations of Patterns. Perception, 31, 1503-1508.
• Pinna, B., & Gregory, R.L. (2009). Continuities and discontinuities in motion perception. In Abram M., Minati G., & Pessa E. (Eds.) Proceedings of the fourth Conference on systems science. New York, Scientific Word, Springer-Verlag, 765-775.
• Pinna, B., & Spillmann, L. (2002a). Apparent motion depending on luminance and hue variations. Second Annual Meeting of the Vision Sciences Society, Journal of Vision, Sarasota.
• Pinna, B., & Spillmann, L. (2002b). A new illusion of floating motion in depth. Perception, 31, 1501-1502.
• Pinna, B., & Spillmann, L. (2005). New illusions of sliding motion in depth. Perception, 34, 1441-1458.
• Purves, D., & Lotto, R.B. (2003). Why we see what we do: An empirical theory of vision. Sunderland, MA: Sinauer Associates.
• Shapiro, A. G., Charles, J. P., & Shear-Heyman, M. (2005). Visual illusions based on single-field contrast asynchronies. Journal of Vision, 5, 764-782.
• Spillmann L., Tulunay-Keesey U., & Olson J. (1993). Apparent floating motion in normal and stabilised vision. Investigative Ophthalmology & Visual Science 34 (4) Abstract 1611, 1031.
• Thiele A., Dobkins K.R., & Albright T.D. (2000). The neural basis of contrast detection at threshold: Neurophysiological evidence from macaque area MT. Neuron, 26, 715-724.
• Thompson P. G., (1982). Perceived rate of movement depends on contrast. Vision Research, 22, 377-380.
• Weiss, Y., & Fleet, D.J. (2002). Velocity likelihoods in biological and machine vision. In Rao, R. P. N., Olshausen, B. A., & Lewicki, M. S. (Eds). Probabilistic Models of the Brain: Perception and Neural Function, MIT Press, 77-96.
• Weiss, Y., Simoncelli, E.P., & Adelson, E.H. (2002). Motion Illusions as Optimal Percepts. Nature Neuroscience, 5, 598-604.
• Zöllner, F. (1860). Über eine neue Art von Pseudoskopie und ihre Beziehungen zu den von Plateau und Oppel beschriebenen Bewegungsphänomenen. Annalen der Physik und Chemie, 110, 500-523.

Internal references

• Rodolfo Llinas (2008) Neuron. Scholarpedia, 3(8):1490.
• Jose-Manuel Alonso and Yao Chen (2009) Receptive field. Scholarpedia, 4(1):5393.
• John Dowling (2007) Retina. Scholarpedia, 2(12):3487.

## Acknowledgements

Supported by: Fondazione Banco di Sardegna, Alexander von Humboldt Foundation and Fondo d’Ateneo (ex 60%). I thank the three anonymous Reviewers for their suggestions that greatly improved the paper. I also thank Maria Tanca, Fabrizio and Francesco Deledda for computer assistance and John S. Werner for helpful discussions and comments on the manuscript.

Gazzaniga, M.S. (Eds.) ( 2004). The Cognitive Neuroscience III. MIT Press, Cambridge, MA. ISBN13: 978-0-262-07254-0.

Palmer, S.E. (Eds.) ( 2004). Vision Science: Photons to Phenomenology. MIT Press, Cambridge, MA. ISBN13: 978-0-262-16183-1.

Pinna, B. (Eds.) ( 2006). Color, Line and Space: The Neuroscience of Spatio-Chromatic Vision. LEIDEN: Brill Academic Publisher (NETHERLANDS). ISBN13: 978-90-04-15306-6.

Pinna, B. (Eds.) ( 2008). Art and Perception. Towards a Visual Science of Art, Part 1. LEIDEN: Brill Academic Publisher (NETHERLANDS). ISBN13: 978-90-04-16629-5.

Pinna, B. (Eds.) ( 2008). Art and Perception. Towards a Visual Science of Art, Part 2. LEIDEN: Brill Academic Publisher (NETHERLANDS). ISBN13: 978-90-04-16630-1.