Distance Deception by Fragmented Objects: How Figures May Alter the Perceived Depth of the Background.

Illusory displacements in depth may be perceived in simple geometric configurations devoid of cues for spatial computation but also in real-world images where there is no shortage of information of this kind. Two of these different contexts drew the attention of vision scientists as sources of depth illusions: the Kanizsa square and the images of statues that Catalano's created with a part missing. Similar depth alterations occur in both cases: the portions of the background surrounded by "inducers" (pacmen or body parts) are perceived as coming to the foreground. These illusory effects appear more vivid and diverse in the real-world context leading to hypothesize an involvement of the figural complexity in the misperception. A check was carried out by testing the effects of the background articulation on the depth perception of the illusory Kanizsa square. It was confirmed that both background and inducers articulation enhance the phenomenon. A large set of Catalano's images was analyzed, looking for basic distorting sources along the torn contours. Several basic factors were found, but not enough to account for the complexity of this variegated, often paradoxical phenomenon.

Saturn and its Rings: Four Centuries of Imperfect Amodal Completion.

The planet Saturn is a familiar image for us, but it presents perceptual peculiarities that impeded the discovery of its structure and which can still be misleading today. Saturn appears to be surrounded by rings which hide it to a certain extent and then continue behind the outline of the planet. What we perceive is the result of a double amodal completion in which the planetary globe and the rings exchange the roles of occluding and occluded surface. Saturn was hidden to 17th-century astronomers for half a century because their rudimentary telescopes did not reveal the pictorial clues that are fundamental for discovering such a complex perceptual organization as that formed by a globe surrounded by rings. Moreover, the existence of a celestial body of this nature was inconceivable in light of the knowledge of those times. The improvement of telescopes has substantially enriched our knowledge of Saturn, but historic documents highlight the importance of perceptual organization factors. Astronomical observations were a rich source of information, but only Huygens was capable of integrating them and hypothesizing the true structure of Saturn. His drawings are the result of a particular ability to integrate observations and also the ability to use pictorial information. It is likely that these diagrams were an important instrument for the solution. The image of Saturn, however clear, will not find universal consensus. The planet has "residual (perceptual) capacities" of hiding itself which can even deceive modern instruments. Here, we will try to understand why.

An unexplained three-dimensional percept emerging from a bundle of lines.

Perceptual grouping has been extensively studied, but some areas are still unexplored-in particular, the figural organizations that emerge when bundles of intersecting lines are drawn. Here, we will describe some figural organizations that emerge after the superimposition of bundles of lines forming the profile of regular triangular waves. By manipulating the lines' jaggedness and junction geometry (regular or irregular X junction) we could generate the following organizations: (a) a grid, or a figural configuration in which both the lines and closed contours are perceived, (b) a figure-ground organization composed of figures separated by portions of the background, and (c) a corrugated surface appearing as a multifaceted polyhedral shell crossed by ridges and valleys. An experiment was conducted with the aim at testing the role of the good-continuation and closure Gestalt factors. Good continuation prevails when the lines are straight or close to straightness, but its role is questionable in the appearance of a corrugated surface. This perceptual organization occurs despite the violation of the good-continuation rule and consists of a structure of such complexity so as to challenge algorithms of computer vision and stimulate a deeper understanding of the perceptual interpretation of groups of lines.

Illusory Streaks from Corners and Their Perceptual Integration.

Perceptual grouping appears both as organized forms of real figural units and as illusory or "phantom" figures. The phenomenon is visible in the Hermann grid and in configurations which generate color spreading, e.g., "neon effects." These configurations, generally regular repetitive patterns, appear to be crossed by illusory bands filled with a brighter shade or a colored tinge connecting the various loci of illusory effects. In this work, we explore a particular new illusion showing a grouping effect. It manifests as illusory streaks irradiating from the vertexes of angular contours and connecting pairs of figures nearby. It is only clearly visible when more than one figure is shown, and takes the shape of a net crossing their corners. Although the grouping effect is vivid, the local source of the illusion is completely hidden. Theories explaining this effect as due to the irradiation of illusory streaks (mainly that of Grossberg and Mingolla, 1985a,b) do not fully explain the figural patterns presented here. Illusory effects have already been documented at the angles of various figures, causing them to alter in amplitude and brightness; however, the figure illustrated here appears to have different features and location. Phenomenological observations and an experiment were conducted to assess the role played by geometric and photometric parameters in this illusion. Results showed that sharp angles, in low contrast with the surround, are the main source of the illusion which, however, only becomes visible when at least two figures are close together. These findings are discussed with respect to theories of contour processing and perceptual grouping, and in relation to other illusions.

Brightness/darkness induction and the genesis of a contour.

Visual contours often result from the integration or interpolation of fragmented edges. The strength of the completion increases when the edges share the same contrast polarity (CP). Here we demonstrate that the appearance in the perceptual field of this integrated unit, or contour of invariant CP, is concomitant with a vivid brightness alteration of the surfaces at its opposite sides. To observe this effect requires some stratagems because the formation in the visual field of a contour of invariant CP normally engenders the formation of a second contour and then the rise of two streams of induction signals that interfere in different ways. Particular configurations have been introduced that allow us to observe the induction effects of one contour taken in isolation. I documented these effects by phenomenological observations and psychophysical measurement of the brightness alteration in relation to luminance contrast. When the edges of the same CP complete to form a contour, the background of homogeneous luminance appears to dim at one side and to brighten at the opposite side (in accord with the CP). The strength of the phenomenon is proportional to the local luminance contrast. This effect weakens or nulls when the contour of the invariant CP separates surfaces filled with different gray shades. These conflicting results stimulate a deeper exploration of the induction phenomena and their role in the computation of brightness contrast. An alternative perspective is offered to account for some brightness illusions and their relation to the phenomenal transparency. The main assumption asserts that, when in the same region induction signals of opposite CP overlap, the filling-in is blocked unless the image is stratified into different layers, one for each signal of the same polarity. Phenomenological observations document this "solution" by the visual system.

Not physically present contours can yield illusory motion.

We demonstrate a perceptual effect whereby contours not physically present in a visual scene can yield striking illusory motion. The not physically present contours are paths of invariant contrast polarity (CP). For example, when a square checkerboard composed of dark and light square checks with small black and white discs covering the vertices is put in lateral motion, there is the striking perception of vertical expansion/contraction. Such a checkerboard has (not physically present) diagonal paths of CP presentation with vertical components. However, when a square checkerboard made up of square black and very light checks with gray discs of luminance intermediate to the checks is put in lateral motion, no expansion/contraction is seen. For this checkerboard the vertical components of paths of CP preservation cancel each other out, predicting the lack of perception of vertical expansion/contraction. We also discuss how not physically present contours can explain previously described effects and suggest new effects to be explored.

Brightness alteration with interweaving contours.

Chromatic induction is observed whenever the perceived colour of a target surface shifts towards the hue of a neighbouring surface. Some vivid manifestations may be seen in a white background where thin coloured lines have been drawn (assimilation) or when lines of different colours are collinear (neon effect) or adjacent (watercolour) to each other. This study examines a particular colour induction that manifests in concomitance with an opposite effect of colour saturation (or anti-spread). The two phenomena can be observed when a repetitive pattern is drawn in which outline thin contours intercept wider contours or surfaces, colour spreading appear to fill the surface occupied by surfaces or thick lines whereas the background traversed by thin lines is seen as brighter or filled of a saturated white. These phenomena were first observed by Bozzi (1975) and Kanizsa (1979) in figural conditions that did not allow them to document their conjunction. Here we illustrate various manifestations of this twofold phenomenon and compare its effects with the known effects of brightness and colour induction. Some conjectures on the nature of these effects are discussed.

Arcs in perceptual space--going off at a tangent.

Underestimating the curvature of an arc may result from our tendency to view it as prolonged in the direction of the tangent to its ends. Support is given here for this hypothesis, but evidence is also provided that tangent deviation may alter an arc's circularity along its whole length.

Features of the selectivity for contrast polarity in contour integration revealed by a novel tilt illusion.

We studied a novel illusion of tilt inside checkerboards due to the role of contrast polarity in contour integration. The preference for binding of oriented contours having same contrast polarity, over binding of opposite polarity ones (CP rule), has been used to explain several visual illusions. In three experiments we investigated how the binding effect is influenced by luminance contrast value, relatability of contour elements, and distance among them. Experiment 1 showed that the effect was indeed present only when the CP rule was satisfied, and found it to be stronger when the luminance contrast values of the elements are more similar. In experiment 2 the illusion was reported only with relatable edges, and its strength was modulated by the degree of relatability. The CP-rule effectiveness, thus, seems to depend on good continuation. The intensity of contrast polarity signals propagating from an oriented contour might be the less intense, the more its direction deviates from linearity. In experiment 3 we estimated the distance threshold and found it to be smaller than the one found for other illusions, arising with collinear fragments. This seems to show that the reach of the contrast polarity signal inside the association field of a contour unit is shorter along non-collinear orientations than along collinear ones.

The brightness of diamonds.

A brightness illusion and transparency effects are described for configurations comprising alternating black and white bars on which are superimposed mid-luminance shapes (diamonds and hexagons). The resulting phenomena are predictable by Anderson's 'scission theory', which is thus given further support.

Draughtsmen at work.

To obtain the representation of a contour, the visual system integrates fragments of a pattern. One of the 'binding rules' governing this process requires that a path of conjunction in which contrast polarity is preserved be followed. Here we show that this rule has a corollary: where two alternative paths compete to emerge in opposite directions, the one with greater contrast luminance is likely to prevail.

Spatial distortions induced by dotted patterns.

Prolonged steady fixation of parallel, radial, or concentric lines positioned close to each other generates phenomena of illusory oscillation, waving, and shimmering. Purkinje reported a first observation of these phenomena almost two centuries ago (review by Wade, 1977 Perception 6 407-433). Here we show that illusory waving and oscillation phenomena arise at first glance when dotted lines are either interposed between continuous lines, or positioned very close to straight edges. Phenomenological and individual observations indicate that dotted and linear patterns are independent sources of different illusory effects: the former of waving, the latter of shimmering/scintillating. The two effects enhance each other when dotted and continuous lines are alternated. Possible accounts of the phenomena are discussed. Waving is likely to originate from the perceived alteration of dot spacing, which in turn gives rise to depth cues and the consequent illusory deviation in depth. Shimmering and scintillating are attributed to imperfect binocular fusion, which can cause phenomena of brightness induction. A theory of the combination of the two illusory effects is put forward.

A new "tilt" illusion reveals the relation between border ownership and border binding.

The "association field" models of contour detection predict specific spatial conditions for linking or grouping neighboring elements into smooth contours. We previously suggested that the "association field" model may account for perceptual binding of near-collinear luminance edges of same contrast polarity and their consequent unification into a unique contrast border with illusory tilt. This approach is now developed into a new version of the tilt illusion, the seesaw illusion, in which the contrast border is perceived as inverting concave-convex illusory curvature when background luminance is inverted, indicating that contrast polarity must be incorporated into the notion of "association field" to account for the seesaw illusion. We found that although tile-edge segmentation into alternating black-white segments produces conflicting local tilts, the illusion remains, up to 16 arcmin edge distance. This occurs at extreme background luminance for long segments (where only congruent edge segments of higher contrast bind, the others being perceptually assimilated into the background surface) and, when segments are too short for their orientation to be detected, at all background luminance values except that equidistant from black and white stripes. Our findings provide further confirmation that these are striking border ownership phenomena, demonstrating that figure/ground organization precedes perceptual binding of edges through association fields.

Boundary completion, contrast polarity, and the perception of illusory tilt.

What we perceive as a unitary object can be the result of integrative processes that generate a whole from parts. Although this issue of visual perception has been widely explored, recent experimental findings demonstrate that our knowledge is still incomplete. In particular, the question whether contour binding is affected by the sign of contrast (contrast polarity) across edges requires more in-depth examination. Here we show the effects of edge bindings that originate from the merging of laterally displaced edges with the same contrast polarity. We have studied a particular context in which such effects may emerge: a checkerboard with a series of alternated dark and light shapes superimposed on the corners of the squares. The phenomenal observations and experimental findings support the theories according to which boundary completions are originated by phenomena of edge propagation within a 'field of completion' (eg Shipley and Kellman, 2003 Perception 32 985-999) adjacent to an edge ending. Our findings conform to the Shipley and Kellman theory that boundary completion results from the interaction of edges as well as from edges and shapes lacking in oriented contours, the latter serving as 'receiving units', anchoring the paths of activations generated by oriented edges. We propose to integrate this theory with the hypothesis that interactions sensitive to the contrast sign generate conjunction paths of edges that alter their perceived orientation. Based on this perspective we propose an alternative account for the Café Wall illusion that can be extended to other phenomena of orientation misperception and to a Café Wall inversion effect that has not been observed previously.

Piranesi and the infinite prisons.

Piranesi was an extraordinarily talented artist who came to be considered the best known engraver and etcher of the 18th century. He spent his lifetime recording the magnificent buildings and ruins of ancient Rome. In his earlier work, he developed architectural fantasies and dark visions of imaginary prisons, the Carceri d'Invenzione (Imaginary Prisons), which have fascinated people ever since they first appeared. They also made an impact in later artistic and literary contexts. Today they are considered the best expression of bewilderment, of the world's massive oppression of man. How did Piranesi generate such a powerful source of meaning? I have reviewed a number of contributions by art essayists in the search for what lies behind the fascination of the 'Carceri'. Analysis of these texts provides a rich set of aesthetic and psychological attributes as well as detailed indications of where to seek the source of the meanings. I suggest here a fruitful integration of this analysis, developed by considering various particular perceptual and geometric cues. I discuss three possible sources of meaning: the combination of architectural elements out of proportion; the difficulty of building a unitary space; and the 'bottom perspective' that gives rise to a sensation of floating.

Texture segregation on the basis of contrast polarity of odd-symmetric filters.

This is the first study to demonstrate the selectivity of learning for contrast polarity. The finding is the main result of an investigation into the existence of central and peripheral vision mechanisms selective for contrast polarity within the texture-segregation process, using the perceptual learning paradigm in a detection task. Energy models (Malik & Perona, 1990) exclude segregation of textures composed of elements of odd-symmetric luminance profile by contrast polarity differences. Here the target was a Gabor patch (0.8 deg) of 1 cyc/deg in sine phase (odd-symmetry) embedded in a background of mirror-image elements. Our results showed that, in fovea, segregation on the basis of contrast polarity was above threshold from the first session. After learning, the target popped-out in both central and peripheral vision for durations over 10 ms. Our major result is that learning is selective for contrast polarity; it is also selective for orientation and position, all characteristics distinctive of early processing. Since the learning effects were obtained with texture composed of odd-symmetric mirror-image elements, they indicate that the output from odd-symmetric filters was not excluded or inhibited in texture segmentation, but instead played an active role. Our data support models of texture segmentation, in which detection of texture gradient is achieved on the basis of early cortical process, before the non-linear transformation of their output.

Orientation misperceptions induced by contrast polarity: comment on "Contrast polarities determine the direction of Café Wall tilts" by Akiyoshi Kitaoka, Baingio Pinna, and Gavin Brelstaff (2004).

According to Kitaoka et al (2004, Perception 33 11-20), the Café Wall illusion can be reduced to misalignment effects produced locally by a large shape on a line passing nearby. I demonstrate here that the interacting units are edges and not whole shapes, and that the source of the illusion does not consist in a local tilt but in a tendency of the edges to join when they have the same contrast polarity.

Illusory boundary interpolation from local association field.

We previously showed that interpolation between vertically misaligned luminance edges of same polarity of contrast is preferred to that between co-linear edges of opposite polarity of contrast, although it results in illusory tilt (Roncato and Casco, 2003). We here analyze the spatial conditions that produce this illusory binding of vertically misaligned edges of light and dark tiles, alternated in a row, and in counterphase with those in the rows above and below. We find that, independently of scale and number of tiles in a row, the illusion is perceived when the vertical misalignment of more than three tiles is smaller than or equal to 9' and the horizontal separation between co-linear edges is smaller than or equal to 13'. These short distances suggest that the underlying mechanism is local. Both our phenomenological and psychophysical results support the notion of a local short-range association field, selective to contrast polarity, which produces a binding solution different from that of a phase-independent long-range mechanism. We suggest that the occurrence of the illusion at local-level is a result of the activation, within a local short-range association field, of units with orientation different from that stimulated by the physical edges. These units are not inhibited when they are close, iso-oriented and co-linear, and the misaligned edges from which they propagate have the same contrast polarity. We found that horizontal and vertical spatial limits for the interpolation covary but not such that their ratio is fixed, indicating that the two edges can be connected by projections having a relatively wide range of orientations.

Lines that induce phenomenal transparency.

Three neighbouring opaque surfaces may appear split into two layers, one transparent and one opaque beneath, if an outline contour is drawn that encompasses two of them. The phenomenon was originally observed by Kanizsa [1955 Rivista di Psicologia 69 3-19; 1979 Organization in Vision: Essays on Gestalt Psychology (New York: Praeger)], for the case where an outline contour is drawn to encompass one of the two parts of a bicoloured figure and a portion of a background of lightest (or darkest) luminance. Preliminary observations revealed that the outline contour yields different effects: in addition to the stratification into layers described by Kanizsa, a second split, opposite in depth order, may occur when the outline contour is close in luminance to one of the three surfaces. An initial experiment was designed to investigate what conditions give rise to the two phenomenal transparencies: this led to the conclusion that an outline contour superimposed on an opaque surface causes this surface to emerge as a transparent layer when the luminances of the contour and the surface differ, in absolute value, by no more than 13.2 cd m(-2). We have named this phenomenon 'transparency of the intercepted surface', to distinguish it from the phenomenal transparency arising when the contour and surface are very different in luminance. When such a difference exists, the contour acts as a factor of surface definition and grouping: the portion of the homogeneous surface it bounds emerges as a fourth surface and groups with a nearby surface if there is one close in luminance. The transparency phenomena ('transparency of the contoured surface') perceived in this context conform to the constraints of Metelli's model, as demonstrated by a second experiment, designed to gather 'opacity' ratings of stimuli. The observer judgments conformed to the values predicted by Metelli's formula for perceived degree of transparency, alpha. The role of the outline contour in conveying figural and intensity information is discussed.

The influence of contrast and spatial factors in the perceived shape of boundaries.

When an edge can be perceived to continue either with a collinear edge of the opposite contrast polarity or with a noncollinear edge of the same contrast polarity, observers perceive an alignment between the edges of the same contrast polarity, even though they are noncollinear. Using several stimulus configurations and both free and tachistoscopic viewing, we studied the luminance and spatial factors affecting the perceived distortion and binding. The results showed that the two noncollinear edges tended to align when they had the same contrast polarity (Experiment 1A) and to misalign when they had opposite contrast polarity (Experiment 2), providing that (1) they were separated by a distance larger than 1 arcmin and smaller than 3-4 arcmin (for all configurations) and (2) they laterally overlapped for about 7 arcmin (Experiment 1B). The results also showed that the direction of apparent distortion depended on the direction of overlapping. The results of Experiment 3 ruled out the local attraction/repulsion explanation but, instead, supported the suggestion that the interaction concerned the global edges, or part of them, and produced an inward tilt, which made the edges of the same contrast polarity perceptually to align, or an outward tilt, so that the edges of opposite contrast polarity were perceived to be more misaligned. From the overlap and distance limits found, it can be inferred that for two noncollinear contours to join perceptually, the tilt must not exceed 18 degrees, a limit compatible with the orientation bandwidth of contrast-sensitive early cortical mechanisms.