Points and endpoints: a size/spacing constraint for dot grouping

One-dimensional arrangements of dots immediately group into contours. It is reported that, when these contours participate in certain larger arrangements, there is an abrupt point at which the percept changes as a function of dot spacing (or density along the contour). Closely spaced arrangements give rise to subjective effects involving apparent brightness and depth, whereas sparsely spaced ones do not. The effects are most clear in configurations that involve endpoints and possible occlusions. For these configurations, densely dotted contours are perceptually equivalent to solid ones, but sparse ones are not. This change in percept occurs abruptly and consistently at a dot to space ratio of 1:5, when the dot density is normalized by dot size, and this point is called the size/spacing constraint. It holds only for dots of the order of 1 min visual angle in diameter when small to modest contrast values are used. The subjective effects are not present for dotted contours (or even for solid ones) that are smaller (less than 0.5 min), and differ for contours that are larger (greater than 10 min). To demonstrate the significance of size/spacing constraints for early vision, a framework for grouping consisting of processes at many different levels is outlined, and the requirements for the earliest one (orientation selection) are sketched in greater detail. The size/spacing constraint follows directly from one of these requirements--receptive field structure--and seems to indicate a switch from early orientation-selection processes to later ones.     

Displacement of the path of perceived movement by intersection with static contours

Observation of a moving dot gives rise to a perceived movement path, which has properties similar to those of real contours. If the dot crosses a line inclined to a horizontal direction of movement, it appears to undergo a vertical displacement. This displacement was found to be greatest for a line orientation of around 15° with respect to the movement. At other relative orientations, the size of the perceived displacement varied in the same manner as the perceived expansion of angles formed by intersection between static contours. Movement path distortions were measured with background fields like those that produce the Hering and Zöllner illusions with continuous lines. Illusory displacements of perceived movement were found to be equivalent to the static forms. The subjective contour formed by observation of movement can therefore give rise to illusions similar to those obtained with real lines.     

Retinal mechanisms in the perception of subjective contours: the contribution of lateral inhibition.

One mechanism frequently proposed for the creation of subjective contours and their related brightness effects involves lateral neural interactions on the retina, such as the lateral inhibitory effects that underlie brightness contrast. Subjective contour stimuli were displayed under an intermittent light source, with rapid onset and slow offset as has been shown to increase lateral inhibitory interactions by allowing summation of neural onset transients. A sample of forty subjects, using magnitude estimates, reported increased subjective contour clarity and brightness effects under these exposure conditions. The effects were larger for relative brightness differences than for contour visibility. It appears that this technique may have applications in exploring retinal contributions to other aspects of the perception of subjective contours.     

Evidence for independent processing of subjective contour brightness and sharpness.

Subjective contours have been of considerable interest because of their importance to theories and physiological models of form perception. In particular, they have recently been characterized as the result of magnocellular cortical processing. There is, however, a paucity of parametric data relating to basic psychophysical parameters in this field. Two experiments are reported in which the roles of subjective contour size, retinal eccentricity, and flicker rate in subjective contour salience were investigated. Eleven observers estimated subjective contour magnitude using an Ehrenstein configuration. Configurations ranging in size from 0.25 to 3 deg were presented to three retinal loci (fovea, 2 deg, and 4 deg) at flicker rates ranging from 5 to 15 Hz. Subjective contour brightness and distinctness were measured separately. Brightness was greatest at a subjective contour size of about 1.25 deg, at flicker rates of 5-7 Hz, and at 3 deg peripheral for all flicker rates and all but the smallest stimulus sizes. Distinctness decreased with eccentricity and flicker, but remained high at small diameters (thus implicating spatially sensitive mechanisms). Taken together, the results support a magnocellular processing of subjective contours with respect to brightness, but also suggest that there is a parvocellular contribution to subjective contour sharpness.     

Perceptual processes that may create stick figures and balance

A series of experiments looked at the pattern of dot placements created when people individually placed a single dot inside empty outline figures. The superimposed results were found to compare better with the predictions of Blum's grassfire model than with a size-constancy process. The pattern of superimposed dots conformed to the stick figure of the outlined contours. A perceptual model based on spatial harmonic analysis of complex visual scenes is offered as an explanation for the pattern of results.     

Perceptual fading without retinal adaptation

A retinally stabilized object readily undergoes perceptual fading and disappears from consciousness. This startling phenomenon is commonly believed to arise from local bottom-up sensory adaptation to edge information that occurs early in the visual pathway, such as in the lateral geniculate nucleus of the thalamus or retinal ganglion cells. Here we use random dot stereograms to generate perceivable contours or shapes that are not present on the retina and ask whether perceptual fading occurs for such "cortical" contours. Our results show that perceptual fading occurs for "cortical" contours and that the time a contour requires to fade increases as a function of its size, suggesting that retinal adaptation is not necessary for the phenomenon and that perceptual fading may be based in the cortex.     

Evidence relating subjective contours and interpretations involving interposition

Subjective contours, according to one theory, outline surfaces that are apparently interposed between the viewer and background (because of the disruption of background figures, sudden termination of lines, and other interposition 'cues') but are not explicitly outlined by intensity discontinuities. This theory predicts that if the cues are not interpreted as evidence of interposition, no intervening surface need be postulated, hence no subjective contours would be seen. This prediction, however, is difficult to test because observers normally interpret the cues as interposition evidence and normally see the subjective contours. Tests are reported on a patient with visual agnosia who is unable to make the usual interposition interpretations and unable to see subjective contours, but has normal ability to interpret standard visual illusions, stereograms, and in particular, stereogram versions of the standard subjective contour figures, which elicit to him strong subjective edges in depth (corresponding to the subjective contours viewed in the monocular versions of the figures.     

Subjective contours in stereoscopic space

Stereoscopic depth and subjective contour clarity were manipulated by varying the type of monocular configuration as well as magnitude and direction of disparity. The clarity of the subjective contours was influenced significantly by both magnitude and direction of disparity and by the type of monocular configuration. Subjective contours were always less clear when the objective monocular contour was discontinuous regardless of disparity. Stereoscopic depth estimates varied directly with magnitude and direction of disparity; however, depth magnitude reports were truncated when the disparity was carried by discontinuously defined patterns.     

Illusory contours and spatial judgment

We investigated whether, in the human visual system, the mechanisms responsible for relative location judgments are the same when those judgments are made in the context of illusory contours and in the context of mentally joining two points. We asked subjects to align a dot with the oblique contour of an illusory surface or to align a dot with two markers at an oblique orientation. The systematic errors differed in direction for these two conditions. All the systematic errors were orientation dependent. The errors in aligning a dot with an illusory contour seem to be related to the asymmetrical shape of the single objects, which are able to induce an illusory contour, as well as figure-ground segregation.     

Subjective contours can produce stereokinetic effects

When a pattern of interrupted concentric circles drawn so as to produce an anomalous contour ellipse is slowly rotated in the frontoparallel plane, the subjective figure appears first to deform and then to tilt as a ring in 3-D space over motionless circles. Also, Benussi's floating cone can be obtained by placing an eccentric gray dot upon an anomalous solid ellipse and setting this figure into rotation. These patterns provide strong evidence that subjective contours can produce stereokinetic effects as effectively as real contours can. Implications for current explanations of stereokinetic effects are presented and discussed.     

The illusion of transparency and chromatic subjective contours

Subjective contours can be produced that include an illusion of edge and an extension of color throughout the area of the illusion. The phenomenological appearance is of a transparent colored shape in front of the background. Two explanations of this illusion are proposed. The first is that there is an assimilation of color analogous to brightness assimilation. The second is a variant of the stratification of depth theory of subjective contours. In it, the pattern elements lead to the illusion of a surface in front of the pattern elements. We thus predicted that an illusion of transparency would enhance the subjective contour, Metelli’s model of transparency was used to quantify our prediction, and it was found that the possibility of transparency was a powerful predictor of the chromatic subjective contour.     

Amodal completion, depth stratification, and illusory figures: a test of Kanizsa's explanation.

Subjective contours have been explained by Kanizsa as being a consequence of amodal completion of incomplete figures. According to the theory of amodal completion, figural incompleteness triggers the emergence of an illusory object superimposed on the gaps in the inducers, which in turn hide parts of the pattern, thus suggesting that the plane of the illusory object must always be seen to be above the plane of the inducers. A figure was created in which subjective contours are seen despite the fact that the perceived depth relationships run counter to that required by the theory of amodal completion. In four experiments, this depth relationship is confirmed by using direct and indirect measures which assess both registered and apprehended depth. By emphasizing a logical inconsistency in the explanation based on amodal completion, the results show that amodal completion, at least in Kanizsa-like patterns, cannot be considered as a causal factor for subjective contour figures.     

Is there a pop-out of exclusively binocular (cyclopean) contours and regions?

In this work, contours and texture regions were designed so that they could not be observed by either eye alone, but only after images from both eyes were fused into a single stereoscopic picture. Two planes of random dots were positioned one in front of the other so that their random-dot patterns were transparently overlaid. In this way the dot pattern in the front plane was completely masked by the dots in the back plane for either eye on its own. Such exclusively binocular or 'cyclopean' stimuli are therefore defined by a conjunction of depth information with other basic visual features. It is shown that, unlike their monocular counterparts, cyclopean contours do not pop-out. It is also shown that cyclopean regions pop-out only when they have either much higher or much lower luminance contrast than their surroundings, or (for some observers) when the cyclopean region is defined by motion contrast. Colour, luminance-contrast sign, and orientation-defined regions are not easily detected even when viewed attentively.     

On the surprising salience of curvature in grouping by proximity

The authors conducted 3 experiments to explore the roles of curvature, density, and relative proximity in the perceptual organization of ambiguous dot patterns. To this end, they developed a new family of regular dot patterns that tend to be perceptually grouped into parallel contours, dot-sampled structured grids (DSGs). DSGs are similar to the dot lattices used to study grouping by proximity, except that only one of the potential organizations is rectilinear; the others are curvilinear. The authors used the method of M. Kubovy and J. Wagemans (1995) to study grouping by proximity in DSGs. They found that in the competition between the most likely organizations, one rectilinear and the other curvilinear, the latter is more salient. This phenomenon cannot be explained by contemporary accounts of grouping by proximity or contour integration.     

Subitizing and counting processes in young children

Children attending the first grade in school were instructed to tell the number of dots (1–9) presented on a screen. The response latencies were related to the number of dots by two different linear relations for each subject. The first of these had a slope of about 0.1 sec/dot, was applicable for the encoding of 1–3 dots, and was taken as an indication of a subitizing process. The second linear relation was applicable for 5–9 dots and had a slope of about 1.0 sec/dot reflecting the speed of a counting process. The average intersection between the functions was located at 3.22 dots. The results were compared with earlier investigations of adult subjects who on the average subitize 6 dots and count 1 dot in about 0.4 sec. It was subitizing process being higher for adults. If the encoding of a stimulus has not been terminated within about 1.5 sec for children and adults the stimulus has instead to be identified in either a counting or an estimating process.     

Shape discrimination for motion-defined and contrast-defined form: squareness in special.

Shape discrimination was measured for: (i) two-dimensional rectangular targets that were perfectly camouflaged within a stationary pattern of random dots and rendered visible by relative motion of the dots, and (ii) similar dotted rectangles that were rendered visible by luminance contrast. Shape discrimination was disconfounded from size discrimination by requiring subjects to discriminate the aspect ratios of rectangles whose areas were altered independently of aspect ratio. When dot speed and contrast were both high, the aspect-ratio discrimination threshold was as acute for motion-defined (MD) rectangles as for contrast-defined (CD) rectangles and, at 2-3%, corresponded to a change of side length of about 24 s arc compared to a mean dot separation of 360 s arc. Discrimination of MD rectangles collapsed at low dot speeds and could not be measured at speeds less than about 0.03-0.08 deg s-1, but discrimination of CD rectangles was almost unaffected by dot speed. The aspect-ratio discrimination threshold was lowest for a square and progressively increased as the rectangle became more asymmetric. It is suggested that the visual system contains a mechanism that compares the separations of pairs of contours along different azimuths, and that, during visual development, this shape-discrimination processing of MD and CD targets is driven by the same environmental and behavioural pressures towards a common end point. The human equivalent of a pathway that includes the cortical area MT is thought to be important for shape discrimination of MD forms.     

Interpolation across surface discontinuities in structure from motion Asad Satdpour

Interpolation across orientation discontinuities in simulated three-dimensional (3-D). surfaces was studied in three experiments with the use of structure-from-motion (SFM). displays. The displays depicted dots on two slanted planes with a region devoid of dots (a gap). between them. If extended through the gap at constant slope, the planes would meet at a dihedral edge. Subjects were required to place an SFM probe dot, located within the gap, on the perceived surface. Probe dot placements indicated that subjects perceived a smooth surface connecting the planes rather than a surface with a discontinuity. Probe dot placements varied with slope of the planes, density of the dots, and gap size, but not with orientation (horizontal or vertical). of the dihedral edge or of the axis of rotation. Smoothing was consistent with models of 2-D interpolation proposed by Ullman (1976). and Kellman and Shipley (1991). and with a model of 3-D interpolation proposed by Grimson (1981).     

The pigeon's discrimination of movement patterns (Lissajous figures) and contour-dependent rotational invariance

The ability of pigeons to discriminate complex motion patterns was investigated with the aid of moving Lissajous figures. The pigeons successfully learned to differentiate two successively presented cyclic trajectories of a single moving dot. This suggests that they can recognize a movement Gestalt when information about shape is minimal. They also quickly learned a new discrimination between moving-outline stimuli with repetitively changing contour patterns. Contrasting results were obtained when the dot or outline stimuli were axis-rotated through 90 degrees. Rotational invariance of pattern discrimination was clearly demonstrated only when moving contours were visible. Nevertheless, pigeons could discriminate the axis-orientation of a moving-dot or moving-outline pattern when trained to do so. Discrimination did not seem to depend on single parameters of motion but rather on the recognition of a temporally integrated movement Gestalt. The visual system of pigeons, as well as that of humans, may be well adapted to recognize the types of oscillatory movements that represent components of the motor behaviour shown by many living organisms.     

Edge-induced illusory contours and visual detection: Subthreshold summation or spatial cueing?

Findings that illusory contours can facilitate visual detection of a subthreshold real line (Dresp & Bonnet, 1995) were not replicated, when line-induced instead of edge-induced illusory contour stimuli were used (Salvano-Pardieu et al., 2006). Rather, the results of the latter study supported the importance of spatial cues. The present study was designed to investigate whether spatial cueing might also facilitate detection of targets superimposed on edge-induced illusory contours. In Experiment 1, a target line was superimposed on the illusory contour of a Kanizsa square, presented between dots with a precise or distant location to the target, or on a homogeneous field (control). Detection of the target was poorest for the control, followed by the distant-dots and Kanizsa conditions, whereas it was best for precisely cueing dots. Experiment 2 replicated the conditions in Experiment 1 (Kanizsa, precisely cueing dots, and control) with additional controls for possible luminance effects. The two new conditions matched the Kanizsa condition for overall luminance and preciseness of spatial cueing without generating illusory contours. Performance was best in the dot condition and worst in the control, but the same across the Kanizsa and matched luminance conditions. In Experiments 3 and 4, the stimuli presented were matched more closely to those used by Dresp and Bonnet, but still the results confirmed those obtained in our Experiments 1 and 2. Together, these experiments strongly suggest that detection is also facilitated by spatial cueing rather than subthreshold summation, in the case of edge-induced illusory contours.     

The observer-relative velocity field as the basis for effective motion parallax

Earlier studies of motion parallax found unambiguous relative depth perception when random dot patterns were systematically translated in accordance with either motion of the observer's head or motion of the display scope. The need for such relative motion between an observer and a flow field was examined by placing a flow field in a limited area (window) in a large scope and translating the window relative to the observer. Accuracy in judging surface orientation and quantitative depth estimates were determined by the velocity field relative to the observer and were not measurably affected by whether this field was produced with a stationary or a moving window. Accuracy was consistently higher for smaller ratios of maximum to minimum projected velocities, reaching 100% in one experiment with a 1.12:1 ratio. We conclude that fully effective motion parallax does not require relative motion between the observer's head and the contours of a flow field.