Bertulis Čerkelis, Algis Povilas

The human visual system overestimates the length of structured contours relative to adjacent empty intervals of the same physical size (Fig. 1) [1]. The effect appears in whole geometric contours and in isolated parts of them alike [2]. Complete rectangles and pentagons, isolated apices and pedestals, and pairs of parallel horizontal or vertical lines all looked longer than they were, with consistently positive mean errors in psychophysical experiments. Overestimation magnitude followed contour geometry rather than physical size alone: an isolated segment could expand as much as, less than, or more than the shape it came from. The sum of the part effects therefore does not predict the whole-object effect, nor can the parts be predicted from the whole. The summed expansion of the isolated apex and pedestal far exceeded that of the corresponding whole pentagon: 25.1 vs. 15.8 arc min (Fig. 2a), 30.0 vs. 13.8 arc min (Fig. 2b), and 30.0 vs. 7.7 arc min (Fig. 2c). Such a pattern is incompatible with a model that assembles perceived size by summing the apparent sizes of parts measured independently. Instead, it suggests that segments within a whole object are integrated into a single representation whose expansion depends on the relational structure of the complete configuration — a holistic rather than structural coding of shape [3, 4]. The comparison between line pairs and rectangles points the same way. Adding two vertical segments to a pair of horizontal lines forms a rectangle, thereby lengthening the contour and closing it. At every length, the rectangle expanded less than the line pair: 7.5 vs. 14.2 arc min, 15.5 vs. 17.4 arc min, and 20.4 vs. 22.9 arc min. The reduction fits the proposal that corner junctions introduce a contraction component that partly offsets expansion. Here too, the summed expansion of the horizontal and vertical line pairs exceeded that of the rectangle: 18.9 vs. 7.5 arc min, 22.9 vs. 15.5 arc min, and 25.5 vs. 20.4 arc min. These findings support a configuration-dependent account of apparent-length expansion and argue against simple additivity of parts.

The visual system overestimates the length of structured contours relative to adjacent empty intervals of the same physical size. This study examined whether apparent-length expansion occurs across isolated contour parts as well as complete objects, and whether the expansion of the whole can be predicted from that of its components. Observers matched the perceived horizontal extent of complete pentagons, incomplete pentagons with one or two missing segments, isolated apices, pedestals, parallel line pairs, and rectangles using an adjustment method. All stimulus types produced consistent positive mean errors, indicating robust apparent-length expansion across a wide range of contour configurations. The magnitude of expansion depended on contour geometry rather than on physical size alone: removing contour segments did not reduce expansion and, in some cases, increased it. Isolated parts produced expansion effects comparable to or larger than those of the corresponding whole pentagons, but the sum of part effects did not predict the whole-object effect. These findings support a configuration-dependent account of apparent-length expansion and appear inconsistent with simple part-based additivity.

This study investigates the visual phenomenon of increasing stimulus size [Bertulis & Bielevicius. Expansion of perceived size. J. Perception, 2025]. In psychophysical experiments, observers adjusted the test distance to match the length of the entire stimulus— the pentagon—and its components: the apex and the rectangular segment, which can be called the pedestal, both when separated and combined. The shape of the pentagon changed during presentations due to three simultaneous variables: a) the length of the apex gradually increased from 30 to 180 arc minutes, b) the horizontal edges of the pentagon decreased from 150 to 0 arc minutes; and c) the apex angle narrowed from 100 to 23 degrees, while the pentagon’s length and height remained constant at 180 and 72 arc minutes, respectively. Based on the averages of the experimental results, the pentagonal-shaped stimulus demonstrated an expansion effect, which, due to shape changes, ranged from 2 to 19 arc minutes. For the isolated apex with increased length and narrowed opening angle, expansion values were higher and, ranging from 10 to 33 arc minutes, showed a consistent upward trend without reaching a peak. In the pentagon’s structure, the apex with similar shape and size dynamics displayed a different expansion profile. The expansion value gradually increased from about 9 to 35 arc minutes (its maximum), then decreased to 30 and 19 arc minutes. Similarly, the pedestal displayed different patterns when viewed as a separate object and as part of the pentagon. The isolated pedestals showed expansion (7 to 30 arc min) throughout. Inside the pentagon, narrow pedestals (30, 60 arc min) did not even exhibit expansion and instead showed a negative error sign. Wider pedestals produced relatively weak expansion, peaking at 8 arc minutes before decreasing to 1.5 arc minutes. The combined curves of the isolated apex and pedestal did not match the experimental curve of the whole pentagon. Based on the data, the perceived shape seems to be a key factor in determining perceived size and, therefore, the expansion effect. During the visual size-matching process, the spatial proportions within the perceived shape are likely to change when combined with another shape, even though the geometry remains unchanged. The representation of a shape (such as a pentagon) in higher neural networks is not simply a sum of its parts’ representations (apex and pedestal).

In psychophysical experiments on a monitor screen, a subjective contour of a rectangular shape was formed by a random dot pattern drifting against a background of static random dots. Bidirectional drifting: divergence, and convergence were applied within the rectangle area. The aim was to answer whether the direction of movement selectively influences the perceived relative length of the motion-defined shape. Subjects judged the relative extension of the reference stimulus by adjusting the perceptually equal length of the test gap. It was demonstrated that dots moving horizontally toward the stimulus periphery and tangentially approaching the rectangle edges in the case of divergence caused an overestimation of the rectangle length. The positive errors of the subjects indicated that the rectangle edges perceptually shifted outward. The shift values were about the same for shorter and middle rectangles but lower for longer ones. The size expansion effect appeared to reduce at a certain motion distance. When convergence was tested, dots escaping the rectangle edges and drifting toward the stimulus center caused relatively low error values that continuously declined with stimulus length. There were even negative signs of errors for six subjects out of eight for longer rectangles. The effect of expansion was questionable. Consequently, the approaching and escaping dots don’t act the same way on the positions of the subjective contour. But was the expansion produced by the divergent motion of the same origin as the expansion of stimuli outlined by a static spatial contrast in luminance, color, or texture, and defined by perceptual grouping and the Kanizsa contours (Bielevicius, et al., 2023)? To compare the two manifestations of expansion, the control stimuli were formed of static lines and exposed on the same background of random dots in the present study. The divergently drifting dots were still presented within the rectangle area. The rectangle sizes were the same as before that. Such stimuli caused overestimation errors exceeding those of the motion defined contours. In addition, the expansion strengthened, while not decreasing, with an increase in the length of the stimulus. As a result, for long stimuli, the expansion of the static contour became two to three times higher than that of the motion-defined contour. The size expansion effects for static and motion-defined contours may have different neural origins.

Introduction. The present study focuses on the expansion effect of the relative size of isolated stimulus parts like angles, broken lines, and short stripes. Subjects (M, N, O, L, Ë, A, B, R, P, H, K, and Г) matched the test distance to the referential stimuli length by adjusting the position of the terminal spot. The testing distance was limited to the terminal spot and the vertex or sideline of a referential figure. The starting referential stimulus was the contour pentagon (facsimile in Fig. 1). Lines and their combinations were removed from the pentagon to show separate parts. The background's luminance and the stimuli lines were 0.01 cd/m2 and 23 cd/m2 , respectively. Results. A. All modified stimuli caused the effect of length expansion, which did not significantly differ in strength from the entire pentagon (13.8 arc min; Fig 1 medial section). The illusion grew slightly from 13.8 to 15.7 arc min P = 0.397 (Welch's t-test) in the stimulus without a lower horizontal line and from 13.8 to 15.2 arc min P = 0.561 in that without the bottom two lines. B. An angle, a pair of wings (Fig. 1 right section) was twice shorter than the pentagon, but the illusion, on the contrary, increased from 13.8 to 16.9 arc min P = 0.176. C. When the open rectangle was presented (left section in Fig.1), the illusion strength did not change: 13.8 → 13.1 arc min P = 0.716, regardless of the stimulus change in spatial structure. D. When the vertical segment was removed from the open rectangle, and two parallel horizontal lines remained, the illusion increased: 13.1 → 17.4 arc min P = 0.015. E. If two vertical segments were added to the two horizontal lines to make the stimulus a rectangle, the strength of the illusion slightly decreased: 17.4 → 15.5 arc min P = 0.278. Conclusions. Components of a visual stimulus presented as isolated should be considered full-fledged objects in the size comparison procedure. The individual shape of an object determines the strength of the size expansion. A sum of the expansions of the size of stimulus parts significantly differs from the expansion of the whole. The present experimental data favor the functional relationships of the contour segments forming the shape, not the integration of reactions to each segment during the relative size estimation.

An increase in the relative size of visual objects (the illusion of expansion) was constantly observed in psychophysical experiments with stimuli that differed in shape, size, and orientation and were outlined by a spatial contrast in luminance, color, or texture, also defined by lines, perceptual grouping, and subjective (illusory). The strength of the illusion monotonously increased from a minimum to about 20 arc min with an increase in the length of the stimuli from 25 to 225 arc min for various contours tested, except the Kanizsa type. The latter caused twice weaker effects: the maximum value approached 10 arc min. Thus, subjective contours provided a weaker spatial signal than real ones. The contour may not be a uniform condition for the illusion. To test the prediction, the following type of contour was taken for experiments - defined by motion. Borders of the rectangular-shaped stimulus were formed by random-dot patterns drifting on a stationary random-dot background. In the absence of drift, the rectangle became invisible. The data obtained showed intriguing news – the absence of overestimation of the relative length of the stimulus in the judgments. Even more, all subjects produced gentle errors of underestimation of the distance. The average value lowered from about zero to -5 arc min with increasing the stimulus length from 25 to 225 arc min. The present result agreed to some extent with previous literature data demonstrating changes in perceived size for moving objects, e.g.: grating motion’s apparent position shifted in the direction of motion, and moving objects seemed smaller. Taken together, the present result showed an exception to the general rule – the contours of motion do not create the illusion of expansion.

The motion-defined contours did not create the illusion of expansion. Conversely, a slight decrease in the relative length was recorded in experiments with a comparison of the reference and test distances. This physiological feature of motion contours distinguished them from other types of edges: outlined by contrast in luminance, color, and texture or determined by lines, perceptual grouping, and imaginary boundaries. According to the literature data, moving objects appeared smaller than static ones, and the decrease in size was greater for faster speeds. But whether this rule of relative size reduction also applies to objects that do not move on the background, and only their contours are determined by moving elements – this was the purpose of this study. In the experimental presentations, random-spot patterns rectangular in shape were sliding top dawn on a stationary random-spot background. Different speeds of surface movement were used: 0.25°, 1°, 2°, 3°, 4°, and 5° per second. Subjects judged the width of the referential rectangle by using the adjustments method. The values of the perceived relative length as functions of the stimulus size were established. The size expansion signs were absent in the data obtained. The average error value reached -3 arc min, and one-on-one dropped to -6 or -10 arc min. A barely noticeable decrease in perceived relative width with increasing stimulus size was present at all speeds. However, it cannot be said with certainty that the speed of internal movement has almost no effect on the perceived relative size. Random spot texture patterns have a wide range of spatial frequencies and can sum up different contributions at different movement speeds. Further studies are recommended. Frequency mixing can be avoided by using sinusoidal gratings.

The aim of the study was the illusion of the stimulus size depending on the configuration of the stimulus contour. Incomplete contour stimuli were obtained by removing from the pentagon: either a horizontal, vertical, or diagonal contour line, or a combination of lines forming the angle or rectangle. The expansion effect was always present without any exceptions, as in psychophysical experiments with stimuli of full contours. If the lower horizontal line was not present in the contour of the pentagon, the illusion did not change much, 8 to 9 arc min. When two lower lines, horizontal and diagonal were absent, there was an increase in strength of the illusion from 8 to 13 arc min. Apparently, this happened because the angular component was destroyed and the effect of the Müller-Lyer inner wings, causing a reduction in distance, weakened. If only the angular component, a pair of wings, was exposed, the strength of the illusion did not decrease, although the stimulus became shorter than the entire figure. On the contrary, there was an increase of the illusion from 8 to 13 arc min. Thus, the ratio of the effects of expansion and reduction changed. The expansion was on the decline, and the reduction was also declining, but to a higher degree. If the angular component was absent, and the contour of the open rectangle remained, the stimulus became shorter again. But the illusion significantly increased (8 to 17 arc min) referring to the strengthening of the expansion effect and weakening of reduction. For two horizontal lines, the result slightly increased. For the full rectangle, the illusion has also increased. In general, the ratio of expansion and reduction processes varied greatly in the responses to the stimuli during the length matching procedure. The local components of the stimuli were clearly affected by the configurations to which they belonged. The visual perception of the form cannot be divided into the perception of components and folded back like geometric drawings. When separated, any single segment, such as a line, angle, and the rest of the figure, become new visual wholes, regardless of the fact that the mosaic of excitations caused by them in the retina remains almost unchanged. The main factor of perceived distortions in the size of visual stimuli should be considered the functional relationships of the contour segments forming the shape, and not the integration of neural reactions for each segment.

In psychophysical experiments with illusory Kanizsa-type rectangles, observers perceived the distance between non-existent boundaries as longer than determined by the stimulus drawings. The elongation value gradually grew when the length of rectangles increased similar to experiments with real contoured and filled rectangles. In experiments with the Oppel-Kundt stimulus, according to the classics, the perceived length of the filled interval first increased from zero to maximum and then slightly decreased with the number of stripes (0–30). If the filling stripes were removed from the stimulus, but their endpoints remained, the perceptual errors did not disappear, only the experimental curve decreased somewhat, and the maximum smoothed. If two horizontal lines were added to the filled Oppel-Kundt stimulus interval, forming a contour rectangle, the perceptual errors were also pre-sent but remained approximately stable with various numbers of the filling stripes, and the curve approached the horizontal line. The data obtained showed that illusory contours could be as effective as real edges in the genesis of size expansion. The sense of illusory outline arose and intensified with increasing number of points in the line. The results confirmed the assumption that the Oppel-Kundt effect is an individual case of a general sensory phenomenon: the illusion of the size of visual objects. The decisive feature of the Oppel-Kundt object is horizontal illusory contours. The filling stripes themselves area uxiliary functional factors that, indicating the properties of the stimulus surface, emphasize its edges.

In a study of whether textural contours evoke the illusion of size, psychophysical experiments were carried out with stimuli of synthetic textures of diagonal lines of fixed spatial frequency. Three versions of stimuli were formed: A, a rectangle and background, which differed from each other in the orientation of the textured lines; B, isolated texture rectangle; and C, dark or light rectangular window framed by texture, C1, and C2. Thus, rectangle A was defined by the boundaries of textural cues, while B, C1, and C2 by a combination of texture and brightness signs. For control, contoured and filled rectangles were used, D and E respectively. The subjects evaluated the perceived length of the rectangles presented on the monitor screen per-forming the distance matching task. The illusion of length manifested itself in all cases. It gradually grew stronger for A, B, C1 and C2 when the length of the rectangle sincreased like in experiments with line contours D and brightness contrast E. The average values of the curves(A), (B), (C1), and (C2) were similar to each other. The data obtained confirm the assumption that the encoding of the contours of visual objects is a main prerequisite of the common sensory phenomenon, the illusion of the size of objects. The perceived shape and size are defined by local boundaries, which in turn are determined by marks of brightness or texture.