Part Boundaries Alter the Perception of Transparency

Beyond scattering and absorption: Perceptual unmixing of translucent liquids

Is perception of translucence based on estimations of scattering and absorption of light or on statistical pseudocues associated with familiar materials? We compared perceptual performance with real and computer-generated stimuli. Real stimuli were glasses of milky tea. Milk predominantly scatters light and tea absorbs it, but since the tea absorbs less as the milk concentration increases, the effects of milkiness and strength on scattering and absorption are not independent. Conversely, computer-generated stimuli were glasses of “milky tea” in which absorption and scattering were independently manipulated. Observers judged tea concentrations regardless of milk concentrations, or vice versa. Maximum-likelihood conjoint measurement was used to estimate the contributions of each physical component—concentrations of milk and tea, or amounts of scattering and absorption—to perceived milkiness or tea strength. Separability of the two physical dimensions was better for real than for computer-generated teas, suggesting that interactions between scattering and absorption were correctly accounted for in perceptual unmixing, but unmixing was always imperfect. Since the real and rendered stimuli represent different physical processes and therefore differ in their image statistics, perceptual judgments with these stimuli allowed us to identify particular pseudocues (presumably learned with real stimuli) that explain judgments with both stimulus sets.

Test of Models of Achromatic Transparency

Consider an achromatic disk transparent on an achromatic background formed by two adjoining rectangles, with the common border of the rectangles dividing the disk in half. Current models of achromatic transparency contend that the perceived extent of transparency of the disk depends on the luminance contrast inside the disk and on the luminance contrast in the background outside the disk. Here, a model is proposed which contends that this perceived extent is determined only by the luminance contrasts inherent in the disk: inside the disk and between the disk and the background. Two experiments were designed to determine which luminance contrasts influence transparency. In the first experiment, subjects rated the perceived extent of transparency of the disk for different combinations of the luminances of the disk and of the background. The results strengthen the view that the perceived extent of transparency depends on the luminance contrasts inherent in the disk. In the second experiment, a test was made of the possibility that luminance contrasts between adjoining areas of the background outside the disk are nonessential for transparency. The results show that transparency occurred both when the areas of the background outside the transparent region adjoined one another and when they were separated, confirming that the perceived extent of transparency depended only on luminance contrasts between adjoining areas inherent in the disk.

Perceptual Transparency in 3- to 4-Month-Old Infants

We examined perceptual transparency in infants. In a previous study, Johnson and Aslin (2000 Developmental Psychology36 808 – 816) found that 4-month-olds could perceive transparency in a moving chromatic display, but not in an achromatic display. In this study, we further examined perceptual transparency in infants using a static achromatic display. Considering the development of figural organisation and contrast sensitivity, we assumed that 3- to 4-month-olds would perceive transparency even in a static achromatic display. We created a transparency and a non-transparent display composed of a partially overlapping circle and square, by switching the colours. Infants aged 3 to 4 months ( n = 24) were familiarised with the transparency display (experiment 1) or with the non-transparent display (experiment 2). Then, they were confronted with a uniform colour and a two-colour figure. Infants showed novelty preference for the two-colour figure after they had been familiarised with the transparency display (experiment 1), but not after they had been familiarised with the non-transparent display (experiment 2). These results suggest that 3- to 4-month-old infants can perceive transparency in a static achromatic display.

Early Computation of Contour Curvature and Part Structure: Evidence from Holes

We used holes to study unilateral border ownership and in particular the information carried by the sign of the curvature along the contour (ie the difference between convex and concave regions). When people perceive a hole, its shape has a reversed curvature polarity (ie a changed sign of curvature) compared to the same region perceived as an object. Bertamini (2001 Perception30 1295–1310), and Bertamini and Croucher (2003 Cognition87 33–54) suggested and found evidence to support the hypothesis that, because convex regions are perceived as parts, positional information is more readily available for convex regions. Therefore a change is predicted when a given region is perceived as either a hole or a figure. We confirm that finding in this study, using holes defined by binocular disparity. We conclude that a change from figure to hole always reverses the encoding of curvature polarity. In turn, polarity obligatorily affects perceived part structure and the processing of position.

The Role of Part Structure in the Perceptual Localization of a Shape

The process of object localization may be accomplished with respect to a particular reference location, such as the center of gravity, COG (eg Vishwanath and Kowler, 2003 Vision Research43 1637 – 1653). Here, we investigated how part structure affects an object's reference location. The reference location was evaluated with a measure of the illusory displacement of an internal target element embedded within a larger object (Morgan et al, 1990 Vision Research30 1793 – 1810). To examine whether the reference location is different for shapes with part structure, two shapes were tested: circle (small and large; no part structure) and bell (shape with two parts, one larger than the other). Results were examined with respect to two predictions: either the location of an object is based on its shape as a whole, disregarding part structure (ie a single, overall COG), or the parts are processed separately (different COGs).

With the circles, the results showed a systematic illusory displacement of the internal target toward the COG. With the bell, the illusion was significantly weaker than with both circles—even though the main part of the bell had the same size as the small circle, and its horizontal axis had the same extent as the large circle. Moreover, the distance judgments for the bell were consistent with a (weaker) reference point being located at the COG of the larger part, rather than at the COG of the entire bell. These results show that the part structure of a shape plays a role in the representation of its location, and that for complex shapes the perceived location of an embedded element depends more on the parts within which it is embedded, rather than on the whole shape.

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 Psicologia69 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, a. The role of the outline contour in conveying figural and intensity information is discussed.

Investigating shape representation using sensitivity to part- and axis-based transformations

Part- and axis-based approaches organize shape representations in terms of simple parts and their spatial relationships. Shape transformations that alter qualitative part structure have been shown to be more detectable than those that preserve it. We compared sensitivity to various transformations that change quantitative properties of parts and their spatial relationships, while preserving qualitative part structure. Shape transformations involving changes in length, width, curvature, orientation and location were applied to a small part attached to a larger base of a two-part shape. Increment thresholds were estimated for each transformation using a 2IFC procedure. Thresholds were converted into common units of shape difference to enable comparisons across transformations. Higher sensitivity was consistently found for transformations involving a parameter of a single part (length, width, curvature) than those involving spatial relations between two parts (relative orientation and location), suggesting a single-part superiority effect. Moreover, sensitivity to shifts in part location - a biomechanically implausible shape transformation - was consistently poorest. The influence of region-based geometry was investigated via stereoscopic manipulation of figure and ground. Sensitivity was compared across positive parts (protrusions) and negative parts (indentations) for transformations involving a change in orientation or location. For changes in part orientation (biomechanically plausible), sensitivity was better for positive than negative parts; whereas for changes in part location (biomechanically implausible), no systematic difference was observed.

Processing convexity and concavity along a 2-D contour: figure-ground, structural shape, and attention

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims--for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure-ground organization and in parsing, but other, more specific claims are not (yet) well supported.

Phenomenal transparency at X-junctions

Phenomenal transparency was studied in a stimulus geometry that differs markedly from the conventional Metelli configuration, namely four squares that abut at a common vertex. In case of subjective transparency one perceives either a bipartite square ground overlaid with a uniform transparent rectangle, or a uniform square background overlaid with a pair of mutually orthogonal, uniform, transparent rectangular regions. Thus, the generic interpretations are limited to "left", "right", "lower", or "upper" transparent rectangles or (when no subjective transparency occurs) "mosaic". All transparent cases are congruent, whereas the Metelli configuration allows distinct Gestalt interpretations. This avoids interactions between Gestalt factors and subjective transparency per se. Formal analysis reveals that as in Metelli's case a number of ambiguous cases (e.g., "left" or "lower") are to be expected. In the experiment we included these ambiguous cases as additional response categories. Observers who differ markedly on the Metelli configuration are virtually indistinguishable under the quad-square configuration. Moreover, observers reliably categorise the ambiguous instances as such; thus, "multiple transparency" has to be reckoned with as a bona fide percept.

Hue-preserving color blending

We propose a new perception-guided compositing operator for color blending. The operator maintains the same rules for achromatic compositing as standard operators (such as the over operator), but it modifies the computation of the chromatic channels. Chromatic compositing aims at preserving the hue of the input colors; color continuity is achieved by reducing the saturation of colors that are to change their hue value. The main benefit of hue preservation is that color can be used for proper visual labeling, even under the constraint of transparency rendering or image overlays. Therefore, the visualization of nominal data is improved. Hue-preserving blending can be used in any existing compositing algorithm, and it is particularly useful for volume rendering. The usefulness of hue-preserving blending and its visual characteristics are shown for several examples of volume visualization.

Transparency and imaginary colors

Unlike the Metelli monochrome transparencies, when overlays and their backgrounds have chromatic content, the inferred surface colors may not always be physically realizable, and are in some sense "imaginary." In these cases, the inferred chromatic transmittance or reflectance of the overlay lies outside the RGB spectral boundaries. Using the classical Metelli configuration, we demonstrate this illusion and briefly explore some of its attributes. Some observer differences in perceiving transparencies are also highlighted. These results show that the perception of transparency is much more complex than conventionally envisioned.

Gestalt and phenomenal transparency

Phenomenal transparency is commonly studied by using a stimulus configuration introduced by Metelli: a bipartite patch, divided into equal left and right halves is overlaid with a smaller, concentric bipartite patch, divided along the same line. Observers are instructed to report either a transparent patch over an opaque bipartite field or a mosaic of four opaque patches. We show theoretically and empirically that these are only two of five generic perceptual categories, namely, transparent patch, transparent annulus (hole), mosaic, partial transparency, and multiple transparency (ambiguous) cases. Thus Gestalt factors complicate the interpretation "phenomenal transparency." We propose a framework that avoids this complication. There is excellent agreement between predictions and results.

Geometric determinants of shape segmentation: tests using segment identification

The geometric determinants of shape decomposition were studied using a performance-based method. Observers' identification of contour segments was shown to be systematically modulated by their curvature properties, and by the geometric properties of the enclosed region. Specifically, negative minima of contour curvature provided the best segment boundaries. Segments with negative-minima boundaries were identified with greater accuracy than those with positive maxima or inflection boundaries of comparable length. Additionally, segment identification was shown to be determined by contour length, the turning angle at part boundaries, and the width at the part's base (hence the part's protrusion). The results indicate that part decomposition is an automatic process. Moreover, this process is graded, i.e. parts are more strongly segmented, or more likely to be perceived, according to the strength of many geometric determinants.

An advantage for concavities in shape perception by chimpanzees (Pan troglodytes)

The significance of concavity in object shape perception by chimpanzees (Pan troglodytes) was investigated in a matching-to-sample procedure. For the task, chimpanzees were required to choose a polygon stimulus that was identical in shape to a sample. The incorrect alternative was defined by the addition or subtraction of a concave or convex apex. Chimpanzees were more sensitive to the concave deformation than to the convex deformation. This tendency conforms to the theories of human visual perception that have treated concave features as important factors in reconstructing three-dimensional structures from two-dimensional images. Our results suggest that shape representation in chimpanzees is similar to that in humans and that chimpanzees visually process two-dimensional images in the same manner as humans.

Photometric determinants of perceived transparency

Photometric constraints for the perception of transparency were investigated using stereoscopic textured displays. A contrast discontinuity divided the textured displays into two lateral halves, with one (reference) half fixed. Observers adjusted the luminance range within the other (test) half in order to perform two tasks: (i) indicate the highest luminance range for which the test side is perceived to be transparent, and (ii) indicate the lowest luminance range for which the test side is seen as being in plain view. Settings were obtained for multiple values of test mean luminance, in order to map out the perceptual locus of transition between transparency and non-transparency. The results revealed a systematic violation of Metelli's magnitude constraint in predicting the percept of transparency. Observer settings were approximated instead by a constraint based on perceived contrast (which matched Michelson contrast for the textures used). The results also revealed large asymmetries between darkening and lightening transparency. When the test was darker than the reference, settings were highly consistent across observers and closely followed the Michelson-contrast prediction. When the test was lighter, however, there was greater variability across observers, with two observers exhibiting shifts toward Metelli's magnitude constraint. Moreover, each observer's setting reliability was significantly worse for lightening transparency than darkening transparency. These results suggest that (polarity-preserving) darkening serves as an additional cue to perceptual transparency.

Segmentation of object outlines into parts: a large-scale integrative study

In this study, a large number of observers (N=201) were asked to segment a collection of outlines derived from line drawings of everyday objects (N=88). This data set was then used as a benchmark to evaluate current models of object segmentation. All of the previously proposed rules of segmentation were found supported in our results. For example, minima of curvature (i.e. locations along the contour where negative curvature takes an extreme value) were often used as segmentation points. The second point of a pair connected by a segmentation line often depended on more global shape characteristics such as proximity, collinearity, symmetry, and elongation. Based on these results, a framework is presented in which all of the previously proposed (and now empirically validated) segmentation rules or rules for part formation are integrated.

Information Along Contours and Object Boundaries

F. Attneave (1954) famously suggested that information along visual contours is concentrated in regions of high magnitude of curvature, rather than being distributed uniformly along the contour. Here the authors give a formal derivation of this claim, yielding an exact expression for information, in C. Shannon's (1948) sense, as a function of contour curvature. Moreover, they extend Attneave's claim to incorporate the role of sign of curvature, not just magnitude of curvature. In particular, the authors show that for closed contours, such as object boundaries, segments of negative curvature (i.e., concave segments) literally carry greater information than do corresponding regions of positive curvature (i.e., convex segments). The psychological validity of this informational analysis is supported by a host of empirical findings demonstrating the asymmetric way in which the visual system treats regions of positive and negative curvature.

Lightness constancy through transparency: internal consistency in layered surface representations

Asymmetric lightness matching was employed to measure how the visual system assigns lightness to surface patches seen through partially-transmissive surfaces. Observers adjusted the luminance of a comparison patch seen through transparency, in order to match the lightness of a standard patch seen in plain view. Plots of matched-to-standard luminance were linear, and their slopes were consistent with Metelli's alpha. A control experiment confirmed that these matches were indeed transparency based. Consistent with recent results, however, when observers directly matched the transmittance of transparent surfaces, their matches deviated strongly and systematically from Metelli's alpha. Although the two sets of results appear to be contradictory, formal analysis reveals a deeper mutual consistency in the representation of the two layers. A ratio-of-contrasts model is shown to explain both the success of Metelli's model in predicting lightness through transparency, and its failure to predict perceived transmittance--and hence is seen to play the primary role in perceptual transparency.

Effects of partial occlusion on perceived surface segregation

Tests are reported of the possibility that local information from contour junctions and from corners of intersecting surfaces is used for perceived surface segregation. Stimuli were two intersecting squares with small disks occluding different parts of the squares. The perceived segregation of the squares from one another decreased as the amount of occlusion of parts of the squares increased. This segregation was less when disks occluded parts of contours than when disks occluded parts entirely inside the squares. Occlusion of parts of contours reduced segregation independently of whether contour junctions or corners were visible or invisible, both where the intersecting surfaces were transparent squares and when they were outlined squares. The present findings show that local information from contour junctions or from corners is not used for surface segregation, and confirm that this segregation is determined by global processes of grouping of areas and of extrapolation of contours.

Visual comparisons within and between object parts: evidence for a single-part superiority effect

Subjects judged whether two marks placed at different positions along a curved contour were physically the same. When targets were separated by a concave curvature extremum--corresponding to a part-boundary--decision latencies were longer than when they straddled an equally curved convex extremum, demonstrating a "single-part superiority effect". This difference increased with both stimulus duration and the magnitude of contour curvature. However, it disappeared when the global configuration was not consistent with a part-boundary interpretation, suggesting a critical role of global organization in part decomposition.

Achromatic transparency and the role of local contours

In this paper we investigate the role of contours and junctions in the perception of single-plane achromatic transparency. In order to measure the accuracy with which observers encode transparency, a six-luminance stimulus was employed in which the figural properties could be easily manipulated. Accuracy was measured by requiring subjects to select (either by the method of adjustment or by using a forced-choice procedure) the luminance that best completed a simulated transparent filter. The X junctions in the stimulus were destroyed or perturbed in three experiments. Simple occlusion of the junction (experiment 1), and perturbation of the orientation of the contours of the filter as they pass through the junction (experiment 3) resulted in small but significant reductions in performance. On the other hand, a sudden change in orientation of the background (material) contours (experiment 2) resulted in a small but significant enhancement of overall performance compared with the control stimulus. In the forced-choice task, reversals in the polarity of contours (as defined by the brightness order of flanking regions) around the junction were shown to effect large changes in subjects' accuracy in processing transparency. The overall results show that X and Psi junctions are indeed salient properties of transparent stimuli. The findings suggest that jagged contours with sudden changes in direction are more likely to be attributed to reflectance (material) changes than to changes due to a transparent filter (or to illumination).

Early computation of part structure: evidence from visual search

The visual system represents object shapes in terms of intermediate-level parts. The minima rule proposes that the visual system uses negative minima of curvature to define boundaries between parts. We used visual search to test whether part structures consistent with the minima rule are computed preattentively--or at least, rapidly and early in visual processing. The results of Experiments 1 and 2 showed that whereas the search for a non-minima-segmented shape is fast and efficient among minima-segmented shapes, the reverse search is slow and inefficient. This asymmetry is expected if parsing at negative minima occurs obligatorily. The results of Experiments 3 and 4 showed that although both minima- and non-minima-segmented shapes pop out among unsegmented shapes, the search for minima-segmented shapes is significantly slower. Together, these results demonstrate that the visual system segments shapes into parts, using negative minima of curvature, and that it does so rapidly in early stages of visual processing.

Toward a perceptual theory of transparency

Theories of perceptual transparency have typically been developed within the context of a physical model that generates the percept of transparency (F. Metelli's episcotister model, 1974b). Here 2 fundamental questions are investigated: (a) When does the visual system initiate the percept of one surface seen through another? (b) How does it assign surface properties to a transparent layer? Results reveal systematic deviations from the predictions of Metelli's model, both for initiating image decomposition into multiple surfaces and for assigning surface attributes. Specifically, results demonstrate that the visual system uses Michelson contrast as a critical image variable to initiate percepts of transparency and to assign transmittance to transparent surfaces. Findings are discussed in relation to previous theories of transparency, lightness, brightness, and contrast-contrast.

Perceptual assignment of opacity to translucent surfaces: the role of image blur

In constructing the percept of transparency, the visual system must decompose the light intensity at each image location into two components one for the partially transmissivc surface, the other for the underlying surface seen through it. Theories of perceptual transparency have typically assumed that this decomposition is defined quantitatively in terms of the inverse of some physical model (typically, Metelli's 'episcotister model'). In previous work, we demonstrated that the visual system uses Michelson contrast as a critical image variable in assigning transmittance to transparent surfaces not luminance differences as predicted by Metelli's model [F Metelli, 1974 Scientific American 230(4) 90 98]. In this paper, we study the contribution of another variable in determining perceived transmittance, namely, the image blur introduced by the light-scattering properties of translucent surfaces and materials. Experiment 1 demonstrates that increasing the degree of blur in the region of transparency leads to a lowering in perceived transmittance, even if Michelson contrast remains constant in this region. Experiment 2 tests how this addition of blur affects apparent contrast in the absence of perceived transparency. The results demonstrate that, although introducing blur leads to a lowering in apparent contrast, the magnitude of this decrease is relatively small, and not sufficient to explain the decrease in perceived transmittance observed in experiment 1. The visual system thus takes the presence of blur in the region of transparency as an additional image cue in assigning transmittance to partially transmissive surfaces.

Precision, accuracy, and range of perceived achromatic transparency

How accurately do human observers perceive the properties of an achromatic transparent filter with both reflective and transmissive components? To address this question, a novel six-luminance stimulus was employed, consisting of three transparent layer luminances set against three background luminances, which satisfied the conventional constraints of perceptual transparency. In one experiment, subjects adjusted one of the three layer luminances to complete the impression of a uniform transparent disk. It was found that the luminance-based formulation of Metelli's episcotister model and a model based on ratios of Michelson contrasts best predicted the subjects' settings, which were both accurate and precise. In another experiment, pairs of stimuli selected from a range with various values of the adjustable layer luminance were presented in a series of forced-choice trials. A modified implementation of the pair comparisons method was employed to recover the distribution that describes each subject's preference pattern. Results showed that there exists a reasonably wide range of stimuli that give rise to at least some degree of perceived transparency.

Completing visual contours: the relationship between relatability and minimizing inflections

Visual completion is a ubiquitous phenomenon: Human vision often constructs contours and surfaces in regions that have no sharp gradients in any image property. When does human vision interpolate a contour between a given pair of luminance-defined edges? Two different answers have been proposed: relatability and minimizing inflections. We state and prove a proposition that links these two proposals by showing that, under appropriate conditions, relatability is mathematically equivalent to the existence of a smooth curve with no inflection points that interpolates between the two edges. The proposition thus provides a set of necessary and sufficient conditions for two edges to be relatable. On the basis of these conditions, we suggest a way to extend the definition of relatability (1) to include the role of genericity, and (2) to extend the current all-or-none character of relatability to a graded measure that can track the gradedness in psychophysical data.

Parsing silhouettes: the short-cut rule

Many researchers have proposed that, for the purpose of recognition, human vision parses shapes into component parts. Precisely how is not yet known. The minima rule for silhouettes (Hoffman & Richards, 1984) defines boundary points at which to parse but does not tell how to use these points to cut silhouettes and, therefore, does not tell what the parts are. In this paper, we propose the short-cut rule, which states that, other things being equal, human vision prefers to use the shortest possible cuts to parse silhouettes. We motivate this rule, and the well-known Petter's rule for modal completion, by the principle of transversality. We present five psychophysical experiments that test the short-cut rule, show that it successfully predicts part cuts that connect boundary points given by the minima rule, and show that it can also create new boundary points.