Gauge Figure Research Articles

Binocular Information Improves the Reliability and Consistency of Pictorial Relief

Binocular disparity is an important cue to three-dimensional shape. We assessed the contribution of this cue to the reliability and consistency of depth in stereoscopic photographs of natural scenes. Observers viewed photographs of cluttered scenes while adjusting a gauge figure to indicate the apparent three-dimensional orientation of the surfaces of objects. The gauge figure was positioned on the surfaces of objects at multiple points in the scene, and settings were made under monocular and binocular, stereoscopic viewing. Settings were used to create a depth relief map, indicating the apparent three-dimensional structure of the scene. We found that binocular cues increased the magnitude of apparent depth, the reliability of settings across repeated measures, and the consistency of perceived depth across participants. These results show that binocular cues make an important contribution to the precise and accurate perception of depth in natural scenes that contain multiple pictorial cues.

Multisensory integration and the experience of scene instability, presence and cybersickness in virtual environments

Multisensory integration is critical for supporting human spatial perception as we move around our environment. In this study, we used a modern head-mounted display (HMD) as a tool for studying the effects of visual-vestibular conflict on human spatial perception, feelings of presence and cybersickness in virtual reality (VR). Thirty participants were recruited and exposed to different levels of sensory conflict as they moved their heads in pitch. This sensory conflict was generated by artificially delaying updates to the visual representations of their virtual environment. On each trial we measured our participants': 1) perceived scene instability using an angular gauge figure task; 2) spatial presence using a subjective rating scale, and 3) cybersickness severity using the fast motion sickness (FMS) scale. As display lag was increased, perceived scene instability and cybersickness were both found to increase, whereas reported presence decreased. Importantly, the difference in the participant's virtual and physical head orientation (DVP) for the trial was also found to predict reported scene instability and cybersickness. Faster head rotations (at 1.0 Hz compared with 0.5 Hz) amplified both of these adverse effects (presumably due to the increase in DVP). These findings are consistent with the view that measurable low-level visual-vestibular conflicts can account for the cybersickness experienced during HMD VR.

Edge-Based Shading as a Depth Cue in Paintings

We explored how an artist who uses a particular monochrome modern painting style generates the impression of relief in paintings. Three portraits, painted after model, were created especially for the experiment. Photographs of the paintings were presented on a computer screen. To investigate the perceived relief of observers we used a gauge figure task. We expected an effect of background contrast on perceived total depth range of the relief, because this is well known in the case of photography. We found that the contrast with the color of the canvas, white, gray or black, influences the perceived articulation of the relief but does not influence the perceived total depth range of the relief. The major difference between photographs and these paintings is that contrasts in the paintings are built up through edge-based shading, whereas photographs mostly contain tonal-area shading. The classical shape from shading cue does not apply to the impressions of depth evoked by the paintings. Perhaps surprisingly edge-based shading can be as effective as classical ways of creating pictorial relief.

Predicting 3D shape perception from shading and texture flows

Perceiving 3D shape involves processing and combining different cues, including texture, shading, and specular reflections. We have previously shown that orientation flows produced by the various cues provide fundamentally different information about shape, leading to complementary strengths and weaknesses (see Cholewiak & Fleming, VSS 2013). An important consequence of this is that a given shape may appear different, depending on whether it is shaded or textured, because the different cues reveal different shape features. Here we sought to predict specific regions of interest (ROIs) within shapes where the different cues lead to better or worse shape perception. Since the predictions were derived from the orientation flows, our analysis provides a key test of how and when the visual system uses orientation flows to estimate shape. We used a gauge figure experiment to evaluate shape perception. Cues included Lambertian shading, isotropic 3D texture, both shading and texture, and pseudo-shaded depth maps. Participant performance was compared to a number of image and scene-based perceptual performance predictors. Shape from texture ROI models included theories incorporating the surface's slant and tilt, second-order partial derivatives (i.e., change in tilt direction), and tangential and normal curvatures of isotropic texture orientation. Shape from shading ROI models included image based metrics (e.g., brightness gradient change), anisotropy of the second fundamental form, and surface derivatives. The results confirm that individually texture and shading are not diagnostic of object shape for all locations, but local performance correlates well with ROIs predicted by first and second-order properties of shape. The perceptual ROIs for texture and shading were well predicted via the mathematical models. In regions that were ROI for both cues, shading and texture performed complementary functions, suggesting that a common front-end based on orientation flows can predict both strengths and weaknesses of different cues at a local scale. Meeting abstract presented at VSS 2014

Is the Perception of 3D Shape from Shading Based on Assumed Reflectance and Illumination?

This research was designed to compare three types of image shading: One generated with a Lambertian BRDF and homogeneous illumination such that image intensity was determined entirely by local surface orientation irrespective of position; one that was textured with a linear intensity gradient, such that image intensity was determined entirely by local surface position irrespective of orientation; and another that was generated with a Lambertian BRDF and inhomogeneous illumination such that image intensity was influenced by both position and orientation. A gauge figure adjustment task was used to measure observers' perceptions of local surface orientation on the depicted surfaces, and the probe points included 60 pairs of regions that both had the same orientation. The results show clearly that observers' perceptions of these three types of stimuli were remarkably similar, and that probe regions with similar apparent orientations could have large differences in image intensity. This latter finding is incompatible with any process for computing shape from shading that assumes any plausible reflectance function combined with any possible homogeneous illumination. Meeting abstract presented at VSS 2014

Is the perception of 3D shape from shading based on assumed reflectance and illumination?

The research described in the present article was designed to compare three types of image shading: one generated with a Lambertian BRDF and homogeneous illumination such that image intensity was determined entirely by local surface orientation irrespective of position; one that was textured with a linear intensity gradient, such that image intensity was determined entirely by local surface position irrespective of orientation; and another that was generated with a Lambertian BRDF and inhomogeneous illumination such that image intensity was influenced by both position and orientation. A gauge figure adjustment task was used to measure observers' perceptions of local surface orientation on the depicted surfaces, and the probe points included 60 pairs of regions that both had the same orientation. The results show clearly that observers' perceptions of these three types of stimuli were remarkably similar, and that probe regions with similar apparent orientations could have large differences in image intensity. This latter finding is incompatible with any process for computing shape from shading that assumes any plausible reflectance function combined with any possible homogeneous illumination.

Shape perception of thin transparent objects with stereoscopic viewing

Many materials, including water surfaces, jewels, and glassware exhibit transparent refractions. The human visual system can somehow recover 3D shape from refracted images. While previous research has elucidated various visual cues that can facilitate visual perception of transparent objects, most of them focused on monocular material perception. The question of shape perception of transparent objects is much more complex and few studies have been undertaken, particular in terms of binocular vision. In this article, we first design a system for stereoscopic surface orientation estimation with photo-realistic stimuli. It displays pre-rendered stereoscopic images and a real-time S3D (Stereoscopic 3D) shape probe simultaneously. Then we estimate people's perception of the shape of thin transparent objects using a gauge figure task. Our results suggest that people can consistently perceive the surface orientation of thin transparent objects, and stereoscopic viewing improves the precision of estimates. To explain the results, we present an edge-aware orientation map based on image gradients and structure tensors to illustrate the orientation information in images. We also decomposed the normal direction of the surface into azimuth angle and slant angle to explain why additional depth information can improve the accuracy of perceived normal direction.

Relative flattening between velvet and matte 3D shapes: Evidence for similar shape-from-shading computations

Among other cues, the visual system uses shading to infer the 3D shape of objects. The shading pattern depends on the illumination and reflectance properties (BRDF). In this study, we compared 3D shape perception between identical shapes with different BRDFs. The stimuli were photographed 3D printed random smooth shapes that were either painted matte gray or had a gray velvet layer. We used the gauge figure task (J. J. Koenderink, A. J. van Doorn, & A. M. L. Kappers, 1992) to quantify 3D shape perception. We found that the shape of velvet objects was systematically perceived to be flatter than the matte objects. Furthermore, observers' judgments were more similar for matte shapes than for velvet shapes. Lastly, we compared subjective with veridical reliefs and found large systematic differences: Both matte and velvet shapes were perceived more flat than the actual shape. The isophote pattern of a flattened Lambertian shape resembles the isophote pattern of an unflattened velvet shape. We argue that the visual system uses a similar shape-from-shading computation for matte and velvet objects that partly discounts material properties.

Probing pictorial relief: from experimental design to surface reconstruction

The perception of pictorial surfaces has been studied quantitatively for more than 20 years. During this time, the “gauge figure method” has been shown to be a fast and intuitive method to quantify pictorial relief. In this method, observers have to adjust the attitude of a gauge figure such that it appears to lie flat on a surface in pictorial space. Although the method has received substantial attention in the literature and has become increasingly popular, a clear, step-by-step description has not been published yet. In this article, a detailed description of the method is provided: stimulus and sample preparation, performing the experiment, and reconstructing a 3-D surface from the experimental data. Furthermore, software (written in PsychToolbox) based on this description is provided in an online supplement. This report serves three purposes: First, it facilitates experimenters who want to use the gauge figure task but have been unable to design it, due to the lack of information in the literature. Second, the detailed description can facilitate the design of software for various other platforms, possibly Web-based. Third, the method described in this article is extended to objects with holes and inner contours. This class of objects have not yet been investigated with the gauge figure task.

The preferred angle of illumination in shape from shading

Recovering 3D shape from shading is an ill-posed problem which the visual system can resolve only after making assumptions about the lighting, surface material, and/or viewpoint. Previous research has shown that people tend to assume light is above and slightly to the left [Sun and Perona 1998], but it is not known whether there is also an assumed elevation angle of the light with respect to the viewpoint. Consider a plane containing the eye, the point of interest, and the assumed light position. In this paper, we investigate whether there is an assumed elevation of light within this plane by measuring observer percepts of surface orientation with varying angles of light above or below the viewpoint. The estimations of surface orientation were made on smooth, virtual 3D shapes displayed monocularly using local Lambertian shading. We varied the elevation angle of light within a range +/66 deg (above/below) from the viewpoint, and subjects indicated local surface orientation at specified points on the shape by rotating a gauge figure to appear normal to the surface [Koenderink et al. 1992]. Observer settings were more accurate when the light was positioned above rather than below the viewpoint. Additionally, the angular difference between the indicated and actual surface normal was minimized when the light was 20-30 deg above the viewpoint. Measurements of slant and tilt error, as well as the variance of settings, support this result. These findings confirm that the human visual system has an aboveand-left prior for light position and demonstrate that the preferred position is 20-30 deg above the viewpoint.

The Effects of Mirror Reflections and Planar Rotations of Pictures on the Shape Percept of the Depicted Object

Mirror reflections and planar rotations of a picture do not result in any variations concerning the internal geometrical layout of the objects depicted in the picture. We examined to what extent these picture plane transformations gave rise to perceptual differences. A large set of pictures was generated by mirror-reflecting and rotating a set of six original photographs in the picture plane. We externalised the percepts of the depicted objects by using a direct perceptual method: the gauge-figure method. Participants had to adjust a gauge figure so that it seemed to be painted on the surface of the depicted object. From an extensive set of settings collected this way, we computed for each picture the three-dimensional interpretation--or pictorial relief--of the depicted object. On the basis of this set of pictorial reliefs, we addressed the effects of mirror reflections and rotations of pictures on the shape percept of the depicted object. Mirror-reflecting a picture around the horizontal axis resulted in large differences in pictorial reliefs, whereas mirror-reflecting pictures around the vertical axis resulted in only small differences in pictorial reliefs. Clockwise 90 degrees, 180 degrees, and 270 degrees rotation affected the pictorial relief significantly. In all cases, the differences between the pictorial reliefs could be resolved by affine transformations, and could thus be ascribed to different solutions of the depth ambiguities inherent in pictures.

Aging and the perception of local surface orientation from optical patterns of shading and specular highlights

Younger and older observers' ability to perceive local surface orientation from optical patterns of shading and specular highlights was investigated in two experiments. On each trial, the observers viewed a randomly generated, smoothly curved 3-D object and manipulated an adjustable gauge figure until its orientation matched that of a specific local region on the object's surface (cf. Koenderink, van Doom, & Kappers, 1992). The performance of both age groups was facilitated by the presence of binocular disparity (Experiment 1) and object rotation in depth (Experiment 2). Observers in both age groups were able to judge the surface tilt component of orientation more precisely than the slant component. Significant, but modest, effects of age were found in Experiment 1, but not in Experiment 2. The ability to perceive local surface orientation appears to be relatively well preserved with increasing age, at least through the age of 80.

Recovering slant and angular velocity from a linear velocity field: modeling and psychophysics

The data from two experiments, both using stimuli simulating orthographically rotating surfaces, are presented, with the primary variable of interest being whether the magnitude of the simulated gradient was from expanding vs. contracting motion. One experiment asked observers to report the apparent slant of the rotating surface, using a gauge figure. The other experiment asked observers to report the angular velocity, using a comparison rotating sphere. The results from both experiments clearly show that observers are less sensitive to expanding than to contracting optic-flow fields. These results are well predicted by a probabilistic model which derives the orientation and angular velocity of the projected surface from the properties of the optic flow computed within an extended time window.

The contributions of slant and tilt to the detection of local surface orientation in structure from motion

The contribution of slant and tilt to the detection of differences in local surface orientation was examined for structure-from-motion (SFM) displays of a complex sinusoidal surface. Observers judged whether an elliptical SFM gauge figure appeared to be lying on the surface or intersecting it. The gauge figure orientation either matched the local surface orientation or differed from it in slant, tilt, or both. Similar sensitivity was found for deviations in slant and tilt, but greater biases and variability were found when the gauge figure deviated from the local surface orientation in slant, depending on the sign of the difference between the gauge figure and local surface orientation and the position of the gauge figure. The results are consistent with Stevens’ ( Biological Cybernetics, 46 (1983) 183–195) discussion of the computational advantages of slant and tilt contributing independently to the detection of differences in local surface orientation. The effects of changes in perceived surface slant and tilt during rotation and of the misperception of surface depth on the detection of local orientation in dynamic images are discussed.

Effects of texture, illumination, and surface reflectance on stereoscopic shape perception.

Observers viewed computer-generated stereograms of randomly structured smooth surfaces and were required to judge the perceived local orientation at numerous probe points by adjusting a monocular gauge figure. The surfaces were depicted with specular or Lambertian reflectance functions, either with or without identifiable texture elements, and with varying directions of illumination. The results revealed a strong linear correlation between the judged patterns of relief and the actual depicted objects, though there were systematic differences in the magnitude of depth scaling in the different conditions. In general, the accuracy and reliability of observers' judgments for the smoothly shaded shiny surfaces was slightly lower than for the textured surfaces and slightly higher than for the smoothly shaded Lambertian surfaces. The direction of illumination had no detectable effect on the observers' judgments.

Perception of local orientation from shaded images.

The perception of local orientation from shaded images was examined. In Experiment 1, subjects viewed a boundaryless Gaussian hill and judged local orientation using both a gauge figure and a pointing method. One subject reported an internally consistent surface which was incompatible with the judged light-source direction and model used to generate the image. The remaining subjects reported a surface similar to the generating one, and analysis of their results indicated a contour of zero difference between response and generating slants. This contour of zero slant difference was explored in three subsequent experiments using the pointing technique. These experiments investigated possible influences of luminance artifact (Experiment 2), perception of global orientation (Experiment 3), and self-occluding contours (Experiment 4). All three of these experiments yielded results similar to those of Experiment 1, with distinct contours of zero slant difference. This contour was explored for relationships with the simulated slant of the generating surface and the differential structure of image intensity. This analysis indicated that the contour of zero slant difference was approximately a line of constant slant which shared large regions of adjacency to the zero crossings of the second directional derivative of image intensity.

Effects of changing viewing conditions on the perceived structure of smoothly curved surfaces.

Observers' perceptions of a male and a female torso were investigated using monocular and stereoscopic images under varying conditions of illumination. Observers judged the shapes of these torsos by adjusting a gauge figure to estimate the local slant and tilt at numerous probe points arranged in a lattice over the torso's surface. The results revealed that the judged surfaces in the monocular and stereoscopic conditions were related by an affine stretching transformation in depth that accounted for approximately 95% of the between-condition variance. There was also a strong affine component between the judgments obtained for the different illumination directions, although a further analysis of the residuals indicated that changing the direction of illumination influenced perceived structure in a piecewise manner.

Effects of changing viewing conditions on the perceived structure of smoothly curved surfaces.

Observers' perceptions of a male and a female torso were investigated using monocular and stereoscopic images under varying conditions of illumination. Observers judged the shapes of these torsos by adjusting a gauge figure to estimate the local slant and tilt at numerous probe points arranged in a lattice over the torso's surface. The results revealed that the judged surfaces in the monocular and stereoscopic conditions were related by an affine stretching transformation in depth that accounted for approximately 95% of the between-condition variance. There was also a strong affine component between the judgments obtained for the different illumination directions, although a further analysis of the residuals indicated that changing the direction of illumination influenced perceived structure in a piecewise manner.

Surface range and attitude probing in stereoscopically presented dynamic scenes.

The authors report on different methods to probe the structure of visually perceived surfaces in 3 dimensions. The surfaces are specified by patterns of shading with Lambertian and specular components, which deform over time and over stereoscopic views. Five observers performed 2 probe tasks, 1 involving the adjustment of a punctate probe so as to be on the apparent surface and the other involving the adjustment of a small gauge figure that indicates surface attitude. The authors found that these rather different methods yielded essentially identical depth maps up to a linear transformations and that the observers all deviate slightly from veridicality in basically identical ways. The nature of this deviation appears to be correlated with the rough topography of the specularities.

Depth relief.

A study is reported of the depth relief in a simple three-dimensional scene consisting of a white, rough sphere on a planar support, illuminated in a natural manner. Viewing conditions included monocular and binocular as well as 'synoptical' viewing. In the synoptical condition the eyes are optically superimposed. The local surface attitude was probed via a gauge figure that had to appear as a circle painted upon the surface of the object. The measurements allow a reconstruction of the depth relief, which can be compared with the (known) range map. Idiosyncratic differences between three subjects were found that are the exact reverse of what was found for these same subjects for the case of pictorial relief reported in an earlier paper. Apparently the subjects put different weights on sources of sometimes conflicting, sometimes corroborative evidence. The relief is deepest for binocular vision, flatter for monocular vision, and flatter still for synoptical vision. Deviations from veridicality that cannot be explained by mere depth scaling exist and may be due to the nature of the monocular cues.