Measuring perceived 3D shape at multiple spatial scales.

We present and test a novel multiscale representation of perceived 3D surface orientation: the orientation path. Using a multiscale probe, we measure perceived surface orientation at multiple spatial scales; linking the measurements for a given surface location yields that location's orientation path. The multiscale data obtained show that observers consistently see different surface orientations at different spatial scales. We demonstrate that such multiscale data can reveal multiscale differences between observers' percepts of a stimulus and the stimulus geometry. We also demonstrate the use of the orientation path in evaluating the multiscale effects of adding a depth cue to a 3D display.

Scaled medial axis representation: evidence from position discrimination task.

Previous experimental studies (e.g. Kovacs I, Julesz B. Nature (London) 1994; 370:644-646) have found enhanced contrast sensitivity at medial locations, supporting theoretical speculations that the visual system represents simple spatial regions by their medial axes. The core model (Burbeck CA, Pizer SM. Vis Res 1995;35:1917-1930) hypothesizes that the medial representation arises in a scale-specific way: the scale is determined by local object width, and it controls the resolution at which the medial locus and object width are encoded. Here we look for further evidence for a medial representation and test the idea that the resolution of the axis depends on object width. A new experimental paradigm was developed to infer sensitivity to position within individual figural regions, using circles as the figural regions. A probe dot was presented within a circle along a diameter at one location in one temporal interval and at a slightly different location on that diameter in a second temporal interval. The observer's task was to report the direction in which the probe dot had been displaced. Position discrimination thresholds were calculated and compared to two-dot separation discrimination thresholds. Data were obtained for two circle sizes. It was found that positional sensitivity was strongly enhanced near the center of the circle, and it was enhanced in a scale-dependent way. The results were tested against a scaled medial (core) model and against models assuming no medial representation. The core model was better able to account for the results.

Across-object relationships in perceived object orientation.

An orientation discrimination paradigm was used to determine whether the perceived orientation of extended objects is based on the distribution of edge-orientations or on the response of mechanisms that encode relationships across the object; specifically we considered large, second-stage filters and cores (the perceived middle of the object) as encoders of the across-object relationship. The stimuli were "rectangles" with sinusoidally modulated long edges. Manipulating the frequency and relative phase of the edge modulation allowed us to assess the importance of the across-object relationships. Evidence was found for the importance of such relationships in determining perceived orientation. No evidence was found for direct use of the distribution of responding edge detectors.

Occlusion edge blur: a cue to relative visual depth.

We studied whether the blur/sharpness of an occlusion boundary between a sharply focused surface and a blurred surface is used as a relative depth cue. Observers judged relative depth in pairs of images that differed only in the blurriness of the common boundary between two adjoining texture regions, one blurred and one sharply focused. Two experiments were conducted; in both, observers consistently used the blur of the boundary as a cue to relative depth. However, the strength of the cue, relative to other cues, varied across observers. The occlusion edge blur cue can resolve the near/far ambiguity inherent in depth-from-focus computations.

Linking object boundaries at scale: a common mechanism for size and shape judgments.

The area over which boundary information contributes to the determination of the center of an extended object was inferred from results of a bisection task. The object to be bisected was a rectangle with two long sinusoidally modulated sides, i.e. a wiggly rectangle. The spatial frequency and amplitude of the edge modulation were varied. Two object widths were tested. The modulation of the perceived center approximately equaled that of the edges at very low edge modulation frequencies and decreased in amplitude with increasing edge modulation frequency. The edge modulation had a greater modulating effect on the perceived center for the narrower object than for the wider object. This scaling with object width didn't follow perfect zoom invariance but was precisely matched by the scaling of the bisection threshold with width, strongly supporting the idea that the same mechanism determines both the location of the perceived center for these stimuli and its variance. We propose that this mechanism is the linking of object boundaries at a scale determined by the object width.

Object representation by cores: identifying and representing primitive spatial regions.

We propose a model of the spatial visual processes underlying the identification and representation of the shape of primitive spatial regions. We propose that a region's boundaries are sensed at multiple scales by boundariness detectors that give graded responses, that stimulated boundariness detectors of similar scale, sigma, connect to one another across a distance that is proportional to their scale, and that they connect via cores, where a core encodes the middles and widths of the region and hence is a trace in (chi, gamma, sigma), i.e. 3-D scale space.

A method for determination of optimal image enhancement for the detection of mammographic abnormalities.

We present a paradigm for empirical evaluation of digital image enhancement algorithms for mammography that uses psychophysical methods for implementation and analysis of a clinically relevant detection task. In the experiment, the observer is asked to detect and assign to a quadrant, or indicate the absence of, a simulated mammographic structure characteristic of cancer embedded in a background image of normal breast tissue. Responses are indicated interactively on a computer workstation. The parameter values for the enhancement applied to the composite image may be varied on each trial, and structure detection performance is estimated for each enhancement condition. Preliminary investigations have provided insight into an appropriate viewing duration, and furthermore, suggest that nonradiologists may be used under this methodology for the tasks investigated thus far, for predicting parameter values for clinical investigation. We are presently using this method in evaluating several contrast enhancement algorithms of possible benefit in mammography. These methods enable an objective, clinically relevant evaluation, for the purpose of optimal parameter determination or performance assessment, of digital image-processing methods potentially used in mammography.

Separation discrimination with embedded targets.

Previous research has shown that separation discrimination thresholds are independent of the internal spatial scale (local spatial frequency) of the targets whose separation is being judged. The experiments reported here tested the generality of this conclusion for separation discrimination of targets that were embedded in an array of identical objects, where crowding could enhance the importance of the scale at which the individual target locations are encoded. No effect of the local spatial scale of the targets was found under these conditions.

Two mechanisms for localization? Evidence for separation-dependent and separation-independent processing of position information.

The Weber function for separation--i.e. delta s as a function of separation s--is typically measured using a pair of targets presented roughly symmetrically relative to the fovea. With this paradigm, as the separation increases, the eccentricity of the individual targets increases also. To disentangle the effects of separation and eccentricity on the Weber function for separation, we systematically examined each of these variables and also examined the effects of target size and exposure duration. Separation discrimination thresholds were measured for average separations from 3 to 6 deg across a wide range of eccentricities, and for eccentricities of 2.5-10 deg for a range of separations. The dependence of threshold on target size was measured by varying the length of the stimuli from 1 to 120 min arc; the dependence on exposure duration was measured using durations of 100 and 500 msec at 10 deg eccentricity for comparison with data collected previously at smaller eccentricities. We found that for separations less than the eccentricity of the targets, thresholds depend primarily on separation; for larger separations, thresholds depend solely on eccentricity. In general, unless the targets are very small or quite brief, the spatial and temporal characteristics of the targets are not major contributors to the slope of the Weber function. Two mechanisms are proposed to account for thresholds in the two regions, one separation-dependent and one separation-independent.

Spatiotemporal limitations in bisection and separation discrimination.

Exposure duration was found to have a different effect on bisection thresholds than on separation-discrimination thresholds. Bisection thresholds were higher than separation discrimination thresholds between 33 and 150 msec but equal to or lower than them at longer durations. Experiments in which stimulus contrast was manipulated showed that the effect of exposure duration on separation-discrimination and bisection thresholds could not be attributed primarily to temporal contrast integration. The data could be accounted for by a model in which bisection is done by encoding the two separations in bisection sequentially.

Spatial-filter selection in large-scale spatial-interval discrimination.

Spatial-interval discrimination thresholds were measured for a pair of bars in the presence of other parallel bars placed far enough from the targets as to be outside the range of neural and optical blurring. Thresholds were elevated when the targets were embedded in an array of four parallel bars (two between and two flanking the targets), but not when there were only two parallels, whether the parallels were between the target bars or flanking them. The threshold elevation was larger with a 100-msec than with a 500-msec exposure duration. Attenuating the high spatial frequencies magnified the threshold elevation. The data indicate that the process responsible for spatial-interval discrimination automatically selects which spatial filters to use; it does not have to scan through all ranges of spatial filters.

Spatial interactions in rapid pattern discrimination.

We measured reaction times (RTs) for identification of a target among distracters under stabilized image conditions in which the positions of the target and the distracters were constant within a single experimental session. Under these conditions, the observer need not search for the target because its position is known. We nevertheless found that the presence of even a single distracter could elevate RTs. The magnitude of this effect depended on the distance of the distracter from the target and, for some observers, the distance of the distracter from the fovea. When we added not one but six background elements in a ring around the target, RT increased even more. If, apart from these neighboring distracters, the target was surrounded by more distracters located beyond the nearest neighbors, RT was, in general, not increased further. These findings suggest that adding background elements in a search task can elevate RTs in ways that are not dependent on the positional uncertainty of the target.

Large-scale relative localization across spatial frequency channels.

Large-scale relative localization accuracy is measured with objects that stimulate different ranges of spatial frequencies. The author has previously made measurements using objects that stimulate only high-spatial-frequency channels or only low-spatial-frequency channels and found no effect of spatial frequency. In the present study, relative localization accuracy, i.e. interval discrimination, is measured with an object pair consisting of a low-spatial-frequency object and a high-spatial-frequency object. Relative localization accuracy for this cross-channel stimulus is as high as for the same-channel stimuli used previously, showing that the relative localization mechanism operates effectively across spatial frequency channels.

Locus of spatial-frequency discrimination.

In standard frequency-discrimination experiments either the retinal spatial frequencies (cycles per degree) or the object spatial frequencies (real world) could be compared, because the retinal and object frequency differences are the same. Current models of spatial-frequency discrimination assume that observers compare the retinal frequencies. I test this assumption by presenting gratings at different viewing distances (with strong depth cues). The object frequencies of the gratings bear the same relationship that they do in a standard frequency-discrimination experiment, but the retinal frequency of the more distant grating is always markedly higher than that of the near grating. The observer's task is to compare the object spatial frequencies. This change from one depth to two (with no change in the stimulus object) has a negligible effect on the observer's performance, suggesting that observers compare object frequencies even in standard spatial-frequency-discrimination experiments. This conclusion is supported by the findings that (1) observers appear unable to learn to compare retinal frequencies and (2) the interstimulus interval has no effect (over the range 0-1020 msec), implying long-term storage of the visual information. Suggests are made about why these results are consistent with good system design.

Position and spatial frequency in large-scale localization judgments.

The frequency-channel model and the position, or "local-signs," model that have been proposed to account for hyperacuity (i.e. small-scale relative spatial localization) are examined in the context of large-scale relative spatial localization. As a basis for subsequent experiments, localization accuracy is measured over a large range of object separations, and previous findings that the "Weber fraction for localization" is constant are replicated. The effects on localization accuracy of both high- and low-spatial frequency components in the objects being localized are examined in some detail. Localization accuracy is found not to rely exclusively on either the high- or the low-frequency components. Neither the frequency-channel nor the position hypothesis as defined here is consistent with all of the observed results. However, with a slight modification, the position hypothesis can account qualitatively for all of the observed results, whereas no reasonable modification of the frequency-channel hypothesis appears able to do as well.

Further evidence for a broadband, isotropic mechanism sensitive to high-velocity stimuli.

Spatial frequency and orientation selectively, the most prominent properties of image-processing in the striate cortex, are not uniform throughout the spatiotemporal frequency domain. Some current models include one "transient" mechanism at very high velocities (i.e. low spatial and high temporal frequencies), and multiple "sustained" mechanisms elsewhere in the spatiotemporal frequency domain, but they do not consider the parameter of orientation. On the basis of earlier, orthogonal masking experiments, we concluded that the high-velocity mechanism is sensitive to a broad band of spatial frequencies, and has little or no orientation selectivity. In the present study we use pattern adaptation to measure the spatiotemporal properties of this mechanism. In other experiments, we attempt to relate it to the direction-selective motion detectors that also respond at high velocities. Finally we compare the pattern-adaptation results to the results of orthogonal subthreshold summation experiments in the same region of high temporal and low spatial frequencies.

Exposure-duration effects in localization judgments.

The effects on localization accuracy of increasing exposure duration beyond 100 msec are explored for a wide range of object separations. Previous reports that localization accuracy for objects separated by a few minutes of arc increases for exposures up to at least 400 msec are confirmed. I report here that localization of larger objects at larger separations does not improve when the exposure duration is increased beyond 100 msec. This difference between the small- and large-scale results can be explained by the difference in the spatial-frequency content of the objects being localized: When high-frequency objects are substituted for spectrally broadband objects in the large-scale case, the exposure-duration effects for widely separated objects become similar to those obtained in the small-scale case. These results suggest that the exposure-duration effect previously reported in hyperacuity studies is not specific to the localization task per se but rather is a suprathreshold version of the familiar form of spatiotemporal interaction seen in contrast-threshold results. They also suggest that a single type of mechanism underlies small- and large-scale localization.

Negative afterimages and photopic luminance adaptation in human vision.

Previous studies of the negative afterimage have reported that the process responsible for these aftereffects has a bandpass spatial characteristic. If this finding is correct, then negative afterimages cannot arise from a simple, local, adaptive process. I remeasure the spatial-frequency characteristic of the negative-afterimage process by using an afterimage contrast-matching procedure with retinally stabilized stimuli and find the spatial characteristic to be constant in the low-spatial-frequency region. This finding is consistent with the theory that the negative afterimage results from local luminance adaptation. As a test of the local adaptation explanation of the negative afterimage, the effect of the negative afterimage on the temporal contrast-sensitivity function (CSF) (measured down to 0.062 Hz) is determined. The apparent contrasts of the negative afterimages associated with very slowly (less than 0.5 Hz) flickering, threshold-contrast stimuli are calculated from power-function descriptions of the temporal development of the negative afterimage, and these afterimage contrasts are then subtracted from the temporal CSF's. The resulting curves are constant for temporal frequencies below 1 Hz, indicating that the decline in sensitivity at lower temporal frequencies is due entirely to the negative-afterimage process. Both the spatial and the temporal characteristics of the negative-afterimage process are consistent with its being a component of local luminance adaptation.

Role of local adaptation in the fading of stabilized images.

We provide evidence that the fading of stabilized images and the formation of negative afterimages result from the same local adaptive process. We measure thresholds for stabilized, static, sine-wave gratings and for stabilized flickering sine-wave gratings. We then measure the contrasts of the negative afterimages formed by the threshold-contrast stabilized, static stimuli. (The threshold-contrast flickering gratings produce no visible afterimages.) We find that the difference between the thresholds for stabilized, static gratings and the thresholds for slowly flickering gratings is equal to the contrasts of the afterimages produced by the stabilized, static gratings. We conclude that the fading of these stabilized gratings can be accounted for completely by local adaptation (the process underlying the formation of negative afterimages.

Critical problems in spatial vision.

In recent years the study of spatial vision seems to have come almost full circle. Localized stimuli (such as lines, bars, and edges) were abandoned in favor of textured patterns (such as sinusoidal gratings), a trend that was accelerated by the discovery that gratings of sufficiently different spatial frequencies or orientations (stimuli localized in the Fourier domain) were detected independently. This led to various attempts to model form vision in terms of spatial frequency analysis. More recently there has been a shift toward models that include, once again, the local aspects of spatial processing; this trend is more consistent with both retinal and cortical physiology. (Still surviving is the notion of a complete set of orthonormal basis functions, but not sinusoidal ones.) Other important developments include attempts to model spatiotemporal interaction, and the discovery that spatial processing takes on an entirely different character in the absence of any temporal variation (i.e., when the retinal image is stabilized). We attempt to trace these developments in terms of a selected group of representative studies, which we examine in some depth.