Stimulus features that determine the visual location of a bright bar.

A modification to the standard vernier target that has a detrimental effect on acuity is described. The addition of an extra bar alongside one of the test bars and directly underneath the other increases thresholds by an amount that is a monotonic function of its luminance. This allows for the hypothesis that the location of a bright bar is a function of some widespread description of the light distribution arising from such a bar on the retina, rather than some local feature of such a distribution. In particular, the data are not consistent with any simple notion of boundary extraction and support the conjecture that position of a bar is assigned to the mean or centroid of its light distribution.

Further evidence concerning the analysis of curvature in human foveal vision.

Data are presented which indicate that a length limit of 20 min arc applies to the highly accurate discrimination of curvature difference. Within this constraint and the previously reported orientational restriction (Watt and Andrews, 1982, Vision Res. 22, 449-460), curvature may determine the level of performance.

Towards a general theory of the visual acuities for shape and spatial arrangement.

A wide range of pattern acuity measurements are presented, and detailed comparisons are made between different acuities for different stimuli and tasks. The most striking finding is that only a small number of cues and mechanisms are involved, and there are thus considerable inhomogeneities in spatial perception, even under focused attention and foveal viewing. A theory for pattern acuity is elaborated, bringing the pattern acuity phenomena into a more general scheme for the visual perception of spatial pattern. Four distinct mechanisms are required to account for all the data. Two of these analyse the shape of small segments of contour using high grade position and slope information; the other two relate the positions of these segments also using position and slope information, but of lower grade.

Hyperacuity for luminance phase angle in the human visual system.

A moving target with identical trajectories in the two eyes appeared shifted in depth if flickered with a phase difference between the eyes. The direction of the depth shift was the same as if the phase-lagging eye had been seeing the target with a spatial advance in the direction of target motion. Maximum acuity for this effect was in the region of 7 deg of phase angle, which may be expressed as a spatial difference between corresponding luminance points of about 13 sec arc. Acuity was approximately constant over a wide range of modulation periods from 50 to 150 msec when expressed in terms of phase angle, but fell off rapidly at higher and at lower frequencies. The results cannot be explained simply by either conventional disparity theory or by spatio-temporal interpolation, but suggest that inter-ocular correspondence is influenced by dynamic luminance information.

Effect of motion sweep duration and number of stations upon interpolation in discontinuous motion.

Spatial and temporal vernier offset thresholds were determined for a target moving in discrete spatial steps between stations. In the spatial case, the two bars comprising the target had a relative spatial offset at each station but were synchronous. In the temporal case the two bars appeared at aligning stations with a temporal asynchrony. Temporal thresholds were converted into spatial units by calculating the distance the target would have travelled during the temporal delay. When compared in this way, temporal and spatial thresholds were very similar if the duration of the motion sequence was 300 msec or greater, but at briefer durations temporal thresholds became progressively higher. The possibility that eye pursuit might account for these data was ruled out by recording eye movements and rejecting trials on which tracking occurred. Analysis of eye records revealed the surprising fact that some tracking can occur even when the duration of the motion sequence is as little as 150 msec and random in direction.

The computation of orientation statistics from visual texture.

This paper examines how observers estimate the overall orientation of spatially disorganised textures containing variable orientation. Experiments used asymmetrical distributions of orientations to separate the predictions from different models of average orientation estimation. Stimuli were composed of two spatially intermingled sets of oriented patches, each set having Gaussian distributed element orientation. The threshold separation of the means of the two sets was determined for a variety of tasks. Discrimination of these textures from a reference composed of two sets with the same mean orientation was well predicted by discrimination of orientation variability. A single interval judgement of which set contained more elements required a greater separation of the set orientations and suggested that the sets must be resolved in the orientation domain for independent representation of their properties. That resolution is required to perform this task further suggests that orientational skew is not coded. Threshold offsets for judgement of average orientation were re-expressed as shifts of four candidate features for coding the central tendency of texel orientations. Comparison with similar thresholds for single distributions of orientations indicated that average orientation is assigned to the centroid of a set of orientation measures.

Regional distribution of the mechanisms that underlie spatial localization.

In order to understand the regional distribution of the mechanisms which underlie localization accuracy we (1) chose a task which is known to involve localization accuracy (2) optimized stimulus parameters for ecentric loci and (3) determined how two key spatial factors which affect localization accuracy vary as a function of ecentricity. These involve Gaussian blur and Gaussian jitter. These results suggest that there are three different functions with ecentricity for the mechanisms underlying this task which we relate to the spatial properties of the retina, namely mean cone density, receptoral convergence and regularity.

Mechanisms responsible for the assessment of visual location: theory and evidence.

Vernier acuity demonstrates a fine sense of relative visual location, which can be exploited to examine the question of mechanisms for the extraction of position information. By determining the appearance and location of composite stimuli consisting of a number of unresolved parallel bars of different luminances, we have demonstrated that vernier acuities of the order of 5 sec arc are due to mechanisms with an inflexible manner of encoding local intensity changes in the retinal image. The results are compared and contrasted with current theoretical approaches to the problems of early visual coding, and are best described by a model which encodes only the occurrence and location of zero-crossings in the second derivative of the retinal light distribution.

The recognition and representation of edge blur: evidence for spatial primitives in human vision.

Experiments are reported that measure the precision with which observers can (a) discern the degree of blur of an edge, (b) distinguish between two different types of blur, and relate the locations of two such edges by judging their (c) misalignment or (d) separation. Three blurring functions were used, and detailed examination of the retinal stimulus in each case leads to a simple hypothesis for the visual coding of edge blur. This is interpreted in terms of a general and primitive code for the transduction of local and widespread spatial luminance changes, in which stationary points in an approximation to the second derivative are detected and localized. The phenomena of illusory brightness changes in Mach bands and the Chevreul illusion find a ready explanation in this theory.

On the failure of spatiotemporal interpolation: a filtering model.

A vernier target moving discontinuously between discrete spatial stations is seen as having a spatial offset if its component bars are presented at spatially aligning stations with a temporal delay (the interpolation effect). In agreement with previous work, we find that the threshold for detecting this virtual spatial offset is the same as that for detecting an explicit spatial offset, provided that certain spatial and temporal constraints are met. Interpolation is a completely efficient process provided that the spatial interval between stations in the movement trajectory is less than 3-4 min arc, but thereafter it shows a gradual decline in efficiency. This paper presents a model of the decline in efficiency which arises, we suggest, not because of a failure of sampling to represent the original stimulus, but because of a progressive mismatch between the sampled signal and the bandwidth of the spatial filters involved in interpolation. Our model is compared with the constant velocity model of Fahle & Poggio [Proc. R. Soc. Lond. B 213, 451-477 (1981)].

Contour curvature analysis: hyperacuities in the discrimination of detailed shape.

Curvature discrimination thresholds were measured for a wide range of stimulus curvatures and sizes. Results are compared with an ideal processor of curvature to provide relative efficiencies. The results lead to three major findings. (i) Curved lines may be processed with the same precision as straight lines for decisions of shape, demonstrating a new class of hyperacuity. (ii) High relative efficiencies are obtained for all curved lines with an orientation range of less than 40 deg. (iii) This performance is not however consistent with common processing for straight and curved lines. The results are discussed, and two or possibly three separate processes are suggested as the basis for detailed shape perception.

The modulation transfer function of a display oscilloscope: measurements and comments.

It is pointed out that "spot size" of high resolution oscilloscope displays typically refers to the width of the spot at its half peak amplitude point, not to the width of the whole light distribution. The modulation transfer function of oscilloscope displays can have a more pronounced effect upon stimulus contrast than is generally realized, particularly when short viewing distances are used. We present measures of the spot profiles of a typical display, and use these to derive the MTF of the instrument. A simple correction is described to derive the actual contrast of a sine wave grating, given the manufacturer's specification of spot size.

Shape recognition in amblyopia.

The results of recent investigations of supra-threshold spatial vision in amblyopia have indicated that the amblyopic eye may be more disadvantaged than acuity or contrast detection measurements have suggested. We report here on the sensitivity of the amblyopic eye when performing tasks requiring the recognition of small spatial differences in thin bright line stimuli displayed in a variety of 2-D configurations. Amblyopes were able to perform these tasks, but their amblyopic eye was generally poorer than their normal eye by a multiplicative factor. It is argued that this pattern of results indicates that spatial scrambling rather than blurring is an appropriate model for amblyopia.

Spatial information and uncertainty in anisometropic amblyopia.

Anisometropic amblyopes were found to have a reduced sensitivity for shape discrimination. The introduction of positional jitter in the elements of the display had a profound effect on the performance of the normal eye, but not on that of the amblyopic eye. On the other hand the introduction of gaussian blur affects the performance of both eyes to the same degree. We conclude that raised spatial uncertainty due to metrical scrambling is a suitable model for anisometropic amblyopia.

The Weber relation for position is not an artefact of eccentricity.

We have measured the spatial threshold for discriminating the length of arcs falling on isoeccentric circles in the periphery out to 4 deg. The just-noticeable-difference rises with the arc length in the range 10-500 arc min, repeating the usual finding with foveally presented straight-line stimuli. Our results do not support a recent suggestion that the Weber relation is mainly due to greater positional uncertainty in the peripheral retina.

Spatial frequency interference effects and interpolation in vernier acuity.

Discrete spatial sampling of sinusoidal gratings has a detrimental effect upon vernier acuity for such stimuli if the sampling rate is less than 20 c/deg. We have examined the possibility that interpolation failure is due to masking by spatial frequency components near to the signal frequency. In an explicit masking paradigm, vernier acuity for a sine wave grating was found to be adversely affected by the presence of a masking grating falling within a critical band of frequencies near the test target. In the sampled stimulus, removal of sampling replicas similar in frequency to the test improved acuity, but the extent of the residual interference by high frequency components could not be predicted from the masking data. The high frequency interference effect depended on fixed phase relations between frequency components, creating narrow bright bars in the spatial luminance profile, and was greatly reduced by phase randomizing the sampling replicas. Various explanations of this nonlinear behaviour are discussed, including the Marr-Hildreth theory of edge detection.

Spatial filters and the localization of luminance changes in human vision.

Relative location acuities similar to vernier acuity were measured for a variety of different luminance profiles and contrasts. The results are interpreted in terms of the extraction of zero-bounded centroids in the responses of a limited range of bandpass spatial filters, with centre frequencies between 3.5 and 30 c/deg. The process by which the outputs of the filters are combined is examined, and MIRAGE, a specific proposal, tested and found to be supported. Analysis of the results obtained at lower contrasts suggests that the major source of noise lies not in the amplification of the filters, but is due to the location of the centroids being distorted by spurious noise zero-crossings. The pattern of noise intrusion is readily explained in terms of MIRAGE.

A theory of the primitive spatial code in human vision.

MIRAGE, a theory for the primitive coding of the (1D) spatial distribution of luminance changes by the human visual system is developed from a theoretical examination of the practical problems associated with the characterization of such changes. The main novel feature of the theory is that the multiplicity of spatial filters in human vision is assumed to exist principally to transmit a broad bandwidth signal of considerable redundancy: the filters are not assumed to be marked with their centre frequency or bandwidth, and are not analyzed independently. The theory is largely independent of the particular filter transfer function form. MIRAGE is applied to a range of one-dimensional luminance patterns, and demonstrates several well-known brightness illusions, and a structured grouping principle. It is finally shown to be supported by a wide range of psychophysical data.

The detection of deviation from straightness in lines.

A wide range of differently shaped perturbations were introduced into long thin straight lines, and threshold amplitude for their detection was measured. This amplitude threshold varies over a 20-fold range, depending on the shape of the cue, but can be economically expressed as just one numerical value, irrespective of the cue shape. This quantity is the area of the largest bump in the target around a least squares regression line axis, and its value is 0.3 arc min2. This value can be related to a fundamental spatial error of 3 arc sec (standard deviation) which is the limiting constraint on shape sensitivity.

The use of different cues in vernier acuity.

The roles of the various cues in the traditional vernier target are examined. We conclude that there are at least two mechanisms by which vernier acuities of the order of 5 sec arc may be obtained. The two cues are the overall slope of the target, and the relative positional differences. By using vernier targets that are degraded in two different ways, we can demonstrate each mechanism.