The detection and identification of lines and edges

Standard models of spatial vision mispredict edge sensitivity at low spatial frequencies

One well-established characteristic of early visual processing is the contrast sensitivity function (CSF) which describes how sensitivity varies with the spatial frequency (SF) content of the visual input. The CSF prompted the development of a now standard model of spatial vision. It represents the visual input by activity in orientation- and SF selective channels which are nonlinearly recombined to predict a perceptual decision. The standard spatial vision model has been extensively tested with sinusoidal gratings at low contrast because their narrow SF spectra isolate the underlying SF selective mechanisms. It is less studied how well these mechanisms account for sensitivity to more behaviourally relevant stimuli such as sharp edges at high contrast (i.e. object boundaries) which abound in the natural environment and have broader SF spectra. Here, we probe sensitivity to edges (2-AFC, edge localization) in the presence of broadband and narrowband noises. We use Cornsweet luminance profiles with peak frequencies at 0.5, 3 and 9 cpd as edge stimuli. To test how well mechanisms underlying sinusoidal contrast sensitivity can account for edge sensitivity, we implement a single- and a multi-scale model building upon standard spatial vision model components. Both models account for most of the data but also systematically deviate in their predictions, particularly in the presence of pink noise and for the lowest SF edge. These deviations might indicate a transition from contrast- to luminance-based detection at low SFs. Alternatively, they might point to a missing component in current spatial vision models.

Estimates of edge detection filters in human vision

Edge detection is widely believed to be an important early stage in human visual processing. However, there have been relatively few attempts to map human edge detection filters. In this study, observers had to locate a randomly placed step edge in brown noise (the integral of white noise) with a 1/f² power spectrum. Their responses were modelled by assuming the probability the observer chose an edge location depended on the response of their own edge detection filter to that location. The observer's edge detection filter was then estimated by maximum likelihood methods. The filters obtained were odd-symmetric and similar to a derivative of Gaussian, with a peak-to-trough width of 0.1-0.15 degrees. These filters are compared with previous estimates of edge detectors in humans, and with neurophysiological receptive fields and theoretical edge detectors.

Detecting and identifying offset gaze

A number of experiments have demonstrated that observers can accurately identify stimuli that they fail to detect (Rollman and Nachmias, 1972; Harris and Fahle, 1995; Allik et al. 1982, 2014). Using a 2x2AFC double judgements procedure, we demonstrated an analogous pattern of performance in making judgements about the direction of eye gaze. Participants were shown two faces in succession: one with direct gaze and one with gaze offset to the left or right. We found that they could identify the direction of gaze offset (left/right) better than they could detect which face contained the offset gaze. A simple Thurstonian model, under which the detection judgement is shown to be more computationally complex, was found to explain the empirical data. A further experiment incorporated metacognitive ratings into the double judgements procedure to measure observers' metacognitive awareness (Meta-d') across the two judgements and to assess whether observers were aware of the evidence for offset gaze when detection performance was at and below threshold. Results suggest that metacognitive awareness is tied to performance, with approximately equal Meta-d' across the two judgements, when sensitivity is taken into account. These results show that both performance and metacognitive awareness rely not only on the strength of sensory evidence but also on the computational complexity of the decision, which determines the relative distance of that evidence from the decision axes.

Detection and identification of spatial offset: double-judgment psychophysics revisited

In a bull's-eye acuity task, we asked observers to identify in which direction, to the left or the right, a spot had been displaced from the center of a circle and-after that, in the same trial-to detect which of the two presented circles contained the displaced spot. Replicating our previous findings (Allik, Dzhafarov, & Rauk, 1982), the spatial offset direction identification probability was higher than the probability with which the correct observation interval could be detected. All data were explained by a Thurstonian model, according to which the spatial positions of both spots are projected onto an internal axis of representation as two random numbers, x and y, drawn from a random distribution with a fixed standard deviation ς (final sigma). The observed identification and detection probabilities were accurately reproduced, provided that the observer tested two different inequalities: x + y > 0 for the identification, and x (2) - y (2) > 0 for the detection. In order to eliminate small discrepancies between the predicted and the observed data, we proposed that the positional error increases with increasing distance from the center of the annulus. It was concluded that, to explain the superiority of the identification over the detection effect, there is no need to propose separate axes of representation for mono- and bipolar information, as is usually postulated in double-judgment psychophysics.

Inter-reader differences in common carotid artery intima-media thickness: implications for cardiovascular risk assessment and vascular age determination

OBJECTIVES

Far wall common carotid artery intima-media thickness, a surrogate measure of atherosclerosis, requires the tracing of two carotid wall interfaces on ultrasound images: the lumen-intima and media-adventitia. Vascular age is derived from intima-media thickness measurements. We studied how tracing the wall interfaces affects intima-media thickness measurements and estimates of vascular age.

METHODS

Five readers made far-wall common carotid intima-media thickness measurements on 26 carotid artery images. Each reader traced lines at the lumen-intima and media-adventitia interfaces. An observer, blinded to reader identity and intima-media thickness values, reviewed the images and estimated the relative location of these lines compared to his judgment of the interface location: +1 for 1 pixel above the interface, 0 at the interface, and -1 if below. The significance of differences was evaluated by analysis of variance.

RESULTS

Mean intima-media thickness measurements ranged between 0.57 and 0.78 mm and showed significant differences between readers (P < .009). Differences in carotid intima-media thickness measurements made by the readers were significantly associated with the location of the media-adventitia interfaces (P < .0001) but not the lumen-intima interfaces (P = .07). The intima-media thickness differences corresponded to mean differences in estimated vascular age ranging from 14 to 21 years.

CONCLUSIONS

Inter-reader differences in common carotid intima-media thickness measurements are mostly seen for the media-adventitia wall interface and are detectable by an experienced observer. These inter-reader differences affect the use of intima-media thickness measurements for cardiovascular risk evaluation, can cause substantial errors in vascular age estimates, and might be correctable by performing replicate readings of standard image sets.

Features and the 'primal sketch'

This review is concerned primarily with psychophysical and physiological evidence relevant to the question of the existence of spatial features or spatial primitives in human vision. The review will be almost exclusively confined to features defined in the luminance domain. The emphasis will be on the experimental and computational methods that have been used for revealing features, rather than on a detailed comparison between different models of feature extraction. Color and texture fall largely outside the scope of the review, though the principles may be similar. Stereo matching and motion matching are also largely excluded because they are covered in other contributions to this volume, although both have addressed the question of the spatial primitives involved in matching. Similarities between different psychophysically-based model will be emphasized rather than minor differences. All the models considered in the review are based on the extraction of directional spatial derivatives of the luminance profile, typically the first and second, but in one case the third order, and all have some form of non-linearity, be it rectification or thresholding.

Only two phase mechanisms, ±cosine, in human vision

We evaluated the proposal that there exist detectors of the following four cardinal phases in human vision: +cosine, -cosine, +sine, and -sine. First, we assessed whether there was evidence that these cardinal phases were processed by independent 'labeled lines,' using a discrimination at detection threshold paradigm. Second, we assessed whether suprathreshold phase discrimination was best at phases intermediate between these cardinal values. Third, we tried to replicate previous evidence showing that an absence of facilitation occurs only between cosine pedestals and sine tests (or vice-versa). In all three experimental approaches we found no compelling evidence for four cardinal phase groupings. We did however find evidence for independent detectors for pure increments and decrements (+/-cosine). We suggest that phase discrimination, whether at threshold or suprathreshold, is mediated by mechanisms that encode the relative positions and contrasts of local increments and decrements within the stimulus.

Detection and discrimination of relative spatial phase by V1 neurons

Edge-like and line-like features result from spatial phase congruence, the local phase agreement between harmonic components of a spatial waveform. Psychophysical observations and models of early visual processing suggest that human visual feature detectors are specialized for edge-like and line-like phase congruence. To test whether primary visual cortex (V1) neurons account for such specificity, we made tetrode recordings in anesthetized macaque monkeys. Stimuli were drifting equal-energy compound gratings composed of four sinusoidal components. Eight congruence phases (one-dimensional features) were tested, including line-like and edge-like waveforms. Many of the 137 single V1 neurons (recorded at 45 sites) could reliably signal phase congruence by any of several response measures. Across neurons, the preferred spatial feature had only a modest bias for line-like waveforms. Information-theoretic analysis showed that congruence phase was temporally encoded in the frequency band present in the stimuli. The most sensitive neurons had feature discrimination thresholds that approached psychophysical levels, but typical neurons were substantially less sensitive. In single V1 neurons, feature discrimination exhibited various dependences on the congruence phase of the reference waveform. Simple cells were over-represented among the most sensitive neurons and on average carried twice as much feature information as complex cells. However, the distribution of the indices of optimal tuning and discrimination of relative phase was indistinguishable in simple and complex cells. Our results suggest that phase-sensitive pooling of responses is required to account for human psychophysical performance, although variation in feature selectivity among nearby neurons is considerable.

Spatiotemporal mechanisms for detecting and identifying image features in human vision

Our visual system constantly selects salient features in the environment, so that only those features are attended and targeted by further processing efforts to identify them. Models of feature detection hypothesize that salient features are localized based on contrast energy (local variance in intensity) in the visual stimulus. This hypothesis, however, has not been tested directly. We used psychophysical reverse correlation to study how humans detect and identify basic image features (bars and short line segments). Subjects detected a briefly flashed 'target bar' that was embedded in 'noise bars' that randomly changed in intensity over space and time. By studying how the intensity of the noise bars affected performance, we were able to dissociate two processing stages: an early 'detection' stage, whereby only locations of high-contrast energy in the image are selected, followed (after approximately 100 ms) by an 'identification' stage, whereby image intensity at selected locations is used to determine the identity (whether bright or dark) of the target.

Characterizing the spatial-frequency sensitivity of perceptual templates

Filtered external noise has been an important tool in characterizing the spatial-frequency sensitivity of perceptual templates. Typically, low-pass- and/or high-pass-filtered external noise is added to the signal stimulus. Thresholds, the signal energy necessary to maintain given criterion performance levels, are measured as functions of the spatial-frequency passband of the external noise. An observer model is postulated to segregate the impact of the external noise and the internal noise. The spatial-frequency sensitivity of the perceptual template is determined by the relative impact exerted by external noise in each frequency band. The perceptual template model (PTM) is a general observer model that provides an excellent account of human performance in white external noise [Vision Res. 38, 1183 (1998); J. Opt. Soc. Am. A 16, 764 (1999)]. We further develop the PTM for filtered external noise and apply it to derive the spatial-frequency sensitivity of perceptual templates.

Nonlinearities of near-threshold contrast transduction

The existence of analytic threshold nonlinearities was probed with 2AFC incremental threshold functions for both local and extended test patterns on stationary matched pedestals of the same and opposite sign. In contrast to the facilitation effect with same-sign pedestals, sensitivity with opposite-sign pedestals first deteriorated up to the mask detection level, abruptly improved and then deteriorated again. Analytic solutions for the transducer function with additive noise were derived to account for the incremental data in all conditions. The results for positive difference-of-Gaussian (DoG) stimuli (whose increment made the central spot lighter) and for 10 c deg-1 Gabor stimuli were consistent with accurate hard-threshold behavior with best-fitting d' powers from 17 to 358. The 10 c deg-1 data further implied that contrast gain control was operating throughout the subthreshold range. The results for negative DoGs (whose increment corresponds to the darkening of the central spot) and 2 c deg-1 Gabor profiles were consistent with mild nonlinearities having d' powers of 1.6-3. Significant differences between the nonlinearities for positive and negative DoGs indicate that only a small portion, if any, of the near-threshold nonlinearity could be attributed to uncertainty. Our analysis suggests that, with low spatial frequency gratings, detection was based on those bars that become darker; with high-frequency gratings, on the bars that become brighter.

Contrast-dependent dissociation of visual recognition and detection fields

Seeing an object 'as something' is different from simply seeing it (see Watanabe, S., 1985, Pattern Recognition: Human and Mechanical, John Wiley). This distinction between recognition and detection often goes unnoticed in physiology and clinical practice, where visual performance is characterized in terms of acuity, visual field and contrast sensitivity. The corresponding functions of stimulus detection are consistent with the neural projection properties from the retina to the striate cortex, i.e. the 'cortical magnification theory'. Yet recognition performance for characters (Strasburger, H. et al., 1994, Eur. J. Neurosci., 6, 1583-1588) and grey-level patterns (Jüttner, M. and Reutschler, I., 1996, Vision Res., 36, 1007-1022) does not fit into this scheme. Here we show that this discrepancy results in the dissociation of visual recognition and detection fields, which is dramatic at low pattern contrast. Form proper can be appreciated exclusively within the much narrower field of recognition, the window of visual intelligence. Its function is, at low contrast, probably mediated by the magnocellular pathway and at all contrasts is determined by the processing characteristics of higher stages of the ventral visual pathway.

Evidence for separate, task dependent noise processes in orientation and size perception

Spatial acuity was estimated as the minimum difference in target spatial frequency which could act as a cue in a double concurrent, single interval orientation discrimination task. Experiments were conducted with vertical and oblique (45 deg) targets at three different spatial frequencies covering a range of two octaves. Frequency thresholds were found to be lower than those estimated by conventional methods by a factor of nearly 50%. They followed Weber's law for target frequency and were independent of target orientation. The orientation thresholds exhibited a normal oblique effect, and were not affected by the simultaneous judgements of target frequency. The data support the contention that the neural codes for image size and image orientation are segregated at an early stage of processing, and that the main source of noise that limits the precision of coding in these domains exists beyond the level of early mechanisms.

A computational examination of image segmentation and the initial stages of human vision

A novel approach to the question of image segmentation is considered. Instead of relying on edge-detection mechanisms to encircle the image of an object, it is proposed that the general Gestalt-like properties of images of objects can be used. These manifest themselves as particularly simple properties at relatively coarse spatial scales when the image is filtered with orientation-selective filters. The first part of the paper is concerned with a computational analysis of this proposal. A key issue is the question of how the information in filtered images is extracted. A simple primitive parametric description of zero-bounded blobs is used in this paper. It is shown how such a scheme can support readily the clustering of features with Gestalt-like properties. In the second part of the paper, two general difficulties for vision that are particularly severe for the present scheme are considered. The first of these are the effects of strongly asymmetric illumination. The second are the effects of using a cluttered scene. In each case the nature of the problem is examined and the nature of the computational solution considered.

Electro-physiological investigation of edge-selective mechanisms of human vision

This study investigates the spatial and temporal characteristics of human visual mechanisms that respond selectively to the polarity of edges. The technique was to record steady-state visual evoked-potentials (VEPs) while visually stimulating with a sawtooth waveform (a series of edges of the same polarity) periodically reversing in contrast (and hence edge-polarity) at a suitable frequency. To ensure that phase-locked VEPs resulted from polarity reversal (rather than local luminance modulation) the stimuli were randomly jittered to a new position between each contrast reversal. The jittered stimulus elicited strong and reliable second-harmonic modulation, usually about one-fifth the amplitude of standard VEPs under similar conditions. The amplitude and extrapolated thresholds of polarity-specific VEPs (relative to standard VEPs) did not vary with eccentricity (up to 10 degrees) or with stimulus orientation. The dependency on spatial frequency was similar to that of standard VEPs, but the polarity-specific VEPs tended to peak at lower temporal frequencies. Perhaps the clearest difference in the two types of VEPs was in the estimated response latency, about 140 msec for the polarity VEPs, compared with 90 msec for standard VEPs.

Evidence for edge and bar detectors in human vision

The structure of receptive fields of human visual detectors was investigated by studying their phase response. Observers were required to discriminate between pairs of periodic stimuli that differed in phase by 180 degrees (reversed in contrast). The stimuli comprised 256 harmonics, smoothly filtered in amplitude, and congruent in phase at the origin. Reversal discrimination thresholds were measured as a function of the phase of the harmonics. Thresholds were slightly higher for phases around 45 degrees, consistent with the idea that all discriminations were mediated by independent detectors with 0 or 90 degrees phase response (assuming probability summation between them). Discrimination thresholds were also measured with a pedestal stimulus, of phase complementary to that of the test gratings. For discriminations between 0 and 180 degrees (cosine phase), or 90 and 270 degrees (sine phase), the complementary pedestal had little effect, implying independence of detectors in sine and cosine phase. However, for discrimination between 45 and 225 degrees (stimuli containing both sine and cosine components) the complementary pedestal, which also contained both sine and cosine components, facilitated greatly discrimination thresholds. The results suggest that there exist two classes of detectors, one with a Fourier phase spectrum of 0, the other with a Fourier phase spectrum of 90 degrees. This implies that the receptive fields are symmetric, one class having even-symmetry (line-detectors), the other odd-symmetry (edge-detectors).

The structure and symmetry of simple-cell receptive-field profiles in the cat's visual cortex

Receptive fields of simple cells in the cat visual cortex have recently been discussed in relation to the 'theory of communication' proposed by Gabor (1946). A number of investigators have suggested that the line-weighting functions, as measured orthogonal to the preferred orientation, may be best described as the product of a Gaussian envelope and a sinusoid (i.e. a Gabor function). Following Gabor's theory of 'basis' functions, it has also been suggested that simple cells can be categorized into even- and odd-symmetric categories. Based on the receptive field profiles of 46 simple cells recorded from cat visual cortex, our analysis provides a quantitative description of both the receptive-field envelope and the receptive-field 'symmetry' of each of the 46 cells. The results support the notion that, to a first approximation, Gabor functions with three free parameters (envelope width, carrier frequency and carrier phase) provide a good description of the receptive-field profiles. However, our analysis does not support the notion that simple cells generally fit into even- and odd-symmetric categories.

A three channel model of temporal frequency perception

This paper derives the constraints on a set of channels that would be consistent with the results of several experiments on the temporal properties of the visual system, and it describes a specific set of channels that meet these constraints. Data on simultaneous detection and discrimination require a minimum of three channels. Temporal frequency discrimination at and above threshold constrain the bandwidths and locations of the channels. The shape of the temporal modulation sensitivity function constrains their sensitivities. The functions that meet these constraints are similar to those derived from masking data, and they can account for data on flicker matching, notch losses in modulation sensitivity, and changes of perceived temporal frequency with changes of modulation depth.

Phase reversal discrimination

In the Fourier representation of space, the parameter of phase plays a crucial role. In this study, several experiments were performed involving discrimination of various phase relations of fundamental (2 c/deg) to second harmonic (4 c/deg) at low contrast levels. The results were consistent with a model involving four "channels", each optimally sensitive to one of the following phase relations: + cosine (bright bar), -cosine (dark bar), +sine (left edge), and -sine (right edge).

Simultaneous visual detection and identification: theory and data

A signal-detection model is presented for the two-alternative forced-choice procedure that gathers simultaneous detection and identification judgments. By using vector representation, a measure of independent processing within the visual system is derived. The independence measure is applied to data on the detection and identification of stimuli that differ along the dimensions of orientation, spatial frequency, and size. Data are presented that favor the signal-detection model over a high-threshold model.