Effects of glyceryl glucoside on AQP3 expression, barrier function and hydration of human skin.

BACKGROUND/AIM: Aquaporins (AQPs) present in the epidermis are essential hydration-regulating elements controlling cellular water and glycerol transport. In this study, the potential of glyceryl glucoside [GG; alpha-D-glucopyranosyl-alpha-(1->2)-glycerol], an enhanced glycerol derivative, to increase the expression of AQP3 in vitro and ex vivo was evaluated. METHODS: In vitro studies with real-time RT-PCR and FACS measurements were performed to test the induction by GG (3% w/v) of AQP3 mRNA and protein in cultured human keratinocytes. GG-containing formulations were applied topically to volunteer subjects and suction blister biopsies were analyzed to assess whether GG (5%) could penetrate the epidermis of intact skin, and subsequently upregulate AQP3 mRNA expression and improve barrier function. RESULTS: AQP3 mRNA and protein levels were significantly increased in cultured human keratinocytes. In the studies on volunteer subjects, GG significantly increased AQP3 mRNA levels in the skin and reduced transepidermal water loss compared with vehicle-controlled areas. CONCLUSION: GG promotes AQP3 mRNA and protein upregulation and improves skin barrier function, and may thus offer an effective treatment option for dehydrated skin.

Three-systems theory of human visual motion perception: review and update.

Lu and Sperling [Vision Res. 35, 2697 (1995)] proposed that human visual motion perception is served by three separate motion systems: a first-order system that responds to moving luminance patterns, a second-order system that responds to moving modulations of feature types-stimuli in which the expected luminance is the same everywhere but an area of higher contrast or of flicker moves, and a third-order system that computes the motion of marked locations in a "salience map," that is, a neural representation of visual space in which the locations of important visual features ("figure") are marked and "ground" is unmarked. Subsequently, there have been some strongly confirmatory reports: different gain-control mechanisms for first- and second-order motion, selective impairment of first- versus second- and/or third-order motion by different brain injuries, and the classification of new third-order motions, e.g., isoluminant chromatic motion. Various procedures have successfully discriminated between second- and third-order motion (when first-order motion is excluded): dual tasks, second-order reversed phi, motion competition, and selective adaptation. Meanwhile, eight apparent contradictions to the three-systems theory have been proposed. A review and reanalysis here of the new evidence, pro and con, resolves the challenges and yields a more clearly defined and significantly strengthened theory.

Sensitive calibration and measurement procedures based on the amplification principle in motion perception.

We compare two types of sampled motion stimuli: ordinary periodic displays with modulation amplitude m(o=e) that translate 90 degrees between successive frames and amplifier sandwich displays. In sandwich displays, even-numbered frames are of one type, odd-numbered frames are of the same or different type, and (1) both types have the same period, (2) translate in a consistent direction 90 degrees between frames, and (3) even frames have modulation amplitude m(e), odd frames have modulation amplitude m(o). In both first-order motion (van Santen, J.P.H. & Sperling, G. (1984). Temporal covariance model of human motion perception. Journal of the Optical Society of America A, 1, 451-73) and second-order motion (Werkhoven, P., Sperling, G., & Chubb, C. (1993). Motion perception between dissimilar gratings: a single channel theory. Vision Research, 33, 463-85) the motion strength of amplifier sandwich displays is proportional to the product m(o)m(e) for a wide range of m(e). By setting m(e) to a large value, an amplifier sandwich stimulus with a very small value of m(o) can still produce visible motion. The amplification factor is the ratio of two threshold modulation amplitudes: ordinary circumflexm(o=e) over amplified circumflexm(o), circumflexm(o=e)/circumflexm(o). We find amplification factors of up to about 8x. Light adaptation and contrast gain control in early visual processing distort the representations of visual stimuli so that inputs to subsequent perceptual processes contain undesired distortion products or 'impurities'. Motion amplification is used to measure and thence to reduce these unwanted components in a stimulus to a small fraction of their threshold. Such stimuli are certifiably pure in the sense that the residual impurity is less than a specified value. Six applications are considered: (1) removing (first-order) luminance contamination from moving (second-order) texture gratings; (2) removing luminance contamination from moving chromatic gratings to produce pure isoluminant gratings; (3) removing distortion products in luminance-modulated (first-order) gratings - by iterative application, all significant distortion products can be removed; (4) removing second-order texture contamination from third-order motion displays; (5) removing feature bias from third-order motion displays; (6) and the same general principles are applied to texture-slant discrimination in which x,y spatial coordinates replace the x,t motion coordinates. In all applicable domains, the amplification principle provides a powerful assay method for the precise measurement of very weak stimuli, and thereby a means of producing visual displays of certifiable purity.

Perceptual motion standstill in rapidly moving chromatic displays.

In motion standstill, a quickly moving object appears to stand still, and its details are clearly visible. It is proposed that motion standstill can occur when the spatiotemporal resolution of the shape and color systems exceeds that of the motion systems. For moving red-green gratings, the first- and second-order motion systems fail when the grating is isoluminant. The third-order motion system fails when the green/red saturation ratio produces isosalience (equal distinctiveness of red and green). When a variety of high-contrast red-green gratings, with different spatial frequencies and speeds, were made isoluminant and isosalient, the perception of motion standstill was so complete that motion direction judgments were at chance levels. Speed ratings also indicated that, within a narrow range of luminance contrasts and green/red saturation ratios, moving stimuli were perceived as absolutely motionless. The results provide further evidence that isoluminant color motion is perceived only by the third-order motion system, and they have profound implications for the nature of shape and color perception.

Second-order reversed phi.

In a first-order reversed-phi motion stimulus (Anstis, 1970), the black-white contrast of successive frames is reversed, and the direction of apparent motion may, under some conditions, appear to be reversed. It is demonstrated here that, for many classes of stimuli, this reversal is a mathematical property of the stimuli themselves, and the real problem is in perceiving forward motion, which involves the second- or third-order motion systems or both. Three classes of novel second-order reversed-phi stimuli (contrast, spatial frequency, and flicker modulation) that are invisible to first-order motion analysis were constructed. In these stimuli, the salient stimulus features move in the forward (feature displacement) direction, but the second-order motion energy model predicts motion in the reversed direction. In peripheral vision, for all stimulus types and all temporal frequencies, all the observers saw only the reversed-phi direction of motion. In central vision, the observers also perceived reversed motion at temporal frequencies above about 4 Hz, but they perceived movement in the forward direction at lower temporal frequencies. Since all of these stimuli are invisible to first-order motion, these results indicate that the second-order reversed-phi stimuli activate two subsequent competing motion mechanisms, both of which involve an initial stage of texture grabbing (spatiotemporal filtering, followed by fullwave rectification). The second-order motion system then applies a Reichardt detector (or equivalently, motion energy analysis) directly to this signal and arrives at the reversed-phi direction. The third-order system marks the location of features that differ from the background (the figure) in a salience map and computes motion in the forward direction from the changes in the spatiotemporal location of these marks. The second-order system's report of reversed movement dominates in peripheral vision and in central vision at higher temporal frequencies, because it has better spatial and temporal resolution than the third-order system, which has a cutoff frequency of 3-4 Hz (Lu & Sperling, 1995b). In central vision, below 3-4 Hz, the third-order system's report of resolvable forward movement of something salient (the figure) dominates the second-order system's report of texture contrast movement.

Measuring the amplification of attention.

An ambiguous motion paradigm, in which the direction of apparent motion is determined by salience (i.e., the extent to which an area is perceived as figure versus ground), is used to assay the amplification of color by attention to color. In the red-green colored gratings used in these experiments, without attention instructions, salience depends on the chromaticity difference between colored stripes embedded in the motion sequence and the yellow background. Selective attention to red (or to green) alters the perceived direction of motion and is found to be equivalent to increasing the physical redness (or greenness) by 25-117%, depending on the observer and color. Whereas attention to a color drastically alters the salience of that color, it leaves color appearance unchanged. A computational model, which embodies separate, parallel pathways for object perception and for salience, accounts for 99% of the variance of the experimental data.

The mechanism of isoluminant chromatic motion perception.

An isoluminant chromatic display is a color display in which the component colors have been so carefully equated in luminance that they stimulate only color-sensitive perceptual mechanisms and not luminance-sensitive mechanisms. The nature of the mechanism by which isoluminant chromatic motion is perceived is an important issue because color and motion processing historically have been associated with different neural pathways. Here we show that isoluminant chromatic motion (i) fails a pedestal test, (ii) has a temporal tuning function that declines to half-amplitude at 3-6 Hz, and (iii) is perceived equally well when the entire motion sequence is presented monocularly (entire motion sequence to one eye) versus interocularly (the frames of motion sequence alternate between eyes so that neither eye individually could perceive motion). These three characteristics indicate that chromatic motion is detected by the third-order motion system. Based on this theory, it was possible to take a moving isoluminant red-green grating and, by simply increasing the chromatic contrast of the green component, to generate the full gamut of motion percepts, from compelling smooth motion to motion standstill. The perception of motion standstill when the third-order mechanism is nullified indicates that there is no other motion computation available for purely chromatic motion. It follows that isoluminant chromatic motion is not computed by specialized chromatic motion mechanisms within a color pathway but by the third-order motion system at a brain level where binocular inputs of form, color, depth, and texture are simultaneously available and where selective attention can exert a major influence.

What you should know about patient billing.

Arming yourself with some knowledge of the billing process will help you understand what can be done to assist with self-pay and insurance claims. It will also provide you with some insight into how you can be part of the solution to this seemingly endless dilemma.

Structure detection: a statistically certified unsupervised learning procedure.

We present a class of structure detection procedures (SDPs) that can extract the characteristic structures in an arbitrary population of images. An SDP adaptively augments the power of a novel, statistical, structure test to reject the null hypothesis that a randomly chosen image is devoid of structure. The core of the structure test consists of an orthonormal basis B of receptive fields that is refined into an increasingly sensitive detector of characteristic image structures. Adaptive refinement is accomplished as follows: for each image x in a random training sequence, B is updated by a planar rotation that decreases the p-value of a statistical structure test for x. This image-by-image refinement procedure is very efficient, obeying time and space constraints similar to those that limit processes of perceptual organization in real organisms. SDPs' capabilities are demonstrated in three test populations: natural images, faulty random number generators, and artificial images composed of mixtures of basis functions. (1) An SDP succeeds in rejecting the null hypothesis that the UNIX random number generator rand() is truly random. (2) When images are composed by adding arbitrary pairs of orthogonal component images, an SDP extracts the components. (3) For a large set of natural image patches, an SDP yields a basis B1 that detects structure with p-value < 0.005 in 88% of a new set of patches. B1's elements resemble the receptive fields of V1 simple cells. (4) Of special interest are biconvergent SDPs that derive in parallel a basis B, as well as a pointwise transformation f, specifically sensitized to evaluate the response values that result from applying B to images in the target population. A biconvergent SDP applied to natural image patches yields a basis B2 similar to B1, as well as a pointwise transformation f with vastly heightened sensitivity to extreme response values. We conjecture that sensory neurons have evolved cooperatively to maximize their collective power to reject the null hypothesis that their input is devoid of structure, thereby evolving receptive fields that efficiently represent characteristic input structures.

Contrast gain control in first- and second-order motion perception.

A novel pedestal-plus-test paradigm is used to determine the nonlinear gain-control properties of the first-order (luminance) and the second-order (texture-contrast) motion systems, that is, how these systems' responses to motion stimuli are reduced by pedestals and other masking stimuli. Motion-direction thresholds were measured for test stimuli consisting of drifting luminance and texture-contrast-modulation stimuli superimposed on pedestals of various amplitudes. (A pedestal is a static sine-wave grating of the same type and same spatial frequency as the moving test grating.) It was found that first-order motion-direction thresholds are unaffected by small pedestals, but at pedestal contrasts above 1-2% (5-10 x pedestal threshold), motion thresholds increase proportionally to pedestal amplitude (a Weber law). For first-order stimuli, pedestal masking is specific to the spatial frequency of the test. On the other hand, motion-direction thresholds for texture-contrast stimuli are independent of pedestal amplitude (no gain control whatever) throughout the accessible pedestal amplitude range (from 0 to 40%). However, when baseline carrier contrast increases (with constant pedestal modulation amplitude), motion thresholds increase, showing that gain control in second-order motion is determined not by the modulator (as in first-order motion) but by the carrier. Note that baseline contrast of the carrier is inherently independent of spatial frequency of the modulator. The drastically different gain-control properties of the two motion systems and prior observations of motion masking and motion saturation are all encompassed in a functional theory. The stimulus inputs to both first- and second-order motion process are normalized by feedforward, shunting gain control. The different properties arise because the modulator is used to control the first-order gain and the carrier is used to control the second-order gain.

Is there feature-based attentional selection in visual search?

A new paradigm combines attentional cuing and rapid serial visual presentation to disentangle the effects of perceptual filtering and location selection. Observers search successive, superimposed arrays, in which feature values are alternated for a target numeral among letters. Two dimensions, size (small, large) and color (red, green) are tested. Selective attention to feature values is jointly manipulated by instructions, presentation probabilities, and payoffs. In Experiment 1, the attended feature provides temporal, not spatial, information; observers show no attentional costs or benefits in response accuracy. In Experiment 2, the attended feature indicates a unique location; observers show consistent attentional costs and benefits. Selective attention to a particular size or color does not cause perceptual exclusion or admission of items containing that feature; it acts by guiding search processes to spatial locations that contain the to-be-attended feature.

Second-order illusions: Mach bands, Chevreul, and Craik--O'Brien--Cornsweet.

Mach bands, which normally occur at the edges of ramp modulations of luminance, are demonstrated to occur in fullwave stimuli that have ramp modulations of contrast while maintaining constant expected luminance. [The fullwave stimuli are random textures that (1) have a ramp contrast modulation that is exposed by fullwave rectification (e.g. absolute value or square) or by halfwave rectification but (2) have a uniform expected luminance throughout, so the modulation remains hidden without rectification.] Two different textures were used: random pixels and 'Mexican hats'. Stimuli were presented dynamically, with a new instantiation of the texture every 67 msec (this enhances the magnitude of the illusion). Both fullwave Mach-band stimuli exhibit perceptual Mach bands that are decreases or increases in apparent texture contrast with no concomitant change in apparent brightness. The perceived contrast bands in fullwave Mach stimuli and the brightness bands in a conventional luminance Mach-band stimulus have approximately the same magnitude. Chevreul (staircase) illusions in luminance and in fullwave patterns also are found to have approximately similar magnitudes, as do luminance and fullwave Craik--O'Brien--Cornsweet illusions. None of these illusions can be perceived with halfwave textures. These results indicate that second-order (texture) illusions result from fullwave, not halfwave, rectification and involve spatial interactions that are remarkably similar to those in first-order (luminance) processing.

The functional architecture of human visual motion perception.

UNLABELLED: A powerful paradigm (the pedestal-plus-test display) is combined with several subsidiary paradigms (interocular presentation, stimulus superpositions with varying phases, and attentional manipulations) to determine the functional architecture of visual motion perception: i.e. the nature of the various mechanisms of motion perception and their relations to each other. Three systems are isolated: a first-order system that uses a primitive motion energy computation to extract motion from moving luminance modulations; a second-order system that uses motion energy to extract motion from moving texture-contrast modulations; and a third-order system that tracks features. Pedestal displays exclude feature-tracking and thereby yield pure measures of the first- and second-order systems which are found to be exclusively monocular. Interocular displays exclude the first- and second-order systems and thereby to yield pure measures of feature-tracking. RESULTS: both first- and second-order systems are fast (with temporal frequency cutoff at 12 Hz) and sensitive. Feature tracking operates interocularly almost as well as monocularly. It is slower (cutoff frequency is 3 Hz) and it requires much more stimulus contrast than the first- and second-order systems. Feature tracking is both bottom-up (it computes motion from luminance modulation, texture-contrast modulation, depth modulation, motion modulation, flicker modulation, and from other types of stimuli) and top-down--e.g. attentional instructions can determine the direction of perceived motion.

Attention-generated apparent motion.

Motion perception mechanisms have recently been divided into three categories. First-order mechanisms primarily extract motion from moving objects or features that differ from the background in luminance. Second-order mechanism extract motion from moving properties, such as a moving area of flicker in which there is no difference in mean luminance between target and background. These first- and second-order motion mechanisms are primarily monocular. The existence of purely binocular, interocular and various other unusual kinds of apparent motion has promoted conjectures of a third-order mechanism, but there has been no clear suggestion as to the actual computations that such a mechanism might perform. Here we demonstrate 'alternating feature' stimuli that produce apparent motion only when the observer selectively attends to one of the embedded features in the display. The latent motion in the alternating feature stimuli is invisible to first- or second-order motion mechanisms, and the direction of apparent motion depends on the particular feature attended. These findings suggest the mechanism of third-order motion: the locations of the most significant features are registered in a salience map, and motion is computed directly from this map.

Measuring the spatial frequency selectivity of second-order texture mechanisms.

Recent investigations of texture and motion perception suggest two early filtering stages: an initial stage of selective linear filtering followed by rectification and a second stage of linear filtering. Here we demonstrate that there are differently scaled second-stage filters, and we measure their contrast modulation sensitivity as a function of spatial frequency. Our stimuli are Gabor modulations of a suprathreshold, bandlimited, isotropic carrier noise. The subjects' task is to discriminate between two possible orientations of the Gabor. Carrier noises are filtered into four octave-wide bands, centered at m = 2, 4, 8, and 16 c/deg. The Gabor test signals are w = 0.5, 1, 2, 4 and 8 c/deg. The threshold modulation of the test signal is measured for all 20 combinations of m and w. For each carrier frequency m, the Gabor test frequency w to which subjects are maximally sensitive appears to be approximately 3-4 octaves below m. The consistent m x w interaction suggests that each second-stage spatial filter may be differentially tuned to a particular first-stage spatial frequency. The most sensitive combination is a second-stage filter of 1 c/deg with first-stage inputs of 8-16 c/deg. We conclude that second-order texture perception appears to utilize multiple channels tuned to spatial frequency and orientation, with channels tuned to low modulation frequencies appearing to be best served by carrier frequencies 8 to 16 times higher than the modulations they are tuned to detect.

1st- and 2nd-order motion and texture resolution in central and peripheral vision.

STIMULI. The 1st-order stimuli are moving sine gratings. The 2nd-order stimuli are fields of static visual texture, whose contrasts are modulated by moving sine gratings. Neither the spatial slant (orientation) nor the direction of motion of these 2nd-order (microbalanced) stimuli can be detected by a Fourier analysis; they are invisible to Reichardt and motion-energy detectors. METHOD. For these dynamic stimuli, when presented both centrally and in an annular window extending from 8 to 10 deg in eccentricity, we measured the highest spatial frequency for which discrimination between +/- 45 deg texture slants and discrimination between opposite directions of motion were each possible. RESULTS. For sufficiently low spatial frequencies, slant and direction can be discriminated in both central and peripheral vision, for both 1st- and for 2nd-order stimuli. For both 1st- and 2nd-order stimuli, at both retinal locations, slant discrimination is possible at higher spatial frequencies than direction discrimination. For both 1st- and 2nd-order stimuli, motion resolution decreases 2-3 times more rapidly with eccentricity than does texture resolution. CONCLUSIONS. (1) 1st- and 2nd-order motion scale similarly with eccentricity. (2) 1st- and 2nd-order texture scale similarly with eccentricity. (3) The central/peripheral resolution fall-off is 2-3 times greater for motion than for texture.

Perception of apparent motion between dissimilar gratings: spatiotemporal properties.

What determines the strength of texture-defined apparent motion perception when the stimulus has no net directional energy in the Fourier domain? In a previous paper [Werkhoven, Sperling & Chubb (1993) Vision Research, 33, 463-485] we demonstrated the counterintuitive finding that the correspondence in spatial frequency and in modulation amplitude between neighboring patches of texture in a spatiotemporal motion path are irrelevant to motion strength. Instead, we found strong support for what we call a single channel or one-dimensional motion computation: a simple nonlinear transformation of the image, followed by standard motion analysis. Here, we further studied the dimensionality of the motion computation in a parameter space that includes texture orientation and stimulus display rate in addition to texture spatial frequency and modulation amplitude. We used ambiguous motion displays in which one motion path, consisting of patches of nonsimilar texture, competes with another motion path comprised entirely of similar texture patches. The data show that motion between dissimilar patches of texture that are orthogonally oriented, have a two octave difference in spatial frequency and differ 50% in modulation amplitude can easily dominate motion between similar patches of texture. A single channel accounts for more than 70% of texture-from-motion strength for the parameter space examined and this channel is invariant for stimulus display rates varying over a four-fold range.

Full-wave and half-wave rectification in second-order motion perception.

UNLABELLED: Microbalanced stimuli are dynamic displays which do not stimulate motion mechanisms that apply standard (Fourier-energy or autocorrelational) motion analysis directly to the visual signal. In order to extract motion information from microbalanced stimuli, Chubb and Sperling [(1988) Journal of the Optical Society of America, 5, 1986-2006] proposed that the human visual system performs a rectifying transformation on the visual signal prior to standard motion analysis. The current research employs two novel types of microbalanced stimuli: half-wave stimuli preserve motion information following half-wave rectification (with a threshold) but lose motion information following full-wave rectification; full-wave stimuli preserve motion information following full-wave rectification but lose motion information following half-wave rectification. Additionally, Fourier stimuli, ordinary square-wave gratings, were used to stimulate standard motion mechanisms. Psychometric functions (direction discrimination vs stimulus contrast) were obtained for each type of stimulus when presented alone, and when masked by each of the other stimuli (presented as moving masks and also as nonmoving, counterphase-flickering masks). RESULTS: given sufficient contrast, all three types of stimulus convey motion. However, only one-third of the population can perceive the motion of the half-wave stimulus. Observers are able to process the motion information contained in the Fourier stimulus slightly more efficiently than the information in the full-wave stimulus but are much less efficient in processing half-wave motion information. Moving masks are more effective than counterphase masks at hampering direction discrimination, indicating that some of the masking effect is interference between motion mechanisms, and some occurs at earlier stages. When either full-wave and Fourier or half-wave and Fourier gratings are presented simultaneously, there is a wide range of relative contrasts within which the motion directions of both gratings are easily determinable. Conversely, when half-wave and full-wave gratings are combined, the direction of only one of these gratings can be determined with high accuracy. CONCLUSIONS: the results indicate that three motion computations are carried out, any two in parallel: one standard ("first order") and two non-Fourier ("second-order") computations that employ full-wave and half-wave rectification.

Non-Fourier motion analysis.

It has been realized for some time that the visual system performs at least two general sorts of motion processing. First-order motion processing applies some variant of standard motion analysis (i.e. spatiotemporal Fourier energy analysis) directly to stimulus luminance, whereas second-order motion processing applies standard motion analysis to one or another grossly non-linear transformation of stimulus luminance. We have developed a method for disentangling the different sorts of mechanisms that may operate in human vision to detect second-order motion. This method hinges on an empirical condition called transition invariance that may or may not be satisfied by a family psi of textures. Any failure of this condition indicates that more than one mechanism is involved in detecting the motion of stimuli composed of the textures in psi. We have shown that the family of sinusoidal gratings oriented orthogonally to the direction of motion and varying in contrast and spatial frequency is transition invariant. We modelled the results in terms of a single-channel motion computation. We have new results indicating that a specific class of textures differing in texture element density and texture element contrast decisively fails the test of transition invariance. These findings suggest that in addition to the single second-order motion channel required by our earlier results there exists at least one other second-order motion channel. We argue that the preprocessing transformation used by this channel is a pointwise non-linearity that maps stimulus contrasts of absolute value less than some relatively high threshold tau onto 0, but increases with magnitude of c-tau for contrasts. c of absolute value greater than tau.

Full-wave and half-wave processes in second-order motion and texture.

A theory of human second-order motion perception is proposed and further applied to the discrimination of texture slant. The computational algorithms for deriving the direction of left-right motion from a sequence of images are equivalent to the algorithms for deriving the direction of slant (e.g. from top left to bottom right or top right to bottom left) in a single 2D image. There is a broad range of phenomena for which Fourier analysis of the image plus a few simple rules gives a good account of human perception. The problem with this first-order analysis is that there exists a broad class of 'microbalanced' stimuli in which the motion or slant is completely obvious to human subjects but is invisible to first-order analysis. Microbalanced stimuli require second-order analysis which consists of non-linear preprocessing (spatiotemporal filtering followed by rectification of the input signal) before standard motion or slant analysis. To determine whether the second-order rectification is half-wave or full-wave, we construct two special microbalanced stimulus types: 'half-wave stimuli' whose motion (or texture slant) is interpretable by a half-wave rectifying system but not by full-wave or a first-order (Fourier) analysis and 'full-wave stimuli' which are interpretable only after full-wave rectification. Such experiments show that second-order texture-slant perception utilizes both half-wave and full-wave processes, second-order motion-direction discrimination depends predominantly on full-wave rectification and second-order spatial interactions such as lateral contrast-contrast inhibition and second-order Mach bands are exclusively full-wave.