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Covariances among join-count spatial autocorrelation measures.

Spatial distributions of biological variables are often well-characterized with pairwise measures of spatial autocorrelation. In this article, the probability theory for products and covariances of join-count spatial autocorrelation measures are developed for spatial distributions of multiple nominal (e.g. species or genotypes) types. This more fully describes the joint distributions of pairwise measures in spatial distributions of multiple (i.e. more than two) types. An example is given on how the covariances can be used for finding standard errors of weighted averages of join-counts in spatial autocorrelation analysis of more than two types, as is typical for genetic data for multiallelic loci.

Analysis of Variance↗

The role of spatial frequency in color induction.

Color induction was measured for test and inducing chromaticities presented in spatial square-wave alternation, with spatial frequencies of 0.7, 4.0, 6.0 and 9.0 cpd. Observers matched the test chromaticities to a rectangular matching field using haploscopic presentation. Data were collected and analyzed within the framework of a cone chromaticity space, allowing analysis of spatial frequency effects on post-receptoral spectral opponent pathways. Assimilation, a shift of chromaticity toward the inducing chromaticity, was found at the highest spatial frequency (9.0 cpd). Contrast, a shift of chromaticity away from the inducing chromaticity, occurred at the lowest spatial frequency (0.7 cpd). The spatial frequency at the transition point from assimilation to contrast was near 4 cpd, independent of the cone axis. Assimilation was unaffected by the presence of a neutral surround and could be described by a spread light model. Contrast was reduced in the presence of a neutral surround. The data suggested that retinal contrast signals are important determinants in the perception of chromatic contrast.

Adult↗

Spatial-frequency properties of letter identification in amblyopia.

Amblyopia is characterized by a deficit in identifying small letters (acuity deficit) in the absence of identifiable ocular pathology. One explanation for this deficit is that the amblyopic visual system lacks appropriate channels tuned to high spatial frequencies for identifying small letters. The purpose of this study was to examine the spatial-frequency properties of letter identification in the amblyopic visual system. To do so, we measured contrast thresholds for identifying letters that were band-pass filtered to different bands of spatial frequencies, for letter sizes ranging from 2x to 19.2x larger than acuity letters. Letters were digitally filtered using a set of band-pass filters, with peak object spatial frequencies ranging from 0.88 to 10 c/letter. The bandwidth of the filters was 1 octave. For any given letter size, contrast sensitivity for identifying letters exhibits a spatial-tuning function. The shape of these tuning functions was found to be similar between amblyopic and non-amblyopic eyes, and across all letter sizes. The peak of these functions shifted progressively toward lower object spatial frequency when the letter size became smaller. When compared with the non-amblyopic eyes, the amblyopic eyes have a limited range of tuning functions sensitive to letters. However, when scaled with respect to acuity, the relationship between the peak frequency of the tuning functions and letter size becomes essentially identical in the amblyopic and non-amblyopic eyes. An ideal-observer analysis that takes into account spectral information about letter identity and the contrast-sensitivity function of the observer, but does not invoke narrow-band channels, also shows that the properties of the tuning functions for letter identification are similar between the amblyopic and non-amblyopic eyes. We conclude that the deficit in identifying small letters in amblyopes is not attributable to differences in the shape or selection of "channels", when compared with the normal visual system. Rather, it is a consequence of the difference in the resolution limit between the amblyopic and the non-amblyopic eyes.

Adolescent↗

The spatial properties of opponent-motion normalization.

The final stage of the Adelson-Bergen model [J. Opt. Soc. Am. A 2 (1985) 284] computes net motion as the difference between directionally opposite energies E(L) and E(R). However, Georgeson and Scott-Samuel [Vis. Res. 39 (1999) 4393] found that human direction discrimination is better described by motion contrast (C(m))--a metric where opponent energy (E(L)-E(R)) is divided by flicker energy (E(L)+E(R)). In the present paper, we used a lateral masking paradigm to investigate the spatial properties of flicker energy involved in the normalization of opponent energy. Observers discriminated between left and right motion while viewing a checkerboard in which half of the checks contained a drifting sinusoid and the other half contained flicker (i.e. a counterphasing sinusoid). The relative luminance contrasts of flicker and motion checks determined the checkerboard's overall motion contrast C(m). We obtained selectivity functions for opponent-motion normalization by measuring C(m) thresholds whilst varying the orientation, spatial frequency, or size of flicker checks. In all conditions, performance (percent correct) decayed lawfully as we decreased motion contrast, validating the C(m) metric for our stimuli. Thresholds decreased with check size and also improved as we increased either the orientation or spatial-frequency difference between motion and flicker checks. Our data are inconsistent with Heeger-type normalization models [Vis. Neurosci. 9 (1992) 181] in which excitatory inputs are normalized by a non-selective pooling of inhibitory inputs, but data are consistent with the implicit assumption in Georgeson and Scott-Samuel's model that flicker normalization is localized in orientation, scale, and space. However, our lateral masking paradigm leaves open the possibility that the spatial properties of flicker normalization would be different if opponent and flicker energies spatially overlapped. Further characterization of motion contrast will require models of the spatial, temporal, and joint space-time properties of mechanisms mediating opponent-motion and flicker normalization.

Contrast Sensitivity↗

Temporal modulation of spatial contrast vision in pigeons (Columba livia).

Spatiotemporal contrast sensitivity (CS) functions were obtained from four White Carneaux pigeons. The spatial frequency for each session was selected randomly from a group of five spatial frequencies ranging from 0.42 to 1.26 c/deg. Within the session, the temporal frequency varied from 1 to 32 Hz. When plotted as a function of spatial frequency, the CS functions peaked in the range 0.7-1.0 c/deg. When compared to data that had been collected at 0 Hz temporal modulation, the temporally modulated spatial CS functions showed reduced CS, especially at the higher spatial frequencies, and reduced peak spatial frequency. When plotted as a function of temporal frequency, the CS functions were flat up to 8-16 Hz. Above 16 Hz, the curves showed a sharp roll off. When plotted as a three-dimensional, spatiotemporal CS surface, the data had a number of characteristics in common with the three-dimensional spatiotemporal model of CS proposed by Burbeck and Kelly (J. Opt. Soc. Am. 70 (1980) 1121).

Animals↗

The effect of spatial frequency and field size on the spread of exclusive visibility in binocular rivalry.

We measured binocular rivalry between dichoptic, orthogonal, sinusoidal gratings both having spatial frequencies of 0.5, 1, 2, 4, 8 or 16 c deg-1 in fields ranging from 0.5 to 8 deg of visual angle in diameter. Total time that one or the other grating was exclusively visible had an inverted U-shaped relationship with spatial frequency, with the peak shifting to coarser spatial frequencies as the field size increased. We computed for each spatial frequency the maximum field size over which a criterion duration of exclusive visibility would spread. When expressed as areas, these sizes were inversely proportional to spatial frequency. This dependence of rivalry on spatial frequency is similar to those for stereopsis and fusion, consistent with the notion that all three binocular phenomena have a common mechanism.

Analysis of Variance↗

Feature asymmetries in visual search: effects of display duration, target eccentricity, orientation and spatial frequency.

In Experiments 1-3, we monitored search performance as a function of target eccentricity under display durations that either allowed or precluded eye movements. The display was present either until observers responded, for 104 msec, or for 62 msec. In all three experiments an orientation asymmetry emerged: observers detected a tilted target among vertical distracters more efficiently than a vertical target among vertical distracters. As target eccentricity increased, reaction times and errors augmented, and the set size effect became more pronounced, more so for vertical than tilted targets. In Experiments 4-7, the stimulus spatial properties were manipulated: spatial frequency; size; and orientation. The eccentricity effect was more pronounced for vertical than tilted targets and for high- than low-spatial frequency targets. This effect was eliminated when either the size, the size and orientation, or the size and spatial frequency were magnified (M-cortical factor). By increasing the signal-to-noise ratio, magnification reduced the extent of both asymmetries; it aided more the detection of tilted than vertical and of high- than low-spatial frequency targets. Experiments 4-7 indicate that performance improvement in the magnified conditions was due to the specific pairing of stimulus size with retinal eccentricity and not to the larger stimulus size of the magnified conditions. We conclude that stimulus size, orientation and spatial frequency influence the extent of the eccentricity effect and the efficiency of search performance.

Eye Movements↗

Spatial sensitization of increments and decrements: a border-contrast process and a net-excitation process.

We investigated the spatially local factors that adjust the sensitivity of the human visual system within a small patch of visual space. A very small adapting field was varied in diameter to map out the strength and extent of the spatially local processes that adjust sensitivity for both increments and decrements. The results demonstrated antagonistic center/surround adaptation regions with a decremental test probe comparable to those demonstrated previously for incremental probes (Westheimer, G., 1965. Spatial interaction in the human retina during scotopic vision, Journal of Physiology 81, 812-894; Westheimer, G., 1967. Spatial interaction in human cone vision, Journal of Physiology 190, 139-154) implying comparable antagonistic regions in the ON and OFF channels. In addition to spatial interactions based on light adaptation, we report a weaker effect that is based on the location of a border (luminance edge) and is governed by the contrast of this edge. Finally, we show that these effects are elicited by both highly localized edges (1' ring pairs) and radial lines (Ehrenstein figure) as well. We conclude that both a border-contrast mechanism and a net-excitation mechanism govern the spatially local adaptation of the visual system and that this view fits well with the behavior of single units reported previously.

Adaptation, Ocular↗

Seeing better at night: life style, eye design and the optimum strategy of spatial and temporal summation.

Animals which need to see well at night generally have eyes with wide pupils. This optical strategy to improve photon capture may be improved neurally by summing the outputs of neighbouring visual channels (spatial summation) or by increasing the length of time a sample of photons is counted by the eye (temporal summation). These summation strategies only come at the cost of spatial and temporal resolution. A simple analytical model is developed to investigate whether the improved photon catch afforded by summation really improves vision in dim light, or whether the losses in resolution actually make vision worse. The model, developed for both vertebrate camera eyes and arthropod compound eyes, calculates the finest spatial detail perceivable by a given eye design at a specified light intensity and image velocity. Visual performance is calculated for the apposition compound eye of the locust, the superposition compound eye of the dung beetle and the camera eye of the nocturnal toad. The results reveal that spatial and temporal summation is extremely beneficial to vision in dim light, especially in small eyes (e.g. compound eyes), which have a restricted ability to collect photons optically. The model predicts that using optimum spatiotemporal summation the locust can extend its vision to light intensities more than 100,000 times dimmer than if it relied on its optics alone. The relative amounts of spatial and temporal summation predicted to be optimal in dim light depend on the image velocity. Animals which are sedentary and rely on seeing small, slow images (such as the toad) are predicted to rely more on temporal summation and less on spatial summation. The opposite strategy is predicted for animals which need to see large, fast images. The predictions of the model agree very well with the known visual behaviours of nocturnal animals.

Animals↗

Modelling spatial contrast sensitivity functions for chromatic and luminance-modulated gratings.

We extended our detection model of achromatic spatial vision (Rovamo, J., Mustonen, J., & Näsänen, R. (1994a). Modelling contrast sensitivity as a function of retinal illuminance and grating area. Vision Research, 34, 1301-1314) to colour vision by taking into account the fact that due to the spatio-chromatic opponency of retinal ganglion cells and dorsal lateral geniculate nucleus (dLGN) neurons, equiluminous chromatic gratings are not affected by precortical lateral inhibition. We then tested the extended model by using Mullen's experimental data (Mullen, K. J. (1985). The contrast sensitivity of human color vision to red-green and blue-yellow chromatic gratings. Journal of Physiology, 359, 381-400). The band-pass shape of the spatial contrast sensitivity function for luminance-modulated green and yellow gratings transformed to a low-pass shape, resembling the chromatic spatial contrast sensitivity function for red-green and blue-yellow equiluminous gratings, when the effect of precortical lateral inhibition on grating contrast was computationally removed by dividing luminance contrast sensitivities by spatial frequency (i.e. by af, where a = 1 degree). After the removal of this direct effect of lateral inhibition, there still remained a residual shape difference between the spatial contrast sensitivity functions for chromatic and luminance gratings. It was due to indirect reduction of grating visibility by quantal noise high-pass filtered by precortical lateral inhibition. When this indirect effect of quantal noise was also removed, contrast sensitivity for luminance gratings was about twice the sensitivity for chromatic gratings at all spatial frequencies. This was evidently due to the fact that the chromatic contrast of the equiluminous grating at the opponent stage (Cole, G. R., Hine, T. & McIihagga, W. (1993). Detection mechanisms in L-, M-, and S-cone contrast space. Journal of the Optical Society of America A, 10, 38-51) was about half of the luminance contrast of either of its chromatic component. Thus, if the contrast of the equiluminous chromatic grating were not expressed as the Michelson contrast of one chromatic component grating against its own background (Mullen, K. J. (1985). The contrast sensitivity of human color vision to red-green and blue-yellow chromatic gratings. Journal of Physiology, 359, 381-400) but as chromatic contrast at the opponent stage, contrast sensitivity would be the same for chromatic and luminance gratings.

Color Perception↗

Second-site adaptation in the red-green detection pathway: only elicited by low-spatial-frequency test stimuli.

The red-green (RG) detection mechanism was revealed by measuring threshold detection contours in the L and M cone contrast plane for sine-wave test gratings of 0.8-6 c deg-1 on bright adapting fields of yellow or red. The slope of the RG detection contours was unity, indicating that the L and M contrast signals contribute equally (with opposite signs) on both the yellow and the red fields: this reflects first-site, cone-selective adaptation. Second-site adaptation, which may reflect saturation at a color-opponent site, was evidenced by the RG detection contours being further out from the origin of the cone contrast plane on the red field than on the yellow field. Second-site adaptation was strong (3-fold) for low spatial frequency test gratings but greatly diminished by 6 c deg-1. The disappearance of second-site adaptation with increasing spatial frequency can be explained by spatial frequency channels. The most sensitive detectors may comprise a low spatial frequency channel which is susceptible to masking by the chromatic, spatial DC component of the red field. The 6 c deg-1 patterns may be detected by a less sensitive, higher frequency channel which is less affected by the uniform red field. The RG spatial frequency channels likely arise in the cortex, implicating a partially central site for the second-site effect.

Adaptation, Physiological↗

Spatial and temporal vision in patients treated for bilateral congenital cataracts.

Using the method of limits, we measured spatial and temporal vision in 13 children who had been deprived of patterned visual input during infancy until they were treated for dense central cataracts in both eyes. Spatial vision was assessed with vertical sine-wave gratings, and temporal vision was assessed with an unpatterned luminance field sinusoidally modulated over time. Under these testing conditions, spatial contrast sensitivity at low and medium spatial frequencies (0.33-2 c deg-1) was within normal limits, but sensitivity at higher spatial frequencies and grating acuity were reduced on average by 1.3 and 0.5 log units, respectively. Temporal vision was affected less severely, with losses in sensitivity only for low temporal frequencies (5 and 10 Hz), which averaged 0.4 log units. Thus, spatial and temporal vision are likely mediated by different neural mechanisms, that are differentially affected by deprivation.

Adolescent↗

The stereoscopic (cyclopean) motion aftereffect is selective for spatial frequency and orientation of disparity modulation.

Across two experiments, this study investigated the spatial frequency tuning and orientation tuning (both in the disparity domain) of the stereoscopic (cyclopean) motion aftereffect. In Experiment 1, observers adapted to a moving stereoscopic grating of a given cyclopean spatial frequency and tested for the motion aftereffect with a static grating of the same or different spatial frequency. Robust motion aftereffects were induced only when the spatial frequency of the adapt and test stimuli was the same. In Experiment 2, observers adapted to a moving stereoscopic grating of a given cyclopean orientation and tested for the motion aftereffect with a static grating of the same or different orientation. Robust motion aftereffects were induced only when the orientation of the adapt and test stimuli was the same. Together, these results suggest that the stereoscopic motion aftereffect is tuned for cyclopean spatial frequency and orientation which, in turn, suggest that the stereoscopic motion aftereffect is mediated by low-level oriented spatial-frequency mechanisms.

Adaptation, Physiological↗

Invariance of the perceived spatial frequency shift of peripherally viewed gratings with manipulations of contrast, duration, and luminance.

Gratings appear of higher spatial frequency when they are viewed peripherally rather than foveally. To test the hypothesis that this effect is an artefact of particular laboratory conditions, we manipulated the contrast, luminance and presentation duration, manipulations which have also been shown to increase the apparent spatial frequency of foveally presented gratings. It has been argued that such shifts reflect an attempt to increase sensitivity by changing the receptive field properties of spatially tuned visual channels, while keeping their size labels constant. If so, and peripheral channels are not otherwise mislabelled, it should be possible to find conditions under which the apparent spatial frequency of peripherally viewed gratings matches that of foveal gratings of the same spatial frequency. In this study, manipulations of contrast, luminance, and duration had no effect on the size of the perceived spatial frequency shift in peripheral vision. Thus the putative inappropriate size labelling of peripheral visual channels is constant over a wide range of stimulus values. We speculate that this apparent constant error may result from a mechanism which normally compensates for another factor such as blur, which may otherwise lead to an overestimation of size.

Contrast Sensitivity↗

Multiplatform optical monitoring of eutrophication in temporally and spatially variable lakes.

Representative spatial patterns of eutrophication variables cannot be produced using traditional in situ sampling techniques. Spatial heterogeneity complicates the study of seasonal and long-term trends and the evaluation of water management policies. Remote sensing, however, with its broad view has the potential to deliver the relevant information. This paper will address the added value of synoptic eutrophication maps to the standard monitoring program of two large, spatially and temporally variable lakes in the Netherlands, Lakes IJssel and Marken. Remote sensing images were obtained from SeaWiFS; and combined with hyperspectral reflectance data from the airborne EPS-a sensor and the shipboard PR-650 spectroradiometer. The PR-650 data were used in selecting the most appropriate algorithms for SeaWiFS and EPS-a. A special algorithm for case II waters with high chlorophyll content was applied to SeaWiFS data to obtain chlorophyll concentrations. Synoptic maps of suspended matter were retrieved using inversion of a model for irradiance reflectance. For the airborne sensor inversion of reflectance was used for both suspended matter and chlorophyll. Satellite and airborne sensors clearly are complementary to each other. Comparison of satellite data with the airborne data and the (scarcely available) in situ data reveal underlying problems with: (i) validation of remote sensing images; and (ii) comparing data at different spatial and temporal scales. In our study, we found a reasonable agreement between different data sources at seasonal time scales, but at shorter time scales the differences can be (much) larger. In situ data suffer from poor reproducibility, related to the natural variability at small spatial scales (patchiness), combined with a significant temporal variability. The standard in situ monitoring program in Lakes IJssel and Marken lacks both the necessary spatial coverage as well as an appropriate sampling frequency. This indicates that for reliable monitoring, a synoptic data set, sampled at a high frequency is required. Remote sensing can partially fulfil this demand but still lacks the demanded frequency, mainly due to regular cloud cover. The answer may be in a multiplatform monitoring approach, as used in our study (combining in situ data with shipboard, airborne and satellite optical data) and in combining monitoring data with models. Satellite remote sensing is most powerful in determining properties that are inherent to the whole lake system, like the overall mean chlorophyll-a concentration. Computational models may meet the demand for a sufficiently high sampling frequency by deterministic interpolation of the data in time.

Chlorophyll↗

Relationships between spatial and temporal variabilities in airborne metal distributions in Won Ju City, Korea.

The relationship between temporal and spatial factors in controlling the metal distribution characteristics was investigated using the monthly metal concentration data collected from four distinctive sampling sites (grassland, residential, commercial, and industrial site) of Won Ju City, Kang Won province for approximately 4-year periods between 1991 and 1995. In order to compare the relative role of spatial and temporal factors, two-factor analysis of variance (ANOVA) was applied to these data sets. For the application of this method, temporal factors were investigated in terms of both annual and seasonal basis. The results of our data analysis indicated several interesting aspects of metal-to-metal distribution behavior such that: (1) Pb, Fe, and Cu tend to exhibit strong variabilities in both spatial and temporal scale, (2) the distribution variabilities for Mn are almost negligible in both temporal and spatial scale, (3) Cd is more variable in temporal, rather than spatial, sense, and (4) Cr and Ni can exhibit more variable patterns depending on temporal scale selected for data analysis. On the basis of this study, the relative roles of spatial and temporal factors are described in relation to each other and to different metal species.

Air Pollutants↗

Effect of excitotoxic lesions of rat medial prefrontal cortex on spatial memory.

The involvement of medial prefrontal cortex (mPFC) in spatial learning was examined in two memory tasks using spatial components, the Morris water maze and the three-panel runway. Using the Morris water maze task, with an invisible platform, the effects of NMDA mPFC lesions were assessed in a procedure reflecting spatial learning and memory, including a spatial reversal. In the three-panel runway, a delayed matching-to-position procedure was used in which rats were required to find food at the end of the runway after passing through one of three panel gates set into four barriers spaced equally apart along the maze. In addition, mPFC lesions were assessed behaviorally in two behavioral tests known to be sensitive to mPFC dysfunction: the food hoarding paradigm and spontaneous locomotion in the open field. Consistent with the documented effects of mPFC damage, NMDA mPFC lesions impaired food hoarding behavior and increased spontaneous exploratory locomotion. In the Morris water maze and the three-panel runway, mPFC-lesioned rats showed relatively few effects, supporting the conclusion that the damage inflicted to the mPFC had no consequence for the processing of spatial information. However, mPFC lesioned animals showed slower acquisition during both the training trial in the three-panel runway and the reversal training in the Morris water maze. These results suggest that spatial memory did not depend on mPFC integrity in the Morris water maze and the three-panel runway experiments, and address the issue of deficits induced by mPFC lesions in memory tasks dependent on non-mnemonic processes such as attentional processes and/or a reduced behavioral flexibility to environmental changes.

Animals↗

Spatial and nonspatial Morris maze learning: impaired behavioral flexibility in mice with ectopias located in the prefrontal cortex.

About half of BXSB/MpJ-Yaa (BXSB) mice have neocortical ectopias (misplaced clusters of neurons located in layer I of cortex). Previous behavioral studies have suggested that ectopic mice have superior spatial, but equivalent nonspatial, reference memory learning. However, since spatial and nonspatial learning were not assessed in the same apparatus and with the same testing procedure, it is unclear if this conclusion is accurate. We have created a new nonspatial Morris maze for mice that differs from the spatial task only in the type of cues that must be utilized to efficiently locate the platform (intra-maze black/white patterns vs. extra-maze room cues) and does not differ in the level of task complexity or the presence of objects within the maze. Ectopic mice were very good in utilizing extra-maze cues when learning the spatial version and in utilizing intra-maze cues when learning the nonspatial version of the Morris maze, while non-ectopics were not, suggesting that ectopics have superior spatial and nonspatial reference memory. Ectopias in BXSB mice are usually located in prefrontal and/or motor cortex. The prefrontal cortex is involved in behavioral flexibility (e.g. being able to easily switch from using spatial to nonspatial cues). Only ectopic mice with ectopias specifically located in the prefrontal region of cortex demonstrated difficulty switching from using extra-maze to intra-maze cues and vice versa. Thus, the presence of one or more ectopias in the prefrontal region of cortex disrupted one of the normal functions of the prefrontal cortex.

Animals↗