Horizontal Contours Research Articles

Non-linear Langevin model of geomorphic erosion processes

SUMMARY Recent spectral studies of vertical transect profiles of landscapes and mountains have shown them to be self-affine fractals, i.e. the rms height fluctuation Ah(L) averaged over a distance L scales as Ah(L) - Lx with x = 0.5 f 0.1, related to the fractal dimension Df = 2 - x = 1.5 of the horizontal contours. We propose that self-affine rough landscapes are created by the interplay of non-linearity and noise. To illustrate this idea and model the formation of such structures, we suggest a non-linear stochastic equation ahla? = DV*h + A(Vh)' + ~(r, t), which is the generalization of the deterministic Culling's linear equation. The non-linear term h(Vh)* comes from the requirement that erosion is proportional to the exposed area of the landscape; the noise term ~(r, t) accounts for the fact that erosion is locally irregular, as a result of the heterogeneity of soils and distribution of storms. Using this general framework, we recover the scaling law Ah(L) - Lx with x 2 0.4. Several novel avenues of research emerge from this analysis to further quantify geological data.

Multisensory Control of Eyestalk Orientation in Decapod Crustaceans: An Ecological Approach

This report reviews literature on multimodal control of eyestalk orientation in decapod crustaceans in relation to the ecological context of the species examined. A trend becomes apparent that the species rely on the various sensory cues with different weight according to their habitat, predominant mode of locomotion, and physical properties of the body. Four hypotheses are formulated that emphasize these trends with the aim of provoking new work on the comparative aspect and adaptive variability of sensory systems as guided by ecological constraints, and of gaining by this a deeper understanding of biological information processing. Eye stabilization in space usually means stabilization in the rotational degrees of freedom (recently discussed in Hengstenberg et al., 1986, and Nalbach and Nalbach, 1987). Without stabilization of eyes in space during walking, the retinal image would be blurred, its signal to noise ratio would decrease, discrimination between objects and background would be impaired, and image flow would be composed of angular velocity vectors of combined translational and rotational origin obscuring motion parallax. Without compensation for tilt of body or substrate, the coordinate system of the eye would be misaligned relative to the external reference. With stabilization, these difficulties are overcome in a comparatively simple mechanical way, and much neural computation to interpret the visual image is circumvented. In many groups of visually active animals, the eyes, or at least the head which carries the eyes, is mobile relative to the body which carries the locomotory organs. During voluntary movements, the body usually is subjected to rotatory and translatory oscillations, although there may be some examples of animals using gaits that prevent oscillations of the body. In general, however, the eyes have to be rotated against the body to stabilize the retinal image. Control of body posture may help in this task during involuntary disturbances of equilibrium. Every available cue is used for gaze stabilization (Sch6ne, 1984). Mechanical senses involved include statoliths and vestibular apparatus in vertebrates, cephalopods, and crabs, halteres in flies, mesenterial receptors, leg proprioceptors in walking animals, etc. Visual cues that are known to be exploited include the dorsoventral gradient of brightness, horizontal or vertical contours, and the movement of structures in large parts of the visual field. In addition to these open and closed loop sensorimotor systems, during voluntary movements efferent control may also serve stabilization of gaze (Dijkgraaf, 1956b, c). During evolution of the decapod crustaceans, stabilization of the eyestalks and equilibrium reactions became more and more refined (Neil, 1982, 1985; Sandeman, 1977, 1983). Although inviting for study, only few attempts exist to relate the different designs of neural control systems to the ecological situation of the species. With this in mind, the present report reviews the literature on multimodal control of eye stabilization in decapod crustaceans in relation to the ecological context of the species examined. Emphasis is placed on the notion that one has to distinguish species according to whether they primarily live in visually well or poorly defined environments, on solid or soft ground, whether they walk or swim, and whether they are highly mobile, sluggish, or sessile. Depending on life-style and habitat, different sensory cues for postural control and eye stabilization are likely to be exploited. Besides these, we have to keep in mind that there may be further ecological constraints and restrictions imposed by evolutionary history on the sensory mechanisms developed by the species. The aim of such an approach is to recognize the sensory systems as matched filters (Wehner, 1987) and in this way to gain a deeper understanding of biological information processing. The presentation of the data is divided

Topographic organization of the orientation column system in large flat‐mounts of the cat visual cortex: A 2‐deoxyglucose study

We developed a flat-mount technique in order to visualize, without additional reconstruction, the system of orientation columns in the cat visual cortex by using 2-deoxyglucose-autoradiography. Experimental animals were injected with 2-deoxyglucose and then stimulated for 45-60 minutes either with vertical or horizontal or oblique gratings alone or with vertical and horizontal gratings presented in alternation. In both areas 17 and 18 stimulation with either vertical or horizontal or oblique stripes produced similar and highly ordered patterns of parallel bands of increased 2-deoxyglucose uptake that were perpendicular to the boundaries of the areas. In area 17 they occasionally extended without interruption from the 17/18 border on the top of the lateral gyrus to the monocular segment in the splenial sulcus. Superposition of serial sections revealed that these bands were present in all cortical layers and in precise register along lines orthogonal to the lamination. The center-to-center spacing of the bands was 1.0-1.1 mm in area 17 and 1.2-1.4 mm in area 18. Stimulation with alternating vertical and horizontal contours led to a pattern the general organization of which resembled that induced by a single orientation but the spacing of which was reduced by a factor of 0.5. This strongly supports the concept that orientation is mapped in a system of parallel bands and argues against a recently formulated hypothesis that iso-orientation bands extend like spokes from centers that lack orientation selectivity (Braitenberg and Braitenberg, Biol. Cybern. 33:179-186, '79). Another characteristic feature, revealed by the flat-mount technique, was a periodic variation of 2-deoxyglucose uptake along the bands that gave them a beaded appearance. The mean center-to-center distance between adjacent beads on the same band was in the range of 0.9-1.2 mm and remained unchanged when horizontal and vertical gratings were presented in alternation. We propose that these beads reflect another columnar system whose features have yet to be determined.

Making ambiguous displays unambiguous: the influence of real colors and colored aftereffects on perceptual alternation.

The relationship between orientation-contingent colored aftereffects (CAEs) and perceptual alternation of ambiguous displays was investigated in three experiments. In all experiments, the ambiguous test display consisted of vertical and horizontal contours that either could be perceived as separate surfaces (the diamond organization) or could be combined to form upright and inverted Us (the rectangles organization). In Experiments 1 and 2, observers inspected the test display when it was achromatic, when it was colored in a manner consistent with the appearance of CAEs, and when it was colored in a non-CAE manner. In Experiment 3, the test display was inspected monocularly before and after monocular color-orientation adaptation. The achromatic viewing conditions of Experiments 1 and 2, both monocular preadaptation achromatic viewing conditions of Experiment 3, and the postadaptation achromatic viewing condition involving the nonadaptation eye in Experiment 3 produced essentially the same results: reports of approximately equal duration for the diamond and rectangles organizations and steady rates ofperceptual alternation. The non-CAE color conditions of Experiment 2 produced a similar pattern of results. However, the color condition of Experiment 1 (i.e., simulated CAEs), and the postadaptation condition involving the adaptation eye in Experiment 3 produced a decrement in the perceptual alternation rate, with the diamond organization being reported almost exclusively. These results indicate that ambiguous displays can be made unambiguous by altering the appearance of the displays either through the addition of appropriate colors or by exposing observers to appropriate adaptation conditions. These results are consistent with stimulus-bound explanations of both CAEs and perceptual alternation.

The precedence of binocular fusion over binocular rivalry

During fusion, when both eyes view a set of identical vertical contours, reaction times (RT) to decrements in contrast of either set of contours are very brief. When the right eye views a set of vertical contours and the left eye views a set of horizontal contours, vigorous binocular rivalry results. RTs to decrements in the contrast of one set of contours is brief if those contours are dominant in rivalry; RT is lengthened considerably if those contours are suppressed. When the right eye views a set of vertical contours and the left eye views a set of horizontal contours and a set of vertical contours, RTs to decrements in contrast of any of those contours are comparable to those measured during fusion, not during rivalry. This pattern of results indicates that the presence of matching features in the two eyes’ views renders those features exempt from binocular suppression; binocular fusion takes precedence over binocular rivalry.

Computerized processing of thorney island trial data for comparison with model predictions

This paper describes a user's experience of the computer processing of the data tapes from Phase I of the Thorney Island trials and the graphical techniques used to present and compare the trial results with model predictions. Six of the sixteen sets of trial data were selected for the comparisons, based on categorization of the trials by wind speed and stability. Both trial data and model results were converted to downwind and crosswind coordinates. In addition to horizontal and vertical concentration contours, plots were produced for maximum concentration versus time and distance. A method was developed to compare, as a function of time, the concurrent areal coverage of horizontal concentration contours of the trial results with the predicted results.

Topographic organization of orientation columns in the cat visual cortex. A deoxyglucose study.

Three-dimensional reconstructions of the orientation column system were obtained from the visual cortex of four cats using the deoxyglucose technique. One cat had normal visual experience, one was monocularly and two had selective experience with vertical and horizontal contours, respectively. In areas 17 and 18 orientation columns form a remarkably regular system of equally spaced parallel bands whose trajectory is orthogonal to the borderline between areas 17 and 18. This topographic organization is resistant to manipulations of early visual experience.

Restriction of visual experience to a single orientation affects the organization of orientation columns in cat visual cortex. A study with deoxyglucose.

In six dark reared, 4-weak-old kittens visual experience was restricted to contours of a single orientation, horizontal or vertical, using cylindrical lenses. Subsequently, the deoxyglucose method was used to determine whether these artificial raising conditions had affected the development of orientation columns in the visual cortex. After application of the deoxyglucose pulse one hemifield was stimulated with vertical, the other with horizontal contours. Thus, from interhemispheric comparison, changes in columnar systems corresponding to experienced and inexperienced orientations could be determined. The following results were obtained: (1) Irrespective of the restrictions in visual experience, orientation columns develop in areas 17, 18, 19 and in the visual areas of the posterior suprasylvian sulcus. (2) Within area 17, spacing between columns encoding the same orientations is remarkably regular (1 mm), is not influenced by selective experience and shows only slight interindividual variation. (3) In non-striate areas the spacing of columns is less regular and the spatial frequency of the periodicity is lower. (4) The modifiability of this columnar pattern by selective experience is small within the granular layer of striate cortex but substantial in non-granular layers: Within layer IV columns whose preference corresponds to the experienced orientation are wider and more active than those encoding the orthogonal orientation but the columnar grid remains basically unaltered. Outside layer IV the columnar system is maintained only for columns encoding the experienced orientations. The deprived columns by contrast frequently fail to extend into non-granular layers and remain confined to the vicinity of layer IV. (5) These modifications in the columnar arrangement are more pronounced in striate cortex than in nonstriate visual areas and, within the former, more conspicuous in the central than in the peripheral representation of the visual field. It is concluded that within layer IV the blue print for the system of orientation columns is determined by genetic instructions: first order cells in layer IV develop orientation selectivity irrespective of experience whereby the preference for a particular orientation is predetermined by the position in the columnar grid. Dependent on experience is, however, the expansion of the columnar system from layer IV into non-granular layers. It is argued that all distortions following selective rearing can be accounted for by competitive interactions between intracortical pathways, the mechanisms being identical to those established for competitive processes in the domain of ocular dominance columns. It is proposed that such experience dependent modifiability of connections between first and second order cells is a necessary prerequisite for the development of orientation selectivity in cells with large and complex receptive fields.

Figure embeddedness as a function of the orientation embedding-field contours.

The 'oblique effect' was studied with the use of an embedded-figures task in which the percentage of contextual or embedding contours aligned in the same orientations as those comprising the hidden forms was systematically varied. For hidden forms comprised either of horizontal and vertical contours, or of oblique (45 degree and 135 degree) contours, search times increased markedly as the percentage of aligned contextual contours increased. Although the rate at which embeddedness increased was the same for both orientations, search times were consistently greater for locating obliquely oriented targets (p less than 0.05), and search time variance was significantly greater (p less than 0.025) on trials in which the hidden form was oblique. The results suggest that the laws of organization governing embeddedness apply equally to oblique and horizontal-vertical orientations, but perceptual processing of oblique orientations is poorer. The relationship between search time and aligned contour is discussed in terms of the dual processes of extraction and synthesis in visual search.

The influence of imagery ability on color aftereffects produced by physically present and imagined induction stimuli.

Two methods of induction were used to produce orientation-contingent color aftereffects for observers assigned to one of three groups (high, medium, and low) on the basis of self-rated imagery ability. In Experiment 1, observers were required to make magnitude estimates of color aftereffects following inspection of stimulus patterns normally used to produce McCollough effects (e.g., red vertical contours, green horizontal contours). Experiment 2 was a partial replication of Experiment 1, with additional induction conditions in which observers were required to imagine the presence of appropriately oriented contours when particular homogeneous color patches were presented. The results indicated that self-rated imagery ability was not a significant factor in differentiating between observers’ performance when orthodox induction procedures were used (Experiment 1). In addition, there were no reliable indications (Experiment 2) that imagined stimulus attributes can be effectively substituted for real stimulus attributes in order to produce orientation-contingent color aftereffects. The results are discussed in terms of their implications for the use of imagery-induced perceptual phenomena as a paradigm for investigating the possibility of common neural mechanisms in perception and imagination; in addition, the general implications of the results for understanding the functional significance of self-reported imagery ability are examined.

A physiological and behavioural study in cats of the effect of early visual experience with contours of a single orientation.

1. Three kittens were reared in visual environments that consisted of stripes at one of three orientations - horizontal, right oblique, or left oblique. Two additional cats were reared as controls. One of these matured viewing right and left oblique stripes on alternate days. The other experienced a normal visual environment. 2. Following the completion of rearing, and after several weeks of normal visual experience, behavioural testing of the stripe-reared animals demonstrated a deficit in visual acuity for orientations which were not present in the early visual environment. No comparable deficit emerged for either of the control cats. 3. Following 1-3 years of further, normal, visual experience, each of the cats was shipped separately to California where single units were recorded from area 17 of the visual cortex and an effort made to guess the early visual history of each animal which was unknown to the experimenters. Cell samples from each experimental cat and the normal control cat allowed the physiologist to guess their early visual experience correctly. The control cat which matured viewing orthogonal sets of oblique stripes on alternate days demonstrated a bias for horizontal contours in his cell sample. In contrast to units recorded from normal cats, about 80% of which are binocular, only about 30% of the cells recorded from the stripe-reared animals could be influenced by both eyes.

Kittens reared in a unidirectional environment: evidence for a critical period.

1. Kittens were reared in the dark from birth except for a period each day when they were put inside a stationary transparent cylinder, around which a drum with vertical black and white stripes on the inside, rotated in one direction. After the end of the period of exposure, we recorded a sample of single cells from their visual cortices, and analysed each cell for direction and orientation sensitivity and other properties. 2. Two kittens were placed inside the drum, rotating rightward, for 2 hr each seekday from 3 1/2 to 7 weeks of age. A greater proportion of the directionally sensitive cells in their cortices showed a preference for rightward movement. 3. Six other kittens were placed inside the drug for 1 hr each weekday from 2 to 12 weeks of age with the drum rotating leftward up to a particular changeover age, then rightward until 12 weeks. The changeover point occurred at 21, 26, 28, 33, 35 and 51 days for different kittens. A changeover earlier than 4 weeks of age led to a preponderance of cells preferring rightward movement. A changeover later than 5 weeks of age led to a preponderance of cells preferring leftward movement. Comparison of these results with others on monocular deprivation suggests that the peak of the critical period for directional deprivation may occur earlier than the peak of the critical period for monocular deprivation. 4. None of the samples of cells showed a preponderance of cells specific for vertical orientations. It is unclear whether this negative effect resulted from the presence of some horizontal contours during exposure, or some more fundamental cause.

Cortical effect of early selective exposure to diagonal lines.

Neurons in the visual cortex that respond preferentially to diagonal contours are present only in cats exposed to diagonal lines early in life. In contrast, cells that prefer horizontal or vertical contours are found following exposure to horizontal, to vertical, and to diagonal lines. Such cells do not require a specific visual input for maintenance or for development; neurons responding preferentially to diagonal lines do.

Simultaneous disappearances of both images during binocular rivalry of contours and effect on eye-blink rate.

Simultaneous disappearances of both rivalry images were reported by 28 women who reported on the rivalry 3.2 degree diagonal rivalry contours for 10 min. of continuous viewing. The data support the notion that suppression of images during binocular rivalry is independent in both eyes. In a second study, 48 women reported simultaneous disappearances during the rivalry of 3.2 degree vertical and horizontal contours for 10 min. of continuous viewing under one of two blink-rate instruction conditions. Fewer simultaneous disappearances were reported by Ss instructed to blink every 5 sec. than by Ss instructed to blink every 15 sec. Blinking may reduce the probability of simultaneous disappearances in rivalry. In both studies, the fusion squares surrounding the rivalry stimuli were continuously perceived.

Optically induced eye torsion. I. Fusion cyclovergence.

Fusional cyclovergence was demonstrated for the first time, using ab objective photographic method. It was discovered that the results of subjective and objective measurements of cyclovergence agreed exactly. The largest fusional cyclovergence observed was 8 degrees. The cyclovergence partly cancels out the cyclodisparity presented. The greater part of the cyclodisparity usually remains. The maximum aplitude of the sensory cyclofusion is of the order of 8 degrees. The cyclovergence response is greatest when large fusion images with numerous horizontal contours are presented. The motor mechanism of cyclofusion presupposes the existence of recently demonstrated cyclodisparity detectors. The amplitude of sensory fusion is determined by the vertical diameter of the peripheral Panum areas.

The effect of early astigmatism on the visual resolution of gratings.

1. Orientational differences in visual resolution were measured at a number of different luminance levels on two subjects with high astigmatism that had remained optically uncorrected until the age of 10. Because of their astigmatism both of these subjects see vertical contours more clearly than horizontal contours with the unaided eye.2. The measurements were made using sinusoidal gratings generated on the face of an oscilloscope with the refractive error carefully corrected with lenses and with the gratings viewed through 3 mm artificial pupils.3. Visual resolution was found to be much better for vertical than for horizontal gratings for both these subjects under these conditions. The difference between the contrast sensitivities for vertical and horizontal gratings was even evident with gratings having spatial frequencies as low as 1 c/deg, but became progressively more pronounced at higher spatial frequencies. In one of the subjects the visual acuity (the cut-off spatial frequency) for horizontal gratings was more than 3/4 of an octave lower than that for vertical gratings.4. This is very different from the results obtained from normal subjects who typically show only a slight reduction in contrast sensitivity for oblique gratings but resolve vertical and horizontal gratings equally well.5. The quantitative differences between the contrast sensitivities for vertical and horizontal gratings of both high and low spatial frequencies cannot be accounted for by either errors of focus in one meridian or by the presence of meridional aniseikonia.6. In order to completely eliminate any optical explanations for these findings measurements of contrast sensitivity were made using sinusoidal interference fringes formed directly on the retina, thereby bypassing the eye's optics. Since the orientational differences in resolution persisted with this method it must be concluded that they are of neural origin.7. By analogy with the effects on cortical physiology that follow early selective visual deprivation in cats and monkeys, it is argued that these orientational differences in resolution are a consequence of changes induced in the neural organization of the astigmat's visual system by the distorted visual input provided by the uncorrected astigmatism early in life. It is furthermore argued that the smaller orientational differences in resolution observed in normal eyes might similarly be induced by certain asymmetries in the early visual input.

INTERPRETATION QUANTITATIVE EN GRAVIMETRIE OU MAGNETISME A PARTIR DE CARTES TRANSFORMEES DE GRADIENT VERTICAL*

AbstractA discussion is given of the requirements, the advantages and the methods to be considered in attempting the quantitative interpretation of gravity or magnetic fields from computed maps of the vertically derived field.The transform which is used here is the first vertical derivative (or vertical gradient) with or without downward continuation, but the computed maps are in fact obtained by a controllable Fourier method in which two kinds of operations can be simultaneously performed in complete independance: on one hand the separation of any part of the data by frequency cut‐off, and on the other hand the transformation by vertical derivation or continuation of the part which is retained.Taking as raw data either actual surveys or artificially constructed maps, it is first shown how separated and transformed maps of this type can be efficiently obtained under quite flexible conditions, using a special computer program. It is further seen that for correctly controlled filterings the accuracy of the computed maps actually permits to take them as the basis for quantitative interpretation.To effect this, any one of the conventional methods which make use of equivalent model computations may in the first place be adapted to the interpretation of gradients, with the benefits, however, of an enhanced lateral separation of the anomalies and of a large attenuation of the regional effects.Particularly, the delineation of horizontal contours for even fairly complex models can often be made directly in a sufficiently safe way on the anomalies as they show on the vertical gradient maps. This greatly accelerates the process of determining equivalent model bodies.More special methods of interpretation can also be designed by taking into account first the fact that the vertical derivation of the field amounts to an operation of separation on the field's sources themselves, and in addition the availability of the frequency form of the information as a result of using a Fourier method of transform computation.Trial utilisations of various such interpretation processes of either the conventional or the less conventional type, are presented especially in connection with an interpretation study on transformed maps of parts of an offshore aeromagnetic survey (English Channel).

Selectivities of human visual mechanisms for direction of movement and contour orientation.

The luminance threshold for horizontal contours which move upward is raised by prior exposure of any of wide range of different directions of movement. The threshold for a stationary grating of horizontal bars is raised only by prior exposure of similarly oriented bars. It is also found that sensitivity to changes in orientation of a stationary grating is greater than sensitivity to changes in the direction in which a grating moves. It is proposed that the interactions between pre-exposed adapting stimuli and the stimuli for which thresholds are determined reflect the orientation and direction selectivities of the underlying mechanisms.

Orientation-specific effects of patterns of adapting light on visual acuity.

Inspection of a pattern of horizontal, vertical, or oblique lines differentially affects the visual acuity for test gratings as a function of their orientation. After a horizontal grating is viewed for 1 sec or longer, the resolution threshold for horizontal contours is greater than the threshold for the identification of vertical and obliquely oriented contours. Conversely, prolonged viewing of vertical contours raises the threshold for the identification of vertical lines above those for other orientations. Similar results are found following adapting exposures to left-and right-oblique contours. The differential masking effects are systematic functions of the duration of exposure to the light-and-dark adapting pattern.

Reflections on a Drawing by Van Gogh*

VAN GOGH'S drawing, Tile Factory near Arles, in the Collection of the Courtauld Institute, London,1 does not, in the reproduction at least (Fig. 1), evoke the immediate enthusiasm inspired by so many of the artist's drawings. In the original, however, the rich gradations of tone in the now brownish ink-strokes of varying thickness, merely suggested in the reproduction, attract us at first sight. The material charm of the India ink, the color modified by age and by variations due to the reed pen, represents of course only a small part of this effect; it merely enhances the considered differentiation in the graphic means. This differentiation is full of subdued effects, and the relationship between the widely divergent graphic forms—pale and dark pen-strokes varied with some of intermediary value, thin and thick lines, many straight lines and few curves—gives rise to a play of values hardly ever exploited to produce sharp contrasts. The result is a kind of smoothing out of the effects, a harmony which, superficially at least, appears the exact opposite of all that is regarded as characteristic of Van Gogh's manner. The composition of the drawing and the view selected are in keeping with this. The horizon, viewed from a normal angle, almost cutting the surface of the picture in two, though at no place actually visible, determines a number of horizontal lines: the edge of the street, the fences with their horizontal bars, the virtually horizontal edges of the roofs. These many horizontal contours and the vertical strokes in the fences and walls of the houses are opposed by only a small number of diagonals, namely, the unavoidable diagonals of the gables of the houses and a series of short dark strokes leading in sharp foreshortening from the grass in the foreground to the field beyond.