On perceptual analyzers underlying visual texture discrimination: Part I

We have found a class of feature detectors, based on the quasi-collinearity of dots, which result in visual texture discrimination even when second order statistics are equal. This degenerate counterexample to the Julesz conjecture on effortless texture discrimination has supplied the key to a simple theory of texture discrimination. Accordingly, effortless texture discrimination is based on two classses of perceptual detectors: Class A, those that measure differences in second-order (dipole) statistics; Class B, those that can still detect statistical differences in some features when second-order statistics are kept identical; for instance, the quasi-collinearity of adjacent dipoles. The difference thresholds (tuning curves) for the perceptual dipole and quasi-collinearity detectors have been determined. These texture pairs were generated by a method that creates micropatterns with iso-dipole duals from 4 disks. The extension of this 4-disk method to 5 and more disks with iso-dipole duals permits the search for other kinds of perceptual detectors and will be discussed in Part II.     

Gabor filters as texture discriminator

The present paper presents a model for texture discrimination based on Gabor functions. In this model the Gabor power spectrum of the micropatterns corresponding to different textures is calculated. A function that measures the difference between the spectrum of two micropatterns is introduced and its values are correlated with human performance in preattentive detection tasks. In addition, a two stage algorithm for texture segregation is presented. In the first stage the input image is transformed via Gabor filters into a representation image that allows discrimination between features by means of intensity differences. In the second stage the borders between areas of different textures are found using a Laplacian of Gaussian operator. This algorithm is sensitive to energy differences, rotation and spatial frequency and is insensitive to local translation. The model was tested by means of several simulations and was found to be in good correlation with known psychophysical characteristics as texton based texture segregation and micropattern density sensitivity. However, this simple model fails to predict human performance in discrimination tasks based on differences in the density of terminators. In this case human performance is better than expected.     

A theory of preattentive texture discrimination based on first-order statistics of textons

The many indistinguishable texture pairs having identical second-, but different third- and higher-order statistics, led to the conjecture thatglobally the preattentive texture discrimination system cannot process statistical parameters of third- or higher-order. Thus in cases when iso-second-order textures yield discrimination this must be based onlocal conspicuous features calledtextons (Julesz, 1980). Here it is shown that globally even second-order statistical parameters, such as autocorrelation, cannot be processed by the textural system, and texture discrimination is solely the result of first-order statistics (density) of textons. It is also shown that the perceivable distance of statistical constraints (coherence distance) in densely packed stochastic textures is very short, four dots or less. As of now, only three texton classes were found: color, elongated blobs (line segments) of given width, orientation, and length, and the terminators (end-points) of these elongated blobs. The strength of these textons is demonstrated by several examples.     

Texture discrimination asymmetries across the visual field

Texture discrimination is sometimes asymmetrical; texture A embedded in texture B is more easily detected than texture B embedded in texture A. Furthermore, texture discrimination often improves as the disparate texture is moved into the periphery; this has been referred to as the central performance drop (CPD). The interaction of these interesting and counter-intuitive aspects of texture discrimination has received very little attention. Using four stimulus pattern pairs that were previously shown to elicit asymmetrical texture discrimination, we examined texture discrimination asymmetries as a function of eccentricity. We found three patterns of results; (i) both texture arrangements (A in B, and B in A) elicit a CPD but do not show an asymmetry, (ii) both texture arrangements elicit a monotonic decrease in performance with eccentricity (i.e. no CPD) but an asymmetry is seen at each eccentricity and (iii) discrimination asymmetries are minimal at fixation and in the far periphery and maximal about 3 degrees from fixation with a CPD generally shown for the 'stronger' member of the pair. These results emphasize that one cannot talk about the 'discriminability' of a particular texture pair without reference to the arrangement of the two textures and the eccentricity of presentation.     

Models for preattentive texture discrimination: Fourier analysis and local feature processing in a unified framework

Spatial frequency analysis and local feature analysis may be considered to be examples of a class of models for texture discrimination. In this theoretical framework, texture discrimination relies on differences in the distribution of responses generated in linear receptive fields placed randomly on the texture. If the set of receptive fields is taken to be a collection of gratings, spatial-frequency analysis is recovered. If the set of receptive-fields is taken to be a collection of local feature templates, a corresponding local-feature model is recovered. In order to test such models, it is necessary to construct distinct texture pairs that elicit similar distributions of responses for all of the postulated receptive field profiles: the model prediction is that such textures are not discriminable. A method is provided for construction of such textures which test generic models within this framework. This framework includes not only strict Fourier analysis, but also models which postulate a collection of arbitrarily-shaped local feature detectors, and models which postulate both Fourier analysis and local feature detection.     

Figure-ground discrimination by relative movement in the visual system of the fly

The visual system of the fly performs various computations on photoreceptor outputs. The detection and measurement of movement is based on simple nonlinear multiplication-like interactions between adjacent pairs and groups of photoreceptors. The position of a small contrasted object against a uniform background is measured, at least in part, by (formally) 1-input nonlinear flicker detectors. A fly can also detect and discriminate a figure that moves relative to a ground texture. This computation of relative movement relies on a more complex algorithm, one which detects discontinuities in the movement field. The experiments described in this paper indicate that the outputs of neighbouring movement detectors interact in a multiplication-like fashion and then in turn inhibit locally the flicker detectors. The following main characteristic properties (partly a direct consequence of the algorithm's structure) have been established experimentally: a) Coherent motion of figure and ground inhibit the position detectors whereas incoherent motion fails to produce inhibition near the edges of the moving figure (provided the textures of figure and ground are similar). b) The movement detectors underlying this particular computation are direction-insensitive at input frequencies (at the photoreceptor level) above 2.3 Hz. They become increasingly direction-sensitive for lower input frequencies. c) At higher input frequencies the fly cannot discriminate an object against a texture oscillating at the same frequency and amplitude at 0° and 180° phase, whereas 90° or 270° phase shift between figure and ground oscillations yields maximum discrimination. d) Under conditions of coherent movement, strong spatial incoherence is detected by the same mechanism. The algorithm underlying the relative movement computation is further discussed as an example of a coherence measuring process, operating on the outputs of an array of movement detectors. Possible neural correlates are also mentioned.     

Discrimination of complex textures by bees

A problem confronted by visual systems is that of discriminating textures. It appears that a recently described class of orientation-tuned neurones in the bee brain embody properties of mechanisms used by humans to discriminate complex textures. In particular these mechanisms would permit bees to discriminate a large range of textures by giving bees access to information related to higher-order correlations between texture elements. To determine if bees can exploit such textural information we have conducted behavioural experiments employing iso-dipole textures, that statistically speaking, differ from binary noise textures, and each other, only in their third-order correlation functions. While these textures are not themselves of any ethological significance their special properties permit us to show that bees can potentially use a very large palette of textures to classify textured objects. In electrophysiological experiments we demonstrate the requisite contrast sign invariance (rectification) of the orientation-selective neurones' responses and discuss other similarities of these neurones' responses to models accounting for human texture discrimination. Accepted: 7 October 1998     

Spatial nonlinearities in the instantaneous perception of textures with identical power spectra

In 1962, Julesz observed that texture pairs with identical second-order statistics but different third- and higher-order statistics were usually not discriminable without scrutiny. Since second-order (dipole) statistics determine the autocorrelation functions and hence the power spectra, this observation also meant that in preattentive perception of texture the phase (position) spectra were ignored. In the last two decades many new classes of texture pairs with identical power spectra have been invented that were not effortlessly discriminable; however, recently (Caelli & Julesz 1978; Caelli et al. 1978; Julesz et al. 1978) several counterexamples were found. In these texture pairs with identical power spectra some local structures of 'quasi-collinearity', 'corner', 'closure' and 'granularity' yielded strong discrimination. These features can be regarded as the fundamental building blocks of form, that is, the essential nonlinearities of the preattentive perceptual system. Here, it will be shown that these counter-examples are not independent of each other, but can be described by two elementary units; bars (line segments) and their terminators. Furthermore, the preattentive texture perception system can count the number of terminators but ignores their positions.     

Three processing characteristics of visual texture segmentation

Three mechanisms are outlined which are sufficient to determine texture segmentation or discrimination. They are: (1) convolution of detector profiles with the input image; (2) impletion, where the perceptual 'filling in' of the input surface occurs via a nonlinear filtering operation on each detector's output (3) grouping, where areas are segregated according to their differences in detector responses after impletion occurs. These mechanisms are compared with those proposed to occur in human visual texture discrimination.     

Discrimination of random dot texture patterns in bluegill sunfish,Lepomis macrochirus

In order to study the ability of fish to perceive and distinguish textures visually, bluegill sunfish (Lepomis macrochirus) were trained to discriminate between pairs of artificial texture patterns. Random dot patterns with different statistical dot distributions were presented to the fish as artificial texture patterns. The results indicate that bluegills have the ability to discriminate many pairs of patterns with different statistical features of dot distributions which have different appearance in texture. This suggests that texture could be one of the important visual features bluegill sunfish recognize and utilize.     

A two dimensional field theory for motion computation

The local extraction of motion information from brightness patterns by individual movement detectors of the correlation-type is considered in the first part of the paper. A two-dimensional field theory of movement detection is developed by treating the distance between two adjacent photoreceptors as a differential. In the first approximation of the theory we only consider linear terms of the time interval between the reception of a contrast element and its delayed representation by the detector and linear terms of the spatial distances between adjacent photoreceptors. As a result we may neglect terms of higher order than quadratic in a Taylor series development of the brightness pattern. The responses of pairs of individual movement detectors are combined to a local response vector. In the first approximation of the detector field theory the response vector is proportional to the instantaneous pattern velocity vector and linearly dependent on local properties of the moving pattern. The linear dependence on pattern properties is represented by a two by two tensor consisting of elements which are nonlinear, local functional of the moving pattern. Some of the properties of the tensor elements are treated in detail. So, for instance, it is shown that the off-diagonal elements of the tensor disappear when the moving pattern consists of x- and y-dependent separable components. In the second part of the paper the tensor relation leading to the output of a movement detector pair is spatially integrated. The result of the integration is an approximation to a summation of the outputs of an array of detector pairs. The spatially integrated detector tensor relates the translatory motion vector to the resultant output vector. It is shown that the angle between the motion vector and the resultant output vector is always smaller than ±90° whereas the angle between the motion vector and local response vectors, elicited by detector pairs, may cover the entire angular range. In the discussion of the paper the limits of the field theory for motion computation as well as its higher approximations are pointed out in some detail. In a special chapter the dependence of the detector response on the pattern properties is treated and in another chapter questions connected with the so called aperture problem are discussed. Furthermore, properties for compensation of the pattern dependent deviation angle by spatial physiological integration are mentioned in the discussion.     

Asymmetries in visual texture discrimination

Recent results have shown that texture discrimination is an asymmetrical process; texture A within texture B may be much easier to detect than texture B within texture A. Two questions regarding discrimination asymmetries are addressed: (i) what sorts of textural properties are associated with discrimination asymmetries; and (ii) what sort of architecture would yield asymmetries. Two experiments show that discrimination asymmetries obtain when textures comprise circles of different sizes (large circles are easier to detect in small than vice versa) and when circles differ only in the regularity of their placement (irregularly placed circles are easier to detect in a background of regularly placed circles than vice versa). A plausible account of texture discrimination would involve the decomposition of images via a set orientation and scale selective filters followed by a second layer of filtering to detect energy differences between adjacent regions in the original convolutions. Discrimination asymmetries provide prima facie evidence against such a model because it involves only local measurements and comparisons. We propose that discrimination asymmetries are elegantly explained if it is assumed that the responses of the orientation and scale selective filters are normalized by the degree to which similarly tuned operators are responding elsewhere in the image; viz., global normalization of filter responses. However, there are cases where such global normalization is not required to explain asymmetrical discrimination.     

The Visual N1 Is Sensitive to Deviations from Natural Texture Appearance

Disruptions of natural texture appearance are known to negatively impact performance in texture discrimination tasks, for example, such that contrast-negated textures, synthetic textures, and textures depicting abstract art are processed less efficiently than natural textures. Presently, we examined how visual ERP responses (the P1 and the N1 in particular) were affected by violations of natural texture appearance. We presented participants with images depicting either natural textures or synthetic textures made from the original stimuli. Both stimulus types were additionally rendered either in positive or negative contrast. These appearance manipulations (negation and texture synthesis) preserve a range of low-level features, but also disrupt higher-order aspects of texture appearance. We recorded continuous EEG while participants completed a same/different image discrimination task using these images and measured both the P1 and N1 components over occipital recording sites. While the P1 exhibited no sensitivity to either contrast polarity or real/synthetic appearance, the N1 was sensitive to both deviations from natural appearance. Polarity reversal and synthetic appearance affected the N1 latency differently, however, suggesting a differential impact on processing. Our results suggest that stages of visual processing indexed by the P1 and N1 are sensitive to high-order statistical regularities in natural textures and also suggest that distinct violations of natural appearance impact neural responses differently.     

Synergy of features enables detection of texture defined figures

Traditional theories of early visual processing suggest that elementary visual features are handled in parallel by independent neural pathways. We studied the interaction of orientation and spatial frequency in the discrimination of Gabor random fields. Target textures differed from reference textures either in mean feature value, showing an edge-like transition between both textures (edge defined), or in the degree of feature homogeneity with smooth transitions (region defined). Irrespective of the kind of texture definition, we found strong cue summation for targets defined by both cues simultaneously, provided two conditions were fulfilled. First, they were barely discriminable when defined by one cue alone. Second, the target elements formed a closed 2D surface. Only marginal cue summation was observed when target elements were heterogeneously distributed in a predefined area, lacking a clear 2D shape. Our findings indicate that feature synergy enables figure-ground segregation when the information from independent feature-specific pathways is insufficient for solving this task.     

Vibrotactile adaptation impairs discrimination of fine,but not coarse,textures

The effect of vibrotactile adaptation on the ability to discriminate textured surfaces was examined in three experiments. The surfaces were rectilinear arrays of pyramids produced by etching of silicon wafers. Adaptation to 100-Hz vibration severely hampered discrimination of surfaces with spatial periods below 100 &#119 m (Experiment 1), but had little effect on the discrimination of coarser textures (Experiment 2). To determine which vibrotactile channel—Rapidly Adapting or Pacinian—plays the larger role in mediating the discrimination of fine textures, widely separated adapting frequencies (10 and 250 Hz) were used in Experiment 3. The fact that high- but not low-frequency adaptation interfered with discrimination suggests that the Pacinian system contributes importantly to this ability. Taken as a whole, the results of this study strongly support the duplex theory of tactile texture perception, according to which different mechanisms—spatial and vibrotactile—mediate the perception of coarse and fine textures, respectively.     

Texture discrimination by Gabor functions

A 2D Gabor filter can be realized as a sinusoidal plane wave of some frequency and orientation within a two dimensional Gaussian envelope. Its spatial extent, frequency and orientation preferences as well as bandwidths are easily controlled by the parameters used in generating the filters. However, there is an uncertainty relation associated with linear filters which limits the resolution simultaneously attainable in space and frequency. Daugman (1985) has determined that 2D Gabor filters are members of a class of functions achieving optimal joint resolution in the 2D space and 2D frequency domains. They have also been found to be a good model for two dimensional receptive fields of simple cells in the striate cortex (Jones 1985; Jones et al. 1985).The characteristic of optimal joint resolution in both space and frequency suggests that these filters are appropriate operators for tasks requiring simultaneous measurement in these domains. Texture discrimination is such a task. Computer application of a set of Gabor filters to a variety of textures found to be preattentively discriminable produces results in which differently textured regions are distinguished by firstorder differences in the values measured by the filters. This ability to reduce the statistical complexity distinguishing differently textured region as well as the sensitivity of these filters to certain types of local features suggest that Gabor functions can act as detectors of certain texton types. The performance of the computer models suggests that cortical neurons with Gabor like receptive fields may be involved in preattentive texture discrimination.     

Illuminant precompensation for texture discrimination using filters

 Texture-discrimination algorithms have often been tested on images containing either mosaics of synthetic textures or artificially created mosaics of real textures – in any case, images in which most of the changes in intensity can be ascribed to the textures themselves. However, real images are not formed like this and may contain steep gradations in intensity which have nothing to do with local texture, such as those caused by incident shadows. A texture discrimination algorithm based on linear filters can fail in the presence of these strong gradations, as they may easily contain an order of magnitude more energy than the gradations in intensity due to texture in the image per se. In these cases, the mechanism may become responsive only to strong luminance effects, and not to texture. I have found that good performance on natural images containing texture can only be obtained from a filter-based texture detection scheme if it includes a stage which attempts to bring large intensity gradients within bounds. The exact nature of the best precompensator appears to depend somewhat on the way the filter outputs are processed. The fit to psychophysical data and the implications for more detailed models of human texture processing will be discussed. Received: 3 May 1993/Accepted in revised form: 7 June 1993     

Discriminable textures with identical buffon needle statistics

A method is presented for generating pairs of textures for which the statistics of intersection with any collinear set of points placed at random on either texture are the same. The constraint that such Buffon needle statistics be identical is stronger than identity of second-order statistics. Nonetheless, many such texture pairs are effortlessly distinguishable. An example is given of such a texture pair, whose components are composed of either congruent ellipses or circles of various radii. The discriminability of such texture pairs implies that adequate models for human texture preception must contain local nonlinearities which receive input from non-collinear points.     

SPATIAL VARIABILITY IN SEED PRODUCTION OF THE PERENNIAL BUNCHGRASS BOUTELOUA GRACILIS (GRAMINEAE)

The effects of soil texture and grazing by cattle on the production of seeds of Bouteloua gracilis were evaluated for a semiarid grassland in northeastern Colorado. Ten locations were chosen to represent the range in soil textures and grazing intensities found at the Central Plains Experimental Range research site. Number of flowering culms, inflorescences and seeds, length of each flowering culm, total biomass of reproductive structures (culms, inflorescences, and seeds), and basal area were assessed for 96 B. gracilis plants at each location. Community-level estimates of density of flowering culms and density of viable seeds were made for each location. Both soil texture and grazing by cattle were important to spatial variability in seed production and other indicators of reproductive effort by B. gracilis. Grazing was important in mediating effects of soil texture. On locations protected from grazing, soil texture had significant effects on seed production; the largest number of seeds was produced on the coarsest-textured soil and the fewest number on the finest-textured soil. Relationships between seed production and clay content and between seed production and other indicators of reproductive effort by B. gracilis were different for grazed and ungrazed locations. Spatial variability in seed production of B. gracilis as a result of spatial variability in soil texture and grazing may be important to the continued dominance of this species in the presence of disturbances that vary in time and space.     

Bone surface texture as an ontogenetic indicator in long bones of the Canada goose Branta canadensis (Anseriformes: Anatidae)

Growth series of femora, tibiotarsi, and humeri of the Canada goose Branta canadensis were examined to evaluate whether bone surface textures are reliable indicators of relative age and skeletal maturity in this taxon. The relationship between surface texture and skeletal maturity was analysed by comparing element texture types with both size-based and size-independent maturity estimates. A subsample of hindlimb elements was thin sectioned to observe histological structures underlying various surface textures. Three relative age classes of elements are identifiable based on surface texture. Juvenile and subadult bone textures have fibrous and/or porous areas on the bone shaft and are distinguished by the presence (in juveniles) or absence (in subadults) of coarse longitudinal striations in proximal and/or distal regions. Adult bone texture lacks surface porosity. Immature textures are caused by channels in fibrolamellar bone intersecting the bone surface; the presence or absence of striations is determined by channel orientation. Mature textures may be underlain by fibrolamellar bone with little to no surface exposure of channels, or by lamellar bone deposited after rapid growth ceases. The utility of the textural ageing method appears intimately related to the uninterrupted determinate growth regime of Branta . This suggests that bone surface textures may prove useful as skeletal maturity indicators in both modern and fossil taxa with similar growth regimes, but may not necessarily be reliable for taxa with interrupted and/or indeterminate growth.  © 2006 The Linnean Society of London, Zoological Journal of the Linnean Society , 2006, 148 , 133–168.