Texton gradients: The texton theory revisited

A brief outline of the texton theory was given in several review papers (Julesz and Bergen 1983; Julesz 1984a, b, 1985) without going into details. Here a more complete version of the texton theory is presented, with emphasis on the critical distances within which the density of textons is determined by the preattentive system. Particularly some recent findings by Sagi and Julesz (1985a, b) influenced the current version of the texton theory. The stimuli are restricted to drawing composed of line segments that permit a precise definition of neighborhoods and distances to which the line segments and texture elements have to be confined in order to quality for preattentive texture discrimination. These critical distances and the aperture of focal attention are scaled by the average size of the texture elements. Furthermore, it is stressed that even when the stimuli are restricted to line segments, the blobs outlined by line segments behave like textons. The preattentive system ignores the exact shape of these blobs, but is sensitive to their average width, length, and orientation.     

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.     

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     

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.     

On perceptual analyzers underlying visual texture discrimination: Part II

In Part I Caelli and Julesz generated texture pairs of 4-disk micropatterns with identical dipole statistics. They found that this iso-dipole constraint could not prevent the quasi-collinearity of certain disk elements which, in turn, yielded effortless discrimination. They proposed two classes of perceptual analyzers to explain discrimination with these micropatern textures: Class A, corresponding to those which detect dipole differences; while Class B detectors, such as the quasi-collinear detector (QCD), acted when isodipole textures were presented. In this paper we show several new methods for generating iso-dipole textures with micropatterns consisting of 5 or more disks or non-disk shaped elements, and we report the discovery of two other Class B detectors, a corner detector (using a 6-disk method), and a closure detector (with 8–11 disk micropatterns). These QCD, corner, and closure detectors were verified by examining several hundred iso-dipole texture pairs. It appears that iso-dipole constraints make ineffective all other feature analyzers involved in effortless texture discrimination than the Class B types. These figural properties of collinearity, corners, and closure can be perceived without scrutiny and are precursors of form perception.     

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.     

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.     

Some psychophysical determinants of discrete Moiré patterns

In a series of experiments we have investigated the perception of Moiré patterns as a function of spatial density, rotation and temporal display parameters. Results indicate that the local correlation extraction process involved in the perception of these patterns is not feature specific, yet is driven by excitatory (correlated) and inhibitory (uncorrelated) information under a form of spatial summation. These results are comparable with recent results on texture discrimination where texture interpoint distance distributions (dipole statistics) have also been discovered to have excitatory and inhibitory components.     

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.     

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.     

Visual discrimination of textures with identical third-order statistics

We found a new class of two-dimensional random textures with identical third-order statistics that can be effortlessly discriminated. Discrimination is based on local granularity differences between these iso-trigon texture pairs. This is the more surprising since it is commonly assumed that texture granularity (grain) is determined by the power spectrum which, in turn, can be obtained from the second-order statistics. Because textures with identical third-order statistics must have identical second-order statistics (i.e., identical power spectra), visible texture granularity is not controlled by power spectra, and not even by third-order statistics.     

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.     

Sound texture perception via statistics of the auditory periphery: evidence from sound synthesis

Rainstorms, insect swarms, and galloping horses produce "sound textures"--the collective result of many similar acoustic events. Sound textures are distinguished by temporal homogeneity, suggesting they could be recognized with time-averaged statistics. To test this hypothesis, we processed real-world textures with an auditory model containing filters tuned for sound frequencies and their modulations, and measured statistics of the resulting decomposition. We then assessed the realism and recognizability of novel sounds synthesized to have matching statistics. Statistics of individual frequency channels, capturing spectral power and sparsity, generally failed to produce compelling synthetic textures; however, combining them with correlations between channels produced identifiable and natural-sounding textures. Synthesis quality declined if statistics were computed from biologically implausible auditory models. The results suggest that sound texture perception is mediated by relatively simple statistics of early auditory representations, presumably computed by downstream neural populations. The synthesis methodology offers a powerful tool for their further investigation.     

How the deposition of cellulose microfibrils builds cell wall architecture

Cell walls, the extracytoplasmic matrices of plant cells, consist of an ordered array of cellulose microfibrils embedded in a matrix of polysaccharides and glycoproteins. This construction is reminiscent of steel rods in reinforced concrete. How a cell organizes these ordered textures around itself, creating its own desirable environment, is a fascinating question. We believe that nature adopted an economical solution to this design problem: it exploits the geometrical constraints imposed by the shape of the cell and the limited space in which microfibrils are deposited, enabling the wall textures essentially to 'build themselves'. This does not imply that the cell cannot control its wall texture. On the contrary, the cell has ample regulatory mechanisms to control wall texture formation by controlling the insertion of synthases and the distance between individual microfibrils within a wall lamella.     

Orientation variance as a quantifier of structure in texture

I consider how structure is derived from texture containing changes in orientation over space, and propose that multi-local orientation variance (the average orientation variance across a series of discrete images locales) is an estimate of the degree of organization that is useful both for spatial scale selection and for discriminating structure from noise. The oriented textures used in this paper are Glass patterns, which contain structure at a narrow range of scales. The effect of adding noise to Glass patterns, on a structure versus noise task (Maloney et al., 1987), is compared to discrimination based on orientation variance and template matching (i.e. having prior knowledge of the target's orientation structure). At all but very low densities, the variance model accounts well for human data. Next, both models' estimates of tolerable orientation variance are shown to be broadly consistent with human discrimination of texture from noise. However, neither model can account for subjects' lower tolerance to noise for translational patterns than other (e.g. rotational) patterns. Finally, to investigate how well these structural measures preserve local orientation discontinuities, I show that the presence of a patch of unstructured dots embedded in a Glass pattern produces a change in multi-local orientation variance that is sufficient to account for human detection (Hel Or and Zucker, 1989). Together, these data suggest that simple orientation statistics could drive a range of 'texture tasks', although the dependency of noise resistance on the pattern type (rotation, translation, etc.) remains to be accounted for.     

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.     

uShuffle: A useful tool for shuffling biological sequences while preserving the k-let counts

Background  

Randomly shuffled sequences are routinely used in sequence analysis to evaluate the statistical significance of a biological sequence. In many cases, biologists need sophisticated shuffling tools that preserve not only the counts of distinct letters but also higher-order statistics such as doublet counts, triplet counts, and, in general, k-let counts.     

Folivory or fruit/seed predation for Mesopithecus, an earliest colobine from the late Miocene of Eurasia?

Here we compare dental microwear textures from specimens of the fossil genus Mesopithecus (Cercopithecidae, Colobinae) from the late Miocene of Eastern Europe with dental microwear textures from four extant primate species with known dietary differences. Results indicate that the dental microwear textures of Mesopithecus differ from those of extant leaf eaters Alouatta palliata and Trachypithecus cristatus and instead resemble more closely those of the occasional hard-object feeders Cebus apella and Lophocebus albigena. Microwear texture data presented here in combination with results from previous analyses suggest that Mesopithecus was a widespread, opportunistic feeder that often consumed hard seeds. These data are consistent with the hypothesis that early colobines may have preferred hard seeds to leaves.