Isodipole Textures Research Articles

The features that control discrimination of an isodipole texture pair

Visual features such as edges and corners are carried by high-order statistics. Previous analysis of discrimination of isodipole textures, which isolate specific high-order statistics, demonstrates visual sensitivity to these statistics but stops short of analyzing the underlying computations. Here we use a new texture centroid paradigm to probe these computations. We focus on two canonical isodipole textures, the even and odd textures: any 2 × 2 block of even (odd) texture contains an even (odd) number of black (and white) checks. Each stimulus comprised a spatially random array of black-and-white texture-disks (background = mean gray) that varied in their fourth-order statistics. In the Even (Odd) condition, disks varied along the continuum between random coinflip texture and pure (highly structured) even (odd) target texture. The task was to mouse-click the centroid of the disk array, weighting each disk location by the target structure level of the disk-texture (ranging from 0 for coinflip to 1 for even or odd). For each of block-sizes S=2×2, 2 × 3, 2 × 4 and 3 × 3, a linear model was used to estimate the weight exerted on the subject’s responses by the differently patterned blocks of size S. Only the results with 2 × 4 and 3 × 3 blocks were consistent with the data. In the Even condition, homogeneous blocks exerted the most weight; in the odd condition, block-pattern symmetry was important. These findings show that visual mechanisms sensitive to four-point correlations do not compute evenness or oddness per se, but rather are activated selectively by features whose frequency varies across isodipole textures.

Isodipole textures in spacetime: a novel non-Fourier and reverse-phi motion stimulus

Isodipole textures in spacetime: a novel non-Fourier and reverse-phi motion stimulus

Local processes and spatial pooling in texture and symmetry detection

We examined the ability of human observers to detect three kinds of statistical structure in binary arrays: first-order statistics (luminance), local fourth-order statistics (isodipole textures), and long-range statistics (bilateral symmetry). Performance was closest to ideal on the luminance task and furthest from ideal on the symmetry task. For each kind of statistic, the dependence of performance on the degree of structure was well described by a model consisting of an initial stage of multiple independent detectors, followed by a pooling stage. For the luminance task and the isodipole task, performance was well-modeled by local processing followed by extensive spatial pooling. For the symmetry task, limitations at the local detection stage and a near-absence of spatial pooling were needed to model for performance.

Interaction of luminance and higher-order statistics in texture discrimination

Most studies of texture processing are based on textures in which individual pixel statistics are varied and spatial correlations are absent (“IID textures”), or textures in which spatial correlation structure is varied and luminance, or first-order, statistics are held constant. Here we jointly examine simple pixel statistics and fourth-order spatial correlation structure along the continuum of “even” and “odd” isodipole textures of Julesz, Gilbert and Victor [Julesz, B., Gilbert, E.N., & Victor, J.D. (1978). Biological Cybernetics, 31(3) 137–140], as well as their interactions. Absolute efficiency to detect either kind of statistical cue is low: approximately 0.05 for luminance statistics, and 0.004 for isodipole statistics. Above threshold, isodipole statistics must change by approximately four times the amount that pixel statistics must change to generate an equally salient texture. When pixel statistics and isodipole statistics are simultaneously varied, the two texture cues combine by probability summation and perceptual distances are approximately Euclidean. Superimposed on this picture are subtle foreground/background asymmetries that suggest properties of the visual mechanisms that are sensitive to these image statistics.

Striate cortex in humans demonstrates the relationship between activation and variations in visual form.

Electrophysiologic and functional imaging studies have shown that the visual cortex produces differential responses to the presence or absence of structure within visual textures. To further define and characterize regions involved in the analysis of form, functional magnetic resonance imaging (fMRI) was used to detect changes in activation during the viewing of four levels of isodipole textures. The texture levels systematically differed in the density of visual features such as extended contours and blocks of solid color present within the images. A linear relationship between activation level and density of structure was observed in the striate cortex of human subjects. This finding suggests that a special subpopulation of striate cortical neurons participates in the ability to extract and process structural continuity within visual stimuli.

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.

The role of high-order phase correlations in texture processing

Isodipole textures are pairs of texture ensembles whose autocorrelations, and hence power spectra, are equal. Examples of readily discriminable isodipole textures are well known. Such discriminations appear to require feature extraction, since the isodipole condition eliminates ensemble differences in spatial frequency content. We studied the effects of phase decorrelation on VEP indices of discrimination of isodipole texture pairs. Phase decorrelation, which ranged from 0.125π radians (slight randomization) to π radians (complete randomization), was introduced in two ways: by independent jittering of each spatial Fourier component, and by a product method, which preserved correlations among certain quadruples of spatial Fourier components, despite pairwise decorrelation. For the even/random isodipole texture pair, independent phase decorrelation greater than 0.5π radians markedly reduced VEP indices of texture discrimination for all check sizes, and eliminated them entirely for check sizes of 8 min or greater. However, the product method preserved texture discrimination signals even with complete pairwise randomization of spatial phases. For the triangle/random isodipole texture pair, both kinds of phase decorrelation eliminated VEP indices of texture discrimination. These results imply that isodipole texture discrimination is based on fundamentally local processing, and not on global Fourier amplitudes—since the phase manipulations which eliminate texture discrimination preserve the Fourier amplitudes. The dependence of the antisymmetric response component (the odd harmonics) on phase decorrelation and texture type is consistent with a previously proposed model for feature extraction, and leads to constraints on how texture processing is modulated by contrast. The limited contribution of global spectral characteristics for small checks is consistent with a previously identified breakdown in scale-invariant processing.

Isodipole textures: A window on cortical mechanisms of form processing

Isodipole textures: A window on cortical mechanisms of form processing

Cortical interactions in texture processing: Scale and dynamics

We investigate the neural computations underlying pattern processing with stimuli based on textures balanced for spatial frequency content (and second-order correlations) but not for higher-order correlations (Julesz et al. 1978). Interchange between two such isodipole textures produces a robust human visual evoked potential (VEP). The difference in population activity driven by two isodipole textures is quantified by the antisymmetric component of the VEP. Statistical properties of the textures eliminate contributions from linear mechanisms to the antisymmetric VEP. The dependence of the antisymmetric VEP on check size and fourth-order correlation statistics is used to test nonlinear models for the underlying neural computations. Linear summation, followed by a simple nonlinearity (such as rectification, saturation, or threshold), is inconsistent with the data. More elaborate models, in which a second nonlinear stage combines the output of local nonlinear mechanisms, are consistent with the data, provided that an appropriate spatial scale is chosen for the second stage of processing. For checks 4 min or smaller, the deduced interaction length is 10-15 min. For checks larger than 4 min, the interaction length is proportional to check size.

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.