Cross-orientation masking is speed invariant between ocular pathways but speed dependent within them

In human (D. H. Baker, T. S. Meese, & R. J. Summers, 2007b) and in cat (B. Li, M. R. Peterson, J. K. Thompson, T. Duong, & R. D. Freeman, 2005; F. Sengpiel & V. Vorobyov, 2005) there are at least two routes to cross-orientation suppression (XOS): a broadband, non-adaptable, monocular (within-eye) pathway and a more narrowband, adaptable interocular (between the eyes) pathway. We further characterized these two routes psychophysically by measuring the weight of suppression across spatio-temporal frequency for cross-oriented pairs of superimposed flickering Gabor patches. Masking functions were normalized to unmasked detection thresholds and fitted by a two-stage model of contrast gain control (T. S. Meese, M. A. Georgeson, & D. H. Baker, 2006) that was developed to accommodate XOS. The weight of monocular suppression was a power function of the scalar quantity ‘speed’ (temporal-frequency/spatial-frequency). This weight can be expressed as the ratio of non-oriented magno- and parvo-like mechanisms, permitting a fast-acting, early locus, as befits the urgency for action associated with high retinal speeds. In contrast, dichoptic-masking functions superimposed. Overall, this (i) provides further evidence for dissociation between the two forms of XOS in humans, and (ii) indicates that the monocular and interocular varieties of XOS are space/time scale-dependent and scale-invariant, respectively. This suggests an image-processing role for interocular XOS that is tailored to natural image statistics—very different from that of the scale-dependent (speed-dependent) monocular variety.

Interocular suppression and contrast gain control in human vision

The human visual system combines contrast information from the two eyes to produce a single cyclopean representation of the external world. This task requires both summation of congruent images and inhibition of incongruent images across the eyes. These processes were explored psychophysically using narrowband sinusoidal grating stimuli. Initial experiments focussed on binocular interactions within a single detecting mechanism, using contrast discrimination and contrast matching tasks. Consistent with previous findings, dichoptic presentation produced greater masking than monocular or binocular presentation. Four computational models were compared, two of which performed well on all data sets. Suppression between mechanisms was then investigated, using orthogonal and oblique stimuli. Two distinct suppressive pathways were identified, corresponding to monocular and dichoptic presentation. Both pathways impact prior to binocular summation of signals, and differ in their strengths, tuning, and response to adaptation, consistent with recent single-cell findings in cat. Strikingly, the magnitude of dichoptic masking was found to be spatiotemporally scale invariant, whereas monocular masking was dependent on stimulus speed. Interocular suppression was further explored using a novel manipulation, whereby stimuli were presented in dichoptic antiphase. Consistent with the predictions of a computational model, this produced weaker masking than in-phase presentation. This allowed the bandwidths of suppression to be measured without the complicating factor of additive combination of mask and test. Finally, contrast vision in strabismic amblyopia was investigated. Although amblyopes are generally believed to have impaired binocular vision, binocular summation was shown to be intact when stimuli were normalized for interocular sensitivity differences. An alternative account of amblyopia was developed, in which signals in the affected eye are subject to attenuation and additive noise prior to binocular combination.

Suppression and summation in contrast gain control for human vision

Over the last ten years our understanding of early spatial vision has improved enormously. The long-standing model of probability summation amongst multiple independent mechanisms with static output nonlinearities responsible for masking is obsolete. It has been replaced by a much more complex network of additive, suppressive, and facilitatory interactions and nonlinearities across eyes, area, spatial frequency, and orientation that extend well beyond the classical recep-tive field (CRF). A review of a substantial body of psychophysical work performed by ourselves (20 papers), and others, leads us to the following tentative account of the processing path for signal contrast. The first suppression stage is monocular, isotropic, non-adaptable, accelerates with RMS contrast, most potent for low spatial and high temporal frequencies, and extends slightly beyond the CRF. Second and third stages of suppression are difficult to disentangle but are possibly pre- and post-binocular summation, and involve components that are scale invariant, isotropic, anisotropic, chromatic, achromatic, adaptable, interocular, substantially larger than the CRF, and saturated by contrast. The monocular excitatory pathways begin with half-wave rectification, followed by a preliminary stage of half-binocular summation, a square-law transducer, full binocular summation, pooling over phase, cross-mechanism facilitatory interactions, additive noise, linear summation over area, and a slightly uncertain decision-maker. The purpose of each of these interactions is far from clear, but the system benefits from area and binocular summation of weak contrast signals as well as area and ocularity invariances above threshold (a herd of zebras doesn't change its contrast when it increases in number or when you close one eye). One of many remaining challenges is to determine the stage or stages of spatial tuning in the excitatory pathway.

The primal sketch revisited: locating and representing edges in human vision via Gaussian-derivative filtering

Marr's work offered guidelines on how to investigate vision (the theory - algorithm - implementation distinction), as well as specific proposals on how vision is done. Many of the latter have inevitably been superseded, but the approach was inspirational and remains so. Marr saw the computational study of vision as tightly linked to psychophysics and neurophysiology, but the last twenty years have seen some weakening of that integration. Because feature detection is a key stage in early human vision, we have returned to basic questions about representation of edges at coarse and fine scales. We describe an explicit model in the spirit of the primal sketch, but tightly constrained by psychophysical data. Results from two tasks (location-marking and blur-matching) point strongly to the central role played by second-derivative operators, as proposed by Marr and Hildreth. Edge location and blur are evaluated by finding the location and scale of the Gaussian-derivative `template' that best matches the second-derivative profile (`signature') of the edge. The system is scale-invariant, and accurately predicts blur-matching data for a wide variety of 1-D and 2-D images. By finding the best-fitting scale, it implements a form of local scale selection and circumvents the knotty problem of integrating filter outputs across scales. [Supported by BBSRC and the Wellcome Trust]

The attenuation surface for contrast sensitivity has the form of a witch’s hat within the central visual field

Over the full visual field, contrast sensitivity is fairly well described by a linear decline in log sensitivity as a function of eccentricity (expressed in grating cycles). However, many psychophysical studies of spatial visual function concentrate on the central ±4.5 deg (or so) of the visual field. As the details of the variation in sensitivity have not been well documented in this region we did so for small patches of target contrast at several spatial frequencies (0.7–4 c/deg), meridians (horizontal, vertical, and oblique), orientations (horizontal, vertical, and oblique), and eccentricities (0–18 cycles). To reduce the potential effects of stimulus uncertainty, circular markers surrounded the targets. Our analysis shows that the decline in binocular log sensitivity within the central visual field is bilinear: The initial decline is steep, whereas the later decline is shallow and much closer to the classical results. The bilinear decline was approximately symmetrical in the horizontal meridian and declined most steeply in the superior visual field. Further analyses showed our results to be scale-invariant and that this property could not be predicted from cone densities. We used the results from the cardinal meridians to radially interpolate an attenuation surface with the shape of a witch's hat that provided good predictions for the results from the oblique meridians. The witch's hat provides a convenient starting point from which to build models of contrast sensitivity, including those designed to investigate signal summation and neuronal convergence of the image contrast signal. Finally, we provide Matlab code for constructing the witch's hat.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Pattern integration in the normal and abnormal human visual system

The processing conducted by the visual system requires the combination of signals that are detected at different locations in the visual field. The processes by which these signals are combined are explored here using psychophysical experiments and computer modelling. Most of the work presented in this thesis is concerned with the summation of contrast over space at detection threshold. Previous investigations of this sort have been confounded by the inhomogeneity in contrast sensitivity across the visual field. Experiments performed in this thesis find that the decline in log contrast sensitivity with eccentricity is bilinear, with an initial steep fall-off followed by a shallower decline. This decline is scale-invariant for spatial frequencies of 0.7 to 4 c/deg. A detailed map of the inhomogeneity is developed, and applied to area summation experiments both by incorporating it into models of the visual system and by using it to compensate stimuli in order to factor out the effects of the inhomogeneity. The results of these area summation experiments show that the summation of contrast over area is spatially extensive (occurring over 33 stimulus carrier cycles), and that summation behaviour is the same in the fovea, parafovea, and periphery. Summation occurs according to a fourth-root summation rule, consistent with a “noisy energy” model. This work is extended to investigate the visual deficit in amblyopia, finding that area summation is normal in amblyopic observers. Finally, the methods used to study the summation of threshold contrast over area are adapted to investigate the integration of coherent orientation signals in a texture. The results of this study are described by a two-stage model, with a mandatory local combination stage followed by flexible global pooling of these local outputs. In each study, the results suggest a more extensive combination of signals in vision than has been previously understood.

Can mean shift trackers perform better?

Many tracking algorithms have difficulties dealing with occlusions and background clutters, and consequently don't converge to an appropriate solution. Tracking based on the mean shift algorithm has shown robust performance in many circumstances but still fails e.g. when encountering dramatic intensity or colour changes in a pre-defined neighbourhood. In this paper, we present a robust tracking algorithm that integrates the advantages of mean shift tracking with those of tracking local invariant features. These features are integrated into the mean shift formulation so that tracking is performed based both on mean shift and feature probability distributions, coupled with an expectation maximisation scheme. Experimental results show robust tracking performance on a series of complicated real image sequences. © 2010 IEEE.

From filters to features:Scale-space analysis of edge and blur coding in human vision

To make vision possible, the visual nervous system must represent the most informative features in the light pattern captured by the eye. Here we use Gaussian scale-space theory to derive a multiscale model for edge analysis and we test it in perceptual experiments. At all scales there are two stages of spatial filtering. An odd-symmetric, Gaussian first derivative filter provides the input to a Gaussian second derivative filter. Crucially, the output at each stage is half-wave rectified before feeding forward to the next. This creates nonlinear channels selectively responsive to one edge polarity while suppressing spurious or "phantom" edges. The two stages have properties analogous to simple and complex cells in the visual cortex. Edges are found as peaks in a scale-space response map that is the output of the second stage. The position and scale of the peak response identify the location and blur of the edge. The model predicts remarkably accurately our results on human perception of edge location and blur for a wide range of luminance profiles, including the surprising finding that blurred edges look sharper when their length is made shorter. The model enhances our understanding of early vision by integrating computational, physiological, and psychophysical approaches. © ARVO.

Mach edges: local features predicted by 3rd derivative spatial filtering

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (1st derivative) filter, or as zero-crossings in the 2nd derivative (ZCs). We tested those ideas using a stimulus that has no local peaks of gradient and no ZCs, at any scale. The stimulus profile is analogous to the Mach ramp, but it is the luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux; the luminance profile is a blurred triangle-wave. For all image-blurs tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These Mach edges correspond to peaks and troughs in the 3rd derivative. Thus Mach edges are inconsistent with many standard edge-detection schemes, but are nicely predicted by a recent model that finds edge points with a 2-stage sequence of 1st then 2nd derivative operators, each followed by a half-wave rectifier.

Blurred edges look faint, and faint edges look sharp:The effect of a gradient threshold in a multi-scale edge coding model

A multi-scale model of edge coding based on normalized Gaussian derivative filters successfully predicts perceived scale (blur) for a wide variety of edge profiles [Georgeson, M. A., May, K. A., Freeman, T. C. A., & Hesse, G. S. (in press). From filters to features: Scale-space analysis of edge and blur coding in human vision. Journal of Vision]. Our model spatially differentiates the luminance profile, half-wave rectifies the 1st derivative, and then differentiates twice more, to give the 3rd derivative of all regions with a positive gradient. This process is implemented by a set of Gaussian derivative filters with a range of scales. Peaks in the inverted normalized 3rd derivative across space and scale indicate the positions and scales of the edges. The edge contrast can be estimated from the height of the peak. The model provides a veridical estimate of the scale and contrast of edges that have a Gaussian integral profile. Therefore, since scale and contrast are independent stimulus parameters, the model predicts that the perceived value of either of these parameters should be unaffected by changes in the other. This prediction was found to be incorrect: reducing the contrast of an edge made it look sharper, and increasing its scale led to a decrease in the perceived contrast. Our model can account for these effects when the simple half-wave rectifier after the 1st derivative is replaced by a smoothed threshold function described by two parameters. For each subject, one pair of parameters provided a satisfactory fit to the data from all the experiments presented here and in the accompanying paper [May, K. A. & Georgeson, M. A. (2007). Added luminance ramp alters perceived edge blur and contrast: A critical test for derivative-based models of edge coding. Vision Research, 47, 1721-1731]. Thus, when we allow for the visual system's insensitivity to very shallow luminance gradients, our multi-scale model can be extended to edge coding over a wide range of contrasts and blurs. © 2007 Elsevier Ltd. All rights reserved.

Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars

Perception of Mach bands may be explained by spatial filtering ('lateral inhibition') that can be approximated by 2nd derivative computation, and several alternative models have been proposed. To distinguish between them, we used a novel set of ‘generalised Gaussian’ images, in which the sharp ramp-plateau junction of the Mach ramp was replaced by smoother transitions. The images ranged from a slightly blurred Mach ramp to a Gaussian edge and beyond, and also included a sine-wave edge. The probability of seeing Mach Bands increased with the (relative) sharpness of the junction, but was largely independent of absolute spatial scale. These data did not fit the predictions of MIRAGE, nor 2nd derivative computation at a single fine scale. In experiment 2, observers used a cursor to mark features on the same set of images. Data on perceived position of Mach bands did not support the local energy model. Perceived width of Mach bands was poorly explained by a single-scale edge detection model, despite its previous success with Mach edges (Wallis & Georgeson, 2009, Vision Research, 49, 1886-1893). A more successful model used separate (odd and even) scale-space filtering for edges and bars, local peak detection to find candidate features, and the MAX operator to compare odd- and even-filter response maps (Georgeson, VSS 2006, Journal of Vision 6(6), 191a). Mach bands are seen when there is a local peak in the even-filter (bar) response map, AND that peak value exceeds corresponding responses in the odd-filter (edge) maps.

Quantification of hydroxycinnamic acids and lignin in perennial forage and energy grasses by Fourier-transform infrared spectroscopy and partial least squares regression

Levels of lignin and hydroxycinnamic acid wall components in three genera of forage grasses (Lolium,Festuca and Dactylis) have been accurately predicted by Fourier-transform infrared spectroscopy using partial least squares models correlated to analytical measurements. Different models were derived that predicted the concentrations of acid detergent lignin, total hydroxycinnamic acids, total ferulate monomers plus dimers, p-coumarate and ferulate dimers in independent spectral test data from methanol extracted samples of perennial forage grass with accuracies of 92.8%, 86.5%, 86.1%, 59.7% and 84.7% respectively, and analysis of model projection scores showed that the models relied generally on spectral features that are known absorptions of these compounds. Acid detergent lignin was predicted in samples of two species of energy grass, (Phalaris arundinacea and Pancium virgatum) with an accuracy of 84.5%.

Equilibrium properties of disordered spin models with two-scale interactions

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

Rotation invariant iris feature extraction using Gaussian Markov random fields with non-separable wavelet

Rotation invariance is important for an iris recognition system since changes of head orientation and binocular vergence may cause eye rotation. The conventional methods of iris recognition cannot achieve true rotation invariance. They only achieve approximate rotation invariance by rotating the feature vector before matching or unwrapping the iris ring at different initial angles. In these methods, the complexity of the method is increased, and when the rotation scale is beyond the certain scope, the error rates of these methods may substantially increase. In order to solve this problem, a new rotation invariant approach for iris feature extraction based on the non-separable wavelet is proposed in this paper. Firstly, a bank of non-separable orthogonal wavelet filters is used to capture characteristics of the iris. Secondly, a method of Markov random fields is used to capture rotation invariant iris feature. Finally, two-class kernel Fisher classifiers are adopted for classification. Experimental results on public iris databases show that the proposed approach has a low error rate and achieves true rotation invariance. © 2010.