Power spectrum model of visual masking: simulations and empirical data.

In the study of the spatial characteristics of the visual channels, the power spectrum model of visual masking is one of the most widely used. When the task is to detect a signal masked by visual noise, this classical model assumes that the signal and the noise are previously processed by a bank of linear channels and that the power of the signal at threshold is proportional to the power of the noise passing through the visual channel that mediates detection. The model also assumes that this visual channel will have the highest ratio of signal power to noise power at its output. According to this, there are masking conditions where the highest signal-to-noise ratio (SNR) occurs in a channel centered in a spatial frequency different from the spatial frequency of the signal (off-frequency looking). Under these conditions the channel mediating detection could vary with the type of noise used in the masking experiment and this could affect the estimation of the shape and the bandwidth of the visual channels. It is generally believed that notched noise, white noise and double bandpass noise prevent off-frequency looking, and high-pass, low-pass and bandpass noises can promote it independently of the channel's shape. In this study, by means of a procedure that finds the channel that maximizes the SNR at its output, we performed numerical simulations using the power spectrum model to study the characteristics of masking caused by six types of one-dimensional noise (white, high-pass, low-pass, bandpass, notched, and double bandpass) for two types of channel's shape (symmetric and asymmetric). Our simulations confirm that (1) high-pass, low-pass, and bandpass noises do not prevent the off-frequency looking, (2) white noise satisfactorily prevents the off-frequency looking independently of the shape and bandwidth of the visual channel, and interestingly we proved for the first time that (3) notched and double bandpass noises prevent off-frequency looking only when the noise cutoffs around the spatial frequency of the signal match the shape of the visual channel (symmetric or asymmetric) involved in the detection. In order to test the explanatory power of the model with empirical data, we performed six visual masking experiments. We show that this model, with only two free parameters, fits the empirical masking data with high precision. Finally, we provide equations of the power spectrum model for six masking noises used in the simulations and in the experiments.

Comparing the effect of the interaction between fine and coarse scales and surround suppression on motion discrimination.

Our ability to discriminate motion direction in a Gabor patch diminishes with increasing size and contrast, indicating surround suppression. Discrimination is also impaired by a static low-spatial-frequency patch added to the moving stimulus, suggesting an antagonism between sensors tuned to fine and coarse features. Using Bayesian staircases, we measured duration thresholds in motion-direction discrimination tasks using vertically oriented Gabor patches moving at 2°/s. In two experiments, we tested two contrasts (2.8% and 46%), five window sizes (from 0.7° to 5°), and two spatial frequencies (1 c/deg and 3 c/deg), either presented alone or added to a static pattern. When the moving pattern was presented alone, duration thresholds increased with size at high contrast and decreased with size at low contrast. At low contrast, when a static pattern of 3 c/deg was added to a moving pattern of 1 c/deg, duration thresholds were similar to the case when the moving pattern was presented alone; however, at high contrast, duration thresholds were facilitated, eliminating the effect of surround suppression. When a static pattern of 1 c/deg was added to a moving pattern of 3 c/deg, duration thresholds increased about 4 times for high contrast and 2 times for low contrast. These results show that the antagonism between sensors tuned to fine and coarse scales is more complex than surround suppression, suggesting that it reflects the operation of a different mechanism.

Application of Riesz transforms to the isotropic AM-PM decomposition of geometrical-optical illusion images.

The existence of a special second-order mechanism in the human visual system, able to demodulate the envelope of visual stimuli, suggests that spatial information contained in the image envelope may be perceptually relevant. The Riesz transform, a natural isotropic extension of the Hilbert transform to multidimensional signals, was used here to demodulate band-pass filtered images of well-known visual illusions of length, size, direction, and shape. We show that the local amplitude of the monogenic signal or envelope of each illusion image conveys second-order information related to image holistic spatial structure, whereas the local phase component conveys information about the spatial features. Further low-pass filtering of the illusion image envelopes creates physical distortions that correspond to the subjective distortions perceived in the illusory images. Therefore the envelope seems to be the image component that physically carries the spatial information about these illusions. This result contradicts the popular belief that the relevant spatial information to perceive geometrical-optical illusions is conveyed only by the lower spatial frequencies present in their Fourier spectrum.

Low spatial frequency filtering modulates early brain processing of affective complex pictures.

Recent research on affective processing has suggested that low spatial frequency information of fearful faces provide rapid emotional cues to the amygdala, whereas high spatial frequencies convey fine-grained information to the fusiform gyrus, regardless of emotional expression. In the present experiment, we examined the effects of low (LSF, <15 cycles/image width) and high spatial frequency filtering (HSF, >25 cycles/image width) on brain processing of complex pictures depicting pleasant, unpleasant, and neutral scenes. Event-related potentials (ERP), percentage of recognized stimuli and response times were recorded in 19 healthy volunteers. Behavioral results indicated faster reaction times in response to unpleasant LSF than to unpleasant HSF pictures. Unpleasant LSF pictures and pleasant unfiltered pictures also elicited significant enhancements of P1 amplitudes at occipital electrodes as compared to neutral LSF and unfiltered pictures, respectively; whereas no significant effects of affective modulation were found for HSF pictures. Moreover, mean ERP amplitudes in the time between 200 and 500ms post-stimulus were significantly greater for affective (pleasant and unpleasant) than for neutral unfiltered pictures; whereas no significant affective modulation was found for HSF or LSF pictures at those latencies. The fact that affective LSF pictures elicited an enhancement of brain responses at early, but not at later latencies, suggests the existence of a rapid and preattentive neural mechanism for the processing of motivationally relevant stimuli, which could be driven by LSF cues. Our findings confirm thus previous results showing differences on brain processing of affective LSF and HSF faces, and extend these results to more complex and social affective pictures.

Single-band amplitude demodulation of Müller-Lyer illusion images.

The perception of the Müller-Lyer illusion has previously been explained as a result of visual low band-pass spatial filtering, although, in fact, the illusion persists in band-pass and high-pass filtered images without visible low-spatial frequencies. A new theoretical framework suggests that our perceptual experience about the global spatial structure of an image corresponds to the amplitude modulation (AM) component (or its magnitude, also called envelope) of its AM-FM (alternatively, AM-PM) decomposition. Because demodulation is an ill-posed problem with a non-unique solution, two different AM-FM demodulation algorithms were applied here to estimate the envelope of images of Müller-Lyer illusion: the global and exact Daugman and Downing (1995) AMPM algorithm and the local and quasi-invertible Maragos and Bovik (1995) DESA. The images used in our analysis include the classic configuration of illusion in a variety of spatial and spatial frequency content conditions. In all cases, including those of images for which visual low-pass spatial filtering would be ineffective, the envelope estimated by single-band amplitude demodulation has physical distortions in the direction of perceived illusion. It is not plausible that either algorithm could be implemented by the human visual system. It is shown that the proposed second order visual model of pre-attentive segregation of textures (or "back-pocket" model) could recover the image envelope and, thus, explain the perception of this illusion even in Müller-Lyer images lacking low spatial frequencies.

The effect of white-noise mask level on sinewave contrast detection thresholds and the critical-band-masking model.

It is known that visual noise added to sinusoidal gratings changes the typical U-shaped threshold curve which becomes flat in log-log scale for frequencies below 10c/deg when gratings are masked with white noise of high power spectral density level. These results have been explained using the critical-band-masking (CBM) model by supposing a visual filter-bank of constant relative bandwidth. However, some psychophysical and biological data support the idea of variable octave bandwidth. The CBM model has been used here to explain the progressive change of threshold curves with the noise mask level and to estimate the bandwidth of visual filters. Bayesian staircases were used in a 2IFC paradigm to measure contrast thresholds of horizontal sinusoidal gratings (0.25-8 c/deg) within a fixed Gaussian window and masked with one-dimensional, static, broadband white noise with each of five power density levels. Raw data showed that the contrast threshold curve progressively shifts upward and flattens out as the mask noise level increases. Theoretical thresholds from the CBM model were fitted simultaneously to the data at all five noise levels using visual filters with log-Gaussian gain functions. If we assume a fixed-channel detection model, the best fit was obtained when the octave bandwidth of visual filters decreases as a function of peak spatial frequency.

Visual chimaeras obtained with the Riesz transform.

Similar to an auditory chimaera (Smith et al, 2002 Nature 416 87-90), a visual chimaera can be defined as a synthetic image which has the fine spatial structure of one natural image and the envelope of another image in each spatial frequency band. Visual chimaeras constructed in this way could be useful to vision scientists interested in the study of interactions between first-order and second-order visual processing. Although it is almost trivial to generate 1-D chimaeras by means of the Hilbert transform and the analytic signal, problems arise in multidimensional signals like images given that the partial directional Hilbert transform and current 2-D demodulation algorithms are anisotropic or orientation-variant procedures. Here, we present a computational procedure to synthesise visual chimaeras by means of the Riesz transform--an isotropic generalisation of the Hilbert transform for multidimensional signals--and the associated monogenic signal--the vector-valued function counterpart of the analytic signal in which the Riesz transform replaces the Hilbert transform. Examples of visual chimaeras are shown for same/different category images.

The effect of spatial-frequency filtering on the visual processing of global structure.

In three experiments we measured reaction times (RTs) and error rates in identifying the global structure of spatially filtered stimuli whose spatial-frequency content was selected by means of three types of 2-D isotropic filters (Butterworth of order 2, Butterworth of order 10, and a filters with total or partial Gaussian spectral profile). In each experiment, low-pass (LP), bandpass (BP), and high-pass (HP) filtered stimuli, with nine centre or cut-off spatial frequencies, were used. Irrespective of the type of filter, the experimental results showed that: (a) RTs to stimuli with low spatial frequencies were shorter than those to stimuli with medium or high spatial frequencies, (b) RTs to LP filtered stimuli were nearly constant, but they increased in a nonmonotonic way with the filter centre spatial frequency in BP filtered stimuli and with the filter cut-off frequency in HP filtered stimuli, and (c) the identification of the global pattern occurred with all visible stimuli used, including BP and HP images without low spatial frequencies. To remove the possible influence of the energy, a fourth experiment was conducted with Gaussian filtered stimuli of equal contrast power (c(rms) = 0.065). Similar results to those described above were found for stimuli with spatial-frequency content higher than 2 cycles deg(-1). A model of isotropic first-order visual channels collecting the stimulus spectral energy in all orientations explains the RT data. A subsequent second-order nonlinear amplitude demodulation process, applied to the output of the most energetic first-order channel, could explain the perception of global structure of each spatially filtered stimulus, including images lacking low spatial frequencies.