Contrast integration over area is extensive: A three-stage model of spatial summation

Abstract

Classical studies of area summation measure contrast detection thresholds as a function of grating diameter. Unfortunately, (i) this approach is compromised by retinal inhomogeneity and (ii) it potentially confounds summation of signal with summation of internal noise. The Swiss cheese stimulus of T. S. Meese and R. J. Summers (2007) and the closely related Battenberg stimulus of T. S. Meese (2010) were designed to avoid these problems by keeping target diameter constant and modulating interdigitated checks of first-order carrier contrast within the stimulus region. This approach has revealed a contrast integration process with greater potency than the classical model of spatial probability summation. Here, we used Swiss cheese stimuli to investigate the spatial limits of contrast integration over a range of carrier frequencies (1-16 c/deg) and raised plaid modulator frequencies (0.25-32 cycles/check). Subthreshold summation for interdigitated carrier pairs remained strong (∼4 to 6 dB) up to 4 to 8 cycles/check. Our computational analysis of these results implied linear signal combination (following square-law transduction) over either (i) 12 carrier cycles or more or (ii) 1.27 deg or more. Our model has three stages of summation: short-range summation within linear receptive fields, medium-range integration to compute contrast energy for multiple patches of the image, and long-range pooling of the contrast integrators by probability summation. Our analysis legitimizes the inclusion of widespread integration of signal (and noise) within hierarchical image processing models. It also confirms the individual differences in the spatial extent of integration that emerge from our approach.

Paradoxical Psychometric Functions (“Swan Functions”) are Explained by Dilution Masking in Four Stimulus Dimensions

“…Nonetheless, we envisage extended integration where appropriate, and we have presented evidence for this elsewhere (e.g. Baker & Meese, 2011). However, from one point of view, the generic model that we propose might appear puzzling: what is the point of integrating signal over a stimulus dimension if it is then to be suppressed by a similar integration over the same dimension?…”

Integration of Motion Responses Underlying Directional Motion Anisotropy in Human Early Visual Cortical Areas

“…In light of current results, motion biases may be a product of motion detector recruitment, which is aborted when a motion detector chain is interrupted. In addition, it has been suggested that the summation of detector information in motion recruitment is linear [8], [29]. The centripetal bias during motion with spatial decorrelations can be the result of a linear spatial integration, given an ineffective disruption of the motion detector chain in the periphery of the stimulus.…”

A Common Rule for Integration and Suppression of Luminance Contrast across Eyes, Space, Time, and Pattern

“…Such an arrangement predicts a triplet of pedestal masking functions, similar to those found here (see Figure A1d in Appendix A). However, there is little or no evidence for such broad tuning at this low level in the hierarchy in the spatial domain (Baker & Meese, 2011a) or in the orientation domain (see Meese & Baker, 2011b, for a review), where receptive fields in the primary visual cortex (filter elements) have a small number of lobes (i.e. are selective to very few stimulus cycles) and are orientation tuned (DeValois & DeValois, 1990).…”

“…The aim of this approach was to clamp the level of internal noise so as to achieve a clean measure of the integration process. In conjunction with extensive modelling, these experiments provided good evidence for narrowband spatial filtering (Meese, 2010), followed by a square-law contrast transducer (Meese, 2010; Meese & Summers, 2009), additive noise and linear summation (integration) of image contrast (Meese, 2010; Meese & Baker, 2011a) that extended over nine or more stimulus cycles (Baker & Meese, 2011). Various models of spatial probability summation (i.e.…”