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


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.

Publication DOI:
Divisions: College of Health & Life Sciences > School of Optometry > Optometry
College of Health & Life Sciences > Clinical and Systems Neuroscience
College of Health & Life Sciences > School of Optometry > Centre for Vision and Hearing Research
Additional Information: Creative Commons Attribution Non-Commercial No Derivatives
Uncontrolled Keywords: contrast detection threshold,spatial summation,area summation,contrast integration,contrast energy,computational modeling,Ophthalmology,Sensory Systems
Publication ISSN: 1534-7362
Last Modified: 23 Jan 2024 17:46
Date Deposited: 05 Jan 2012 11:27
Full Text Link:
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://www.jour ... (Publisher URL)
PURE Output Type: Article
Published Date: 2011-12
Authors: Baker, Daniel H.
Meese, Tim S. (ORCID Profile 0000-0003-3744-4679)

Export / Share Citation


Additional statistics for this record