Efficient integration across spatial frequencies for letter identification in foveal and peripheral vision

Abstract

Objects in natural scenes are spatially broadband; in contrast, feature detectors in the early stages of visual processing are narrowly tuned in spatial frequency. Earlier studies of feature integration using gratings suggested that integration across spatial frequencies is suboptimal. Here we re-examined this conclusion using a letter identification task at the fovea and at 10 deg in the lower visual field. We found that integration across narrow-band (1-octave) spatial frequency components of letter stimuli is optimal in the fovea. Surprisingly, this optimality is preserved in the periphery, even though feature integration is known to be deficient in the periphery from studies of other form-vision tasks such as crowding. A model that is otherwise a white-noise ideal observer except for a limited spatial resolution defined by the human contrast sensitivity function and using internal templates slightly wider in bandwidth than the stimuli is able to account for the human data. Our findings suggest that deficiency in feature integration found in peripheral vision is not across spatial frequencies.

The perception of a familiar face is no more than the sum of its parts

“…As described in Gold et al (2012) and in further detail by Nandy and Tjan (2008), the contrast of an image on a given trial was set by adjusting the RMS contrast (i.e., square root of the mean across contrast values) of the combined image to the desired level and then removing all of the unwanted features (e.g., removing the left eye, nose and mouth from the combined image in the right eye only condition) 3 . Weibull psychometric functions were fit to the staircase data in each condition in order to estimate 50% correct RMS contrast thresholds.…”

“…They measured each observer's contrast sensitivity (i.e., the reciprocal of their RMS contrast threshold) in each of the four isolated feature conditions as well as for the combination of all four features. Using these sensitivities, it can be shown (Nandy & Tjan, 2008) that an observer's squared contrast sensitivity for the combination of features will equal the sum of her squared sensitivities across the individual features if the context within which the features are presented has no impact upon her ability to make use of information. That is, if an observer's performance with the combination can be directly predicted from her performance with each of the features shown in isolation, then her squared sensitivity to the combination should equal the sum of her squared sensitivities to the isolated features.…”

“…This prediction can be expressed mathematically by computing an integration index Φ: $$\Phi =\frac{S_{combined}^2}{S_{\text{left eye}}^2+S_{\text{right eye}}^2+S_{\text{mouth}}^2+S_{\text{nose}}^2}$$ where S is contrast sensitivity, and Φ = 1. This is referred to as ‘optimal’ integration, because it is the integration index that is predicted for a Bayesian observer that integrates across features in an optimal manner (Nandy & Tjan, 2008). If, however, an observer derives some additional benefit from viewing the features in combination that she did not derive when the features were shown in isolation (e.g., relational or ‘configural’ processing), Φ should exceed 1.…”

“…Previous research has suggested that familiarity may induce a qualitative shift in visual processing from an independent analysis of individual facial features to an analysis that includes information about the relationships amongst features (Farah, Wilson, Drain, & Tanaka, 1998; Maurer, Grand, & Mondloch, 2002). We tested this idea by using a ‘summation-at-threshold’ technique (Gold, Mundy, & Tjan, 2012; Nandy & Tjan, 2008), in which an observer's ability to recognize each individual facial feature shown independently is used to predict their ability to recognize all of the features shown in combination. We find that, although people are better overall at recognizing familiar than unfamiliar faces, their ability to integrate information across features is similar for unfamiliar and highly familiar faces and is well predicted by their ability to recognize each of the facial features shown in isolation.…”

“… 3 This definition of contrast is called nominal contrast, and is necessary for the computation of the integration index given in Equation 1 (see Nandy & Tjan, 2008 for a formal treatment of the integration index and nominal contrast). …”