The Oriented Difference of Gaussians (ODOG) model of brightness perception: Overview and executable Mathematica notebooks

Abstract

The Oriented Difference of Gaussians (ODOG) model of brightness (perceived intensity) by Blakeslee & McCourt (1999), which is based on linear spatial filtering by oriented receptive fields followed by contrast normalization, has proven highly successful in parsimoniously predicting the perceived intensity (brightness) of regions in complex visual stimuli such as White's effect, which had been believed to defy filter-based explanations. Unlike competing explanations such as anchoring theory (Gilchrist, Kossyfidis, Bonato, Agostini, Cataliotti, Li, Spehar, Annan & Economou, 1999; Gilchrist, 2006), filling-in (Grossberg & Todorovic, 1988), edge-integration (Land & McCann, 1971; Rudd & Zemach, 2004; 2007), or layer decomposition (Anderson, 1997), the spatial filtering approach embodied by the ODOG model readily accounts for the often overlooked but ubiquitous gradient structure of induction which, while most striking in grating induction (McCourt, 1982; McCourt & Blakeslee, 2014; Blakeslee & McCourt, 1999; 2013; Kingdom, 1999), also occurs within the test fields of classical simultaneous brightness contrast and the White stimulus (Blakeslee & McCourt, 1999; 2014). Also, because the ODOG model does not require defined regions of interest it is generalizable to any stimulus, including natural images. The ODOG model has motivated other researchers (Robinson, Hammon & de Sa, 2007) to develop modified versions (LODOG and FLODOG), and has served as an important counterweight and proof of concept to constrain high-level theories which rely on less well understood or justified mechanisms such as unconscious inference, transparency, perceptual grouping, and layer decomposition. Here we provide a brief but comprehensive description of the ODOG model as it has been implemented since 1999, as well as working Mathematica (Wolfram, Inc.) notebooks which users can employ to generate ODOG model predictions for their own stimuli.

Brightness induction and suprathreshold vision: Effects of age and visual field

“…This is consistent with the Oriented Difference of Gaussians (ODOG) model of brightness perception (Blakeslee & McCourt, 1999; Blakeslee, Cope & McCourt, 2014). …”

Cortical-Inspired Wilson–Cowan-Type Equations for Orientation-Dependent Contrast Perception Modelling

“…While this variation of the model (LHE-2D) is effective in describing assimilation effects, the lack of dependence on the local orientation makes such modelling intrinsically not adapted to explain orientation-induced contrast and colour perception effects such as the ones described in [36,41,12]. Reference models capable to explain these effects are mostly based on oriented Difference of Gaussian linear filtering coupled with some non-linear processing, such as the ODOG and the BIWaM models described in [12,11] and [36], respectively. However, despite their good effectiveness in the description of several visual perception phenomena, these are not based on any neuronal evolution modelling nor on any efficient representation principle.…”

A model of lightness perception guided by probabilistic assumptions about lighting and reflectance

“…It is based on the responses of oriented filters at several orientations and scales, and also incorporates a response normalization stage. To test this model, I used a MATLAB translation of the Mathematica code in Blakeslee et al. (2016 ).…”