When identifying confusable visual stimuli, accumulation of information over time is an obvious
strategy of the observer. However, the nature of the accumulation process is unresolved: for example
it may be discrete or continuous in terms of the information encoded. Another unanswered question
is whether or not stimulus sampling continues after the stimulus offset. In the present paper we
propose various continuous Gaussian counter models of the time course of visual identification of briefly
presented, mutually confusable single stimuli in a pure accuracy task. During stimulus analysis, tentative
categorizations that stimulus i belongs to category j are made until a maximum time after the stimulus
disappears. Two classes of models are proposed. First, the overt response is based on the categorization
that had the highest value at the time the stimulus disappears (race models). Second, the overt response
is based on the categorization that made the minimum first passage time through a constant boundary
(first passage time models).Within this framework, multivariateWiener and Ornstein–Uhlenbeck counter
models are considered under different parameter regimes, assuming either that the stimulus sampling
stops immediately or that it continues for some time after the stimulus offset. Each type of model was
evaluated by Monte Carlo tests of goodness of fit against observed probability distributions of responses
in two extensive experiments. A comparison of these continuous models with a simple discrete Poisson
counter model proposed by Kyllingsbæk, Markussen, and Bundesen (2012) was carried out, together
with model selection among the competing candidates. Both the Wiener and the Ornstein–Uhlenbeck
race models provide a close fit to individual data on identification of both digits and Landolt rings,
outperforming the first passage time model and the Poisson counter race model.