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Classification images have recently become a widely used tool in visual psychophysics. Here, I review the development of classification image methods over the past fifteen years. I provide some historical background, describing how classification images and related methods grew out of established statistical and mathematical frameworks and became common tools for studying biological systems. I describe key developments in classification image methods: use of optimal weighted sums based on the linear observer model, formulation of classification images in terms of the generalized linear model, development of statistical tests, use of priors to reduce dimensionality, methods for experiments with more than two response alternatives, a variant using multiplicative noise, and related methods for examining nonlinearities in visual processing, including second-order Volterra kernels and principal component analysis. I conclude with a selective review of how classification image methods have led to substantive findings in three representative areas of vision research, namely, spatial vision, perceptual organization, and visual search.

The visual system is constantly faced with the problem of identifying partially occluded objects from incomplete images cast on the retinae. Phenomenologically, the visual system seems to fill in missing information by interpolating illusory and occluded contours at points of occlusion, so that we perceive complete objects. Previous behavioural [1] [2] [3] [4] [5] [6] [7] and physiological [8] [9] [10] [11] [12] studies suggest that the visual system treats illusory and occluded contours like luminance-defined contours in many respects. None of these studies has, however, directly shown that illusory and occluded contours are actually used to perform perceptual tasks. Here, we use a response-classification technique [13] [14] [15] [16] [17] [18] [19] [20] to answer this question directly. This technique provides pictorial representations - 'classification images' - that show which parts of a stimulus observers use to make perceptual decisions, effectively deriving behavioural receptive fields. Here we show that illusory and occluded contours appear in observers' classification images, providing the first direct evidence that observers use perceptually interpolated contours to recognize objects. These results offer a compelling demonstration of how visual processing acts on completed representations, and illustrate a powerful new technique for constraining models of visual completion.

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In signal detection theory, an observer's responses are often modeled as being based on a decision variable obtained by cross-correlating the stimulus with a template, possibly after corruption by external and internal noise. The response classification method estimates an observer's template by measuring the influence of each pixel of external noise on the observer's responses. A map that shows the influence of each pixel is called a classification image. Other authors have shown how to calculate classification images from external noise fields, but the optimal calculation has never been determined, and the quality of the resulting classification images has never been evaluated. Here we derive the optimal weighted sum of noise fields for calculating classification images in several experimental designs, and we derive the signal-to-noise ratio (SNR) of the resulting classification images. Using the expressions for the SNR, we show how to choose experimental parameters, such as the observer's performance level and the external noise power, to obtain classification images with a high SNR. We discuss two-alternative identification experiments in which the stimulus is presented at one or more contrast levels, in which each stimulus is presented twice so that we can estimate the power of the internal noise from the consistency of the observer's responses, and in which the observer rates the confidence of his responses. We illustrate these methods in a series of contrast increment detection experiments.