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These models also account for the perceived collinear grouping observed in columns of dots, as in (b) below.
But there are many other patterns of completion observed in patterns of dots which are not collinear. For example these patterns exhibit perceptual completion through illusory vertices composed of (c) three, (d) four, or more illusory contours that meet at a point, as well as "end stop" vertices composed of one contour, as in (a). The various grouping percepts are shown schematically to the right. In order to extend the collinear completion models to account for these groupings would require a separate set of completion receptive fields, one set for each of the different completion patterns observed. And these detectors would each have to be replicated at every location and at every orientation across the visual field.
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