Geometric organization is readily detected in discrete textures such as dot patterns. A common proposal is that orientation-tuned receptive field mechanisms provide the local orientation information from which the global organizations emerge. Alternatively, the local orientation might be attributed to grouping constructions between adjacent tokens, each representing the position of a dot and its attributes such as color, size and contrast. Geometric organization would then emerge by grouping operations on selected tokens that are similar, adjacent and aligned. It is the ability to group on the basis of similarity that most strongly differentiates this from the energy-summating receptive field approach. Using dot patterns with rivalrous organization, we demonstrate grouping phenomena that are difficult to attribute to a broad class of energy summ­tion detectors operating in the spatial frequency domain, which we therefore attribute to percep­tual groupings on tokens. We discuss the computational differences between feature detection and structure detection, and suggest that orientation-tuned receptive field mechanisms, while appropriate for the former task, have little application to the latter.