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In geometry, shape is the object of theorems associated to a class of transformations. It corresponds to the invariant properties of regions, figures, solids, which are not altered by transformations. The concept of shape implies the concepts of space, upon which transformations are acted, and metric, if distance is preserved, or a measurement function. The invariant properties of shape are fundamental to perception too. However, the classes of transformations build a hierarchy along which shape is more and more abstract from the Euclidean to the topological group, and accordingly, a greater number of perceptual properties are being lost. The science of perception addresses also the question about the perceptual primitives for shape recognition.