Figure 2: The components of the distal to proximal mapping, M (see section 3.2.2). In this schematic illustration, the shape of the object is determined by three parameters p (depicted by the three ``slider'' controls). The appearance of the object is governed by these parameters and by variables z that represent factors such as orientation and illumination direction. To ensure proper representation of the original parameter space, a typical perceptual system must carry out many measurements and then reduce the dimensionality of the resulting space while getting rid of the extraneous variables z.