Relief: Pictorial and otherwise

Surfaces play an important role in visual perception. They are perceived as "(per-ceptual) reliefs", that are surfaces in 2+1D perceptual space, that is the product space of the 2D visual field and the *D "depth dimension". It is in many respects irrelevant whether the observer views a true 3D scene or a flat (2D) picture of a scene. In both cases the percepts are reliefs in 2+1D perceptual space. In the latter case one speaks of "pictorial relief". We discuss how perceptual reliefs can be measured and which aspects of these reliefs are especially robust against day to day intraobserver variations, changes of viewing conditions, and interobserver differences. It turns out that only aspects of the partial depth order (based on depth precedence in infinitesimal regions) are stable. Thus features of the relief are invariants of general "relief preserving transformations " that may actually scram-ble depth values at different locations. This is evident from the fact that human observers can only judge depth precedence with some degree of certainty for points that are on a single slope. We discuss the formal structure of these relief invari-ants. Important ones are the Morse critical points and the ridges and courses of the relief. 1 The notion of "pictorial relief" The concept of "relief " originally derives from the arts of sculpting and painting. Sculpture designed for a particular vantage point (the generic sit-uation for classical sculpture[22], e.g., pieces designed to be placed against a wall) need not be worked "in the round " in order to look natural, it can be squashed in depth to various degrees, even to almost flat work, and still appear as true threedimensional structure. Paintings are by nature totally "flat", nevertheless vivid relief may appear due to shading, etc. For instance, the work by the dutch painter Jacob de Wit[18] can hardly be distinguished from sculpted relief from its intended viewing position. (He made a successful living on this type of "illusion".) The concept of relief has been important in the theory of sculpture from renaissance times (vide Vasari's discusssion[21] of "Michelangelo's method"). Its general signifi-BMVC 1994 doi:10.5244/C.8.1 cance for the visual arts and indeed vision in general was recognized by th