Relief: Pictorial and otherwise

Surfaces play an important role in visual perception. They are perceived as ‘(perceptual) reliefs’. that are surfaces in 2 + 1D perceptual space, that is the product space of the 2D visual field and the ID ‘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 + ID perceptual space. In the latter case, one speaks of ‘pictorial relief’. We discuss how perceptual reliefs can be ~~rrr.rz~~~l 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 scramble 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 invariants. Important ones are the Morse critical points and the ridges and courses of the relief.