RELIEF - PICTORIAL AND OTHERWISE

Surfaces play an important role in visual perception. They are perceiv ed as'(perceptual) reliefs', that are surfaces in 2+1D perceptual spac e, that is the product space of the 2D visual field and the 1D 'depth dimension'. It is in many respects irrelevant whether the observer vie ws a true 3D scene or a flat (2D) picture of a scene. In both cases, t he percepts are reliefs in 2+1D perceptual space. In the latter case, one speaks of 'pictorial relief'. We discuss how perceptual reliefs ca n be measured and which aspects of these reliefs are especially robust against day-to-day intraobserver variations, changes of viewing condi tions and interobserver differences. It turns out that only aspects of the partial depth order (based on depth precedence in infinitesimal r egions) are stable. Thus, features of the relief are invariants of gen eral 'relief preserving transformations' that may actually scramble de pth values at different locations. This is evident from the fact that human observers can only judge depth precedence with some degree of ce rtainty far points that are on a single slope. We discuss the formal s tructure of these relief invariants. Important ones are the Morse crit ical points and the ridges and courses of the relief.