Under the assumption of a general viewpoint, particular image properties, such as cotermination, straightness, and parallelism, can be used to infer, more or less reliably, the corresponding characteristics in the world. In this paper, the literature about these nonaccidental properties (NAPs) is reviewed to trace its historical roots, to list the properties that function as NAPs, and to discuss the psychological evidence for their detection and use. Against this background, four experiments are reviewed and four are fully described that were designed to test the perceptual use of skewed symmetry (SS), which results from orthographic projection of planar bilateral or mirror symmetry (BS). Despite the large symmetry advantage obtained in all experiments, SS is only perceived as BS-in-depth in cases of closed polygons or dot patterns with higher-order types of symmetry. In all random dot patterns and in some symmetric patterns with low "Gestalt", subjects relied on more local groupings which are qualitatively affine invariant, such as clusters based on proximity or curvilinearity. Based on previous approaches in the literature and these new findings, I suggest some distinctions between different ways of using NAPs, which might foster further research.
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