Contours projected from geodesic boundaries of developable surfaces (as are formed by folding and twisting flat surfaces) are particularly salient cues to 3-D surface shape. Textures which are strongly anisotropic (highly oriented) provide a similar source of information. The natural definition of homogeneity for such textures leads to the constraint that the oriented ‘flow’ of texture on a surface follows geodesics of the surface (on average). In the current work, it is shown that the shapes of contours projected from geodesics of developable surfaces, and analogously of oriented texture flow, reliably determine the shapes of the surfaces. On the basis of this analysis, it is suggested that human perception of surface shape from texture has two modes of operation: an isotropic mode, in which the visual system infers surface shape from local texture compression information, and a texture flow mode, in which the curvature of local texture flow determines local surface curvature, based on a geodesic constraint. In order to test the theory, planar texture patterns have been isometrically mapped with varying degrees of global orientation (ranging from isotropic to purely oriented) onto developable surfaces. The theory predicts that subjects' ability to make judgements about surface shape will be good for the isotropic textures and for highly oriented textures, but not for anisotropic textures that are only weakly oriented. As predicted, images of the surfaces with isotropic texture patterns induce strong percepts of shape, as do those of highly oriented textures. Images of anisotropic, weakly oriented patterns, however, elicit only weak percepts of shape.
Defence strategies of the smaller NATO states – a comparative study
