Both surface contours and texture patterns can provide strong cues to the three-dimensional shape of a surface in space. Many of the most perceptually salient texture patterns have a strong flowlike structure, resulting from the directional nature of the surface textures from which they project. Under the minimal assumption that an oriented surface texture is homogeneous, the texture flow on a developable surface can be shown to follow parallel geodesics of the surface. The geometry of texture flow is therefore equivalent to that of an important class of surface contours: those that project from parallel geodesics of a developable surface. I derive a set of differential equations that support the estimation of surface shape from geodesic surface contours under spherical perspective, for both parallel and nonparallel contours. For perfectly oriented textures, the equations apply directly to the integrated flow lines in a texture image. For weakly oriented textures, perspective projection distorts the projected orientation of flow lines away from the idealized case of pure contours; however, simulations show that for a large class of textures, these distortions will be small and limited largely to extreme surface poses. The geometrical analysis, along with a number of phenomenal demonstrations and psychophysical results, suggests that the human visual system co-opts shape from contour mechanisms to estimate surface shape from texture flow.
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