Contour into texture: information content of surface contours and texture flow

Both surface contours and texture patterns can provide strong cues to the t hree-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. Und er the minimal assumption that an oriented surface texture is homogeneous, the texture flow on a developable surface can be shown to follow parallel g eodesics of the surface. The geometry of texture flow is therefore equivale nt to that of an important class of surface contours: those that project fr om parallel geodesics of a developable surface. I derive a set of different ial equations that support the estimation of surface shape from geodesic su rface contours under spherical perspective, for both parallel and nonparall el contours. For perfectly oriented textures, the equations apply directly to the integrated flow lines in a texture image. For weakly oriented textur es, perspective projection distorts the projected orientation of flow lines away from the idealized case of pure contours; however, simulations show t hat for a large class of textures, these distortions will be small and limi ted 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 estim ate surface shape from texture flow. (C) 2001 Optical Society of America.