- A central notion in the study of texture segregation is that of feature gradient (or feature contrast). In orientation-based texture segregation (OBTS), where the dominant (and sometimes sole) feature of consideration is local orientation, orientation gradients have indeed played a key role in explaining behavioral results (Nothdurft, 1985,1991; Landy&Bergen, 1991; Mussap&Levi ,1999). However, in this paper we present clear evidence that orientation contrast does not account for all OBTS phenomena. We first demonstrate how orientation-defined textures (ODTs) of constant orientation gradient exhibit salient perceptual singularities (i.e., boundaries between perceptually coherent regions). More generally, we study smoothly varying ODTs that exhibit salient perceptual singularities despite having no outstanding orientation contrasts. While our psychophysical investigation proves these singularities robust and consistent across observers, we show that they defy not only popular texture segregation theories, but virtually all neural models (e.g., Li, 2000) and computational segmentation methods, either local (e.g., Malik&Perona, 1990) or global (e.g., Shi&Malik, 2000). To better understand this hitherto neglected aspect of texture segregation, which possibly confounds all previous studies with varying ODTs, here we first analyze the (differential) geometry underlying general ODTs and derive multiple ODT curvatures, and then we show psychophysically that unlike orientation gradients, these curvatures fully predict the perceptual singularities reported. Given the central role of feature gradients in early vision, the significance of our findings extends well beyond OBTS, and here we establish links to segregation/grouping based on other visual features and to the perception of 3D-shape from texture, shading, and surface contours.