Recent work has shown that salient perceptual singularities occur in visual textures even in the absence of feature gradients. In smoothly varying orientation-defined textures, these striking non-smooth percepts can be predicted from two texture curvatures, one tangential and one normal [ Proc. Natl. Acad. Sci. USA 103, 15704 (2006) ]. We address the issue of detecting these perceptual singularities in a biologically plausible manner and present three different models to compute the tangential and normal curvatures using early cortical mechanisms. The first model relies on the response summation of similarly scaled even-symmetric simple cells at different positions by utilizing intercolumnar interactions in the primary visual cortex (V1). The second model is based on intracolumnar interactions in a two-layer mechanism of simple cells having the same orientation tuning but significantly different scales. Our third model uses a three-layer circuit in which both even-symmetric and odd-symmetric receptive fields (RFs) are used to compute all possible directional derivatives of the dominant orientation, from which the tangential and normal curvatures at each spatial position are selected using nonlinear shunting inhibition. We show experimental results of all three models, we outline an extension to oriented textures with multiple dominant orientations at each point, and we discuss how our results may be relevant to the processing of general textures.