Endstopping and curvature

Hypercomplex or endstopped visual cortical neurons are usually supposed to be concerned with length or end point analysis. However, recent evidence demonstrates that endstopped neurons are curvature-selective, a connection that we explore here in some detail. A model of endstopped simple cells is developed and a variety of computational simulations examine the connection of the model to the reported length and orientation responses of endstopped neurons. Even and odd versions of the model are described, both of which are shown to be curvature-selective. Even-symmetric instances of the model respond well to thin curves over a range of curve orientation and curvature, independent of sign of curvature. In contrast, odd-symmetric instances respond to both thin and thick curves while exhibiting a more complex curvature-sign dependence--responding in a sign-selective fashion to curved lines but not to curved edges. Finally, the response of the endstopped model to curve singularities is explored, and the possible role of nonendstopped and endstopped cells in building curve descriptions is discussed.