Localized operators, like Gabor wavelets and difference-of-gaussian filters, are considered useful tools for image representation. This is due to their ability to form a sparse code that can serve as a basis set for high-fidelity reconstruction of natural images. However, for many visual tasks, the more appropriate criterion of representational efficacy is recognition rather than reconstruction. It is unclear whether simple local features provide the stability necessary to subserve robust recognition of complex objects. In this article, we search the space of two-lobed differential operators for those that constitute a good representational code under recognition and discrimination criteria. We find that a novel operator, which we call the dissociated dipole, displays useful properties in this regard. We describe simple computational experiments to assess the merits of such dipoles relative to the more traditional local operators. The results suggest that nonlocal operators constitute a vocabulary that is stable across a range of image transformations.