The lobula giant motion detector (LGMD) is a wide-field bilateral visual interneuron in North American locusts that acts as an angular threshold detector during the approach of a solid square along a trajectory perpendicular to the long axis of the animal (Gabbiani et al., 1999a). We investigated the dependence of this angular threshold computation on several stimulus parameters that alter the spatial and temporal activation patterns of inputs onto the dendritic tree of the LGMD, across three locust species. The same angular threshold computation was implemented by LGMD in all three species. The angular threshold computation was invariant to changes in target shape (from solid squares to solid discs) and to changes in target texture (checkerboard and concentric patterns). Finally, the angular threshold computation did not depend on object approach angle, over at least 135 degrees in the horizontal plane. A two-dimensional model of the responses of the LGMD based on linear summation of motion-related excitatory and size-dependent inhibitory inputs successfully reproduced the experimental results for squares and discs approaching perpendicular to the long axis of the animal. Linear summation, however, was unable to account for invariance to object texture or approach angle. These results indicate that LGMD is a reliable neuron with which to study the biophysical mechanisms underlying the generation of complex but invariant visual responses by dendritic integration. They also suggest that invariance arises in part from non-linear integration of excitatory inputs within the dendritic tree of the LGMD.