Images rendered using global illumination algorithms are considered amongst the most realistic in 3D computer graphics. However, this high fidelity comes at a significant computational expense. A major part of this cost arises from the sampling required to eliminate aliasing errors. These errors occur due to the discrete sampling of continuous geometry space inherent to these techniques. In this paper we present a fast analytic method for predicting in advance where antialiasing needs to be computed. This prediction is based on a rapid visualisation of the scene using a GPU, which is used to drive a selective renderer. We are able to significantly reduce the overall number of aniti-aliasing rays traced, producing an image that is perceptually indistinguishable from the high quality image at a much reduced computational cost.