In previous work, we presented an algorithm to accelerate z-buffer rendering of enormously complex scenes. Here, we extend the approach to antialiased rendering with an algorithm that guarantees that each pixel of the output image is within a user-specified error tolerance of the filtered underlying continuous image. As before, we use an object-space octree to cull hidden geometry rapidly. However, instead of using an image-space depth pyramid to test visibility of collections of pixel samples, we use a quadtree data structure to test visibility throughout image-space regions. When regions are too complex, we use quadtree subdivision to simplify the geometry as in Warnock's algorithm. Subdivison stops when the algorithm can either analytically filter the required region or bound the convolution integral appropriately with interval methods. To the best of our knowledge, this is the first algorithm to antialias with guaranteed accuracy scenes consisting of hundreds of millions of polygons.