Label fusion is a multi-atlas segmentation approach that explicitly maintains and exploits the entire training dataset, rather than a parametric summary of it. Recent empirical evidence suggests that label fusion can achieve significantly better segmentation accuracy over classical parametric atlas methods that utilize a single coordinate frame. However, this performance gain typically comes at an increased computational cost due to the many pairwise registrations between the novel image and training images. In this work, we present a modified label fusion method that approximates these pairwise warps by first pre-registering the training images via a diffeomorphic groupwise registration algorithm. The novel image is then only registered once, to the template image that represents the average training subject. The pairwise spatial correspondences between the novel image and training images are then computed via concatenation of appropriate transformations. Our experiments on cardiac MR data suggest that this strategy for nonparametric segmentation dramatically improves computational efficiency, while producing segmentation results that are statistically indistinguishable from those obtained with regular label fusion. These results suggest that the key benefit of label fusion approaches is the underlying nonparametric inference algorithm, and not the multiple pairwise registrations.