Image segmentation using the piecewise smooth variational model proposed by Mumford and Shah is both robust and computationally expensive. Fortunately, both the intermediate segmentations computed in the process of the evolution, and the final segmentation itself have a common structure. They typically resemble a linear combination of blurred versions of the original image. In this paper, we present methods for fast approximations to Mumford-Shah segmentation using reduced image bases. We show that the majority of the robustness of Mumford-Shah segmentation can be obtained without allowing each pixel to vary independently in the implementation. We illustrate segmentations of real images that show how the proposed segmentation method is both computationally inexpensive, and has comparable performance to Mumford-Shah segmentations where each pixel is allowed to vary freely.