<p>The preservation of morphological features, such as protrusions and concavities, and of the topology of input shapes is important when establishing reference data for benchmarking segmentation algorithms or when constructing a mean or median shape. We present a contourwise topology-preserving fusion method, called shape-aware topology-preserving means (SATM), for merging complex simply connected shapes. The method is based on key point matching and piecewise contour averaging. Unlike existing pixelwise and contourwise fusion methods, SATM preserves topology and does not smooth morphological features. We also present a detailed comparison of SATM with state-of-the-art fusion techniques for the purpose of benchmarking and median shape construction. Our experiments show that SATM outperforms these techniques in terms of shape-related measures that reflect shape complexity, manifesting itself as a reliable method for both establishing a consensus of segmentation annotations and for computing mean shapes.</p>