Medial axis (surface in 3D) is a powerful tool for describing structure of geometric models and is used in various applications such as visualization, shape abstraction and reverse engineering. One of the major issues in medial axis transforms is its sensitivity to topological noises, or its structure is easily changed by small holes. This can be seen in scanned models and this is a bottleneck in the application to reverse engineering. We introduce a medial axis transform method robust to topological noises. Our idea is to use mathematical morphology to fill topological noises. Then, we extend morphological operations so that unnecessary filling by dilation is prevented. As a result, we can fill only topological noises and intrinsic structure of the input geometric data can be extracted.