We propose a new method for removing topological defects in sur- faces and volumes segmented from medical images. Unlike current topology cor- rection approaches, we define a smoothing operator that acts solely on the im- age volume and can be integrated into segmentation procedures. The method is based on an analysis of the scalar field underlying the isosurface of interest, and performs only local changes. No assumptions are required on the structure to segment, or on the desired topology. We show that segmentation algorithms that incorporate toplogical smoothing produce results with fewer topological defects.