Medical images pose a major challenge for image analysis: often they have poor signal-to-noise, necessitating smoothing; yet such smoothing needs to preserve the boundaries of regions of interest and small features such as mammogram microcalcifications. We show how circular integral invariants (II) may be adapted for feature-preserving smoothing to facilitate segmentation. Though II is isotropic, we show that it leads to considerably less feature deterioration than Gaussian blurring and it improves segmentation of regions of interest as compared to anisotropic diffusion, particularly for hierarchical contour based segmentation methods.