The medial loci called cores are generalized maxima in scale space of a form of medial information that is invariant to translation, rotation, and zoom. S. M. Pizeret al.show that these invariances imply medial loci having the property that boundary sensing is made with apertures proportional to figural width (Comput. Vision Image Understand.69, 1998). This property of cores leads to an insensitivity to image disturbances, in strong contrast to previously available medial loci. In particular, image disturbances whose amplitude under the core's aperture, proportional to the figural width, is small compared to the intensity difference of the figure and its background produce only small changes in the position and width given by the core. These insensitivities to image disturbances, including additive intensity noise, imaging blur, boundary perturbations, and object variations are discussed and demonstrated here.