Scale Space Analysis by Stabilized Inverse Diiusion Equations ?

We introduce a family of rst-order multi-dimensional ordinary diierential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diiusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations \stabilized inverse diiusion equations" (\SIDEs"). A SIDE in one spatial dimension may be interpreted as a limiting case of a semi-discretized Perona-Malik equation 3, 4]. In an experimental section , SIDEs are shown to suppress noise while sharpening edges present in the input signal. Their application to image segmentation is demonstrated .