Scale Space Analysis by Stabilized Inverse Diffusion Equations

Abstract. We introduce a family of first-order multi-dimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations "stabilized inverse diffusion 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.

• Type: Conference
• Year: 1997
• Where: SCALESPACE
• Authors: Ilya Pollak, Alan S. Willsky, Hamid Krim
• Keywords: Computer Vision, Discontinuous Right-hand Sides, Inverse Diffusion, Inverse Diffusion Equations, SCALESPACE 1997