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.
The work of the authors was supported in part by AFOSR grant F49620-95-1-0083, ONR grant N00014-91-J-1004, and by subcontract GC123919NGD from Boston University under the AFOSR Multidisciplinary Research Program on Reduced Signature Target Recognition.
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© 1997 Springer-Verlag Berlin Heidelberg
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Pollak, I., Willsky, A.S., Krim, H. (1997). Scale space analysis by stabilized inverse diffusion equations. In: ter Haar Romeny, B., Florack, L., Koenderink, J., Viergever, M. (eds) Scale-Space Theory in Computer Vision. Scale-Space 1997. Lecture Notes in Computer Science, vol 1252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63167-4_51
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DOI: https://doi.org/10.1007/3-540-63167-4_51
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