Image segmentation and edge enhancement with stabilized inverse diffusion equations

Author

Pollak, Ilya ; Willsky, Alan S. ; Krim, Hamid

Author_Institution

Div. of Appl. Math., Brown Univ., Providence, RI, USA

Volume

9

Issue

2

fYear

2000

fDate

2/1/2000 12:00:00 AM

Firstpage

256

Lastpage

266

Abstract

We introduce a family of first-order multidimensional 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). Existence and uniqueness of solutions, as well as stability, are proven for SIDEs. A SIDE in one spatial dimension may be interpreted as a limiting case of a semi-discretized Perona-Malik equation (1990, 19994). In an experiment, SIDE´s are shown to suppress noise while sharpening edges present in the input signal. Their application to image segmentation is also demonstrated

Keywords

differential equations; image enhancement; image segmentation; image texture; inverse problems; numerical stability; radar imaging; synthetic aperture radar; SAR log-magnitude image; discontinuous right-hand sides; edge enhancement; experiment; first-order multidimensional ordinary differential equations; image processing; image segmentation; input signal; inverse diffusion; noise suppression; semi-discretized Perona-Malik equation; solution existence; solution stability; solution uniqueness; spatial dimension; stabilized inverse diffusion equations; synthetic aperture radar; textural regions; Differential equations; Helium; Image analysis; Image processing; Image segmentation; Limiting; Multidimensional systems; Noise robustness; Stability; Synthetic aperture radar;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.821738

Filename

821738