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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Pollak, I. |
| Copyright Year | 2001 |
| Description | Author affiliation: Purdue Univ., West Lafayette, IN, USA (Pollak, I.) |
| Abstract | Summary form only given, as follows. Building on our image restoration and segmentation algorithms developed in Pollak et al. (2000), we present a very simple nonlinear diffusion equation and show its utility both for image segmentation and for the detection of abrupt changes in 1-D. We show that it may be interpreted as a variant of the Perona-Malik (1990) equation, as the steepest descent equation for the total variation (Bouman and Sauer 1991, Rudin et al. 1992), and-in 1-D-as a solver of a simple version of the Mumford-Shah (1985) problem. The analysis of our equation in 1-D reveals it to be an exact solver of certain maximum likelihood detection/estimation problems. The major advantage over other methods to solve these problems is O(N log N) computational complexity in one spatial dimension. Finally, we show our method to be a robust estimator (in the spirit of H-infinity estimation (Nagpal and Khargonekar 1991)) for a restricted class of 1-D problems. Experiments suggest that the 2-D version of our algorithm retains robustness properties of the 1-D version. Moreover, if only a binary segmentation is required, the computational complexity of our 2-D algorithm is still O(N log N). A remaining challenge is to extend our probabilistic analysis of the 1-D algorithm to 2-D, designing fast and optimal image segmentation algorithms. |
| Sponsorship | IEEE Signal Process. Soc |
| File Size | 70673 |
| File Format | |
| ISBN | 0780367251 |
| DOI | 10.1109/ICIP.2001.958554 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2001-10-07 |
| Publisher Place | Greece |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Image segmentation Nonlinear equations Maximum likelihood detection Computational complexity H infinity control Algorithm design and analysis USA Councils Image edge detection Image restoration Maximum likelihood estimation |
| Content Type | Text |
| Resource Type | Article |
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