Edge-Preserving Noise Removal, Part I: Second-Order Anisotropic Di usion

The article is concerned with eÆcient edge-preserving numerical techniques for noise removal via anisotropic di usion. New minimum-biased (MB) nite di erence formulas are introduced to minimize di usion on both the piecewise smooth portions and their boundaries. Locally one-dimensional time-stepping algorithms are analyzed and a formula for eÆcient timestep sizes is suggested, to remove the high-frequency components of the error (the noise) more eÆciently and to minimize the torture of lower-frequency components of the image. An e ective strategy is suggested for an automatic stopping of the di usion process. It is numerically veri ed that the MB formulas eliminate, rather than di use, the noise of piecewise constant images. With such a property, the MB formulas are successfully applied to noise removal of general images. Numerical examples carried out with various images are presented to demonstrate superior properties of (a) the new MB formulas, (b) the formula for timestep sizes, and (c) the automatic stopping strategy of the di usion process.