Image Processing: Flows under Min/Max Curvature and Mean Curvature

part, based on a local decision. This approach has several We present a class of PDE-based algorithms suitable for key virtues. First, it contains only one enhancement paramimage denoising and enhancement. The techniques are applicaeter, which in most cases is automatically chosen. Second, ble to both salt-and-pepper gray-scale noise and full-image the scheme automatically picks the stopping criteria; concontinuous noise present in black and white images, gray-scale tinued application of the scheme produces no further images, texture images, and color images. At the core, the change. Third, the method is one of the fastest possible techniques rely on two fundamental ideas. First, a level set schemes based on a curvature-controlled approach. formulation is used for evolving curves; use of this technique to The methods presented in this paper are derived from flow isointensity contours under curvature is known to remove noise and enhance images. Second, the particular form of the the Osher–Sethian [17] level set formulation of front propcurvature flow is governed by a min/max switch which selects agation, which grew out of earlier by Sethian [23] on the a range of denoising dependent on the size of switching window. mathematical formulation of curve and surface motion. Our approach has several virtues. First, it contains only one The application of this level set perspective to image proenhancement parameter, which in most cases is automatically cessing, and the design of a PDE-based approach to image chosen. Second, the scheme automatically stops smoothing at enhancement and noise removal was introduced in two a point which depends on the switching window size; continued pivotal papers; the work of Alvarez et al. [3] and the work application of the scheme produces no further change. Third, of Osher and Rudin [16]. While the work presented here the method is one of the fastest possible schemes based on a starts from the original curve evolution work [23] and level curvature-controlled approach.  1996 Academic Press, Inc. set formulation presented in [17, 24], it owes a significant debt to the ground-breaking work of Alvarez et al. and Osher and Rudin.