Nonlinear optimisation method for image segmentation and noise reduction using geometrical intrinsic properties

This paper considers the optimisation of a nonlinear functional for image segmentation and noise reduction. Equations optimising this functional are derived and employed to detect edges using geometrical intrinsic properties such as metric and Riemann curvature tensor of a smooth differentiable surface approximating the original image. Images are then smoothed using a Helmholtz type partial differential equation. The proposed approach is shown to be very efficient and robust ill the presence of noise, and the reported results demonstrate better performance than the conventional derivative based edge detectors. (c) 2005 Elsevier B.V. All rights reserved.