Optimal Performance of the Watershed Segmentation of an Image Enhanced by Teager Energy Driven Diffusion

In this paper we study a non-linear diffusion process to reduce the influence of noise in the watershed segmentation of an image. Instead of the squared amplitude of the gradient that is traditionally used to drive the non-linear diffusion, we use the Teager energy, which is known to be less sensitive to noise. To evaluate the performance of the segmentation processes studied in this paper, we introduce an objective measure to assess the quality of a segmentation when the ground truth segmentation is known. With this objective performance measure we determine the optimal parameters of the Teager energy driven nonlinear diffusion process. 1. Teager Energy Driven Diffusion A stack of images I(x,y,t), with I (x,y,0) the original image and t the scale parameter, is constructed using the diffusion equation: [ ] ∇⋅ ∇ = c x y t I x y t I x y t t ( , , ) ( , , ) ( , , ) ∂ ∂ . (1) In the linear diffusion of Witkin [1] and Koenderink [2] the diffusion velocity is constant: c (x, y, t)=1. In the non-linear diffusion the diffusion velocity depends on a local activity that indicates the presence of an edge. Perona and Malik [3] used the (squared) amplitude of the gradient as activity image: ( ) c x y t g I x y t ( , , ) ( , , ) = ∇ 2 . (2) The function g (.) is a soft threshold function: