1 Optimal Performance of the Watershed Segmentation of an Image Enhanced by Teager Energy Driven Diffusion Danny De Vleeschauwer 1 , Patrick De Smet 1 , Faouzi Alaya Cheikh 2 , Ridha Hamila 2 , Moncef Gabbouj 2 1 University of Ghent, Belgium Department of Telecommunications and Information Processing Sint-Pietersnieuwstraat 41, B-9000 Gent, BELGIUM 2 Tampere University of Technology, Finland Signal Processing Laboratory P.O. Box 553, FIN- 33101 Tampere, FINLAND Email: faouzi@cs.tut.fi ABSTRACT 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 non- linear 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: ( 29 cx y t g I x y t ( , , ) ( , , ) = ∇ 2 . (2) The function g (.) is a soft threshold function: gu c u T max d a ( ) = +       1 . (3) Under the threshold T d , the function g(.) takes approximately the value c max; above the threshold T d , the function g(.) tends to 0. The parameter a determines the steepness of the function g(.) at the threshold. The larger this parameter a is, the steeper the function g(.) is, and the more crisp the threshold is. In Perona and Malik [3] the steepness parameter a is equal to 1. In this paper we study two extensions of the non-linear diffusion process of Perona and Malik [3]. As a first extension, the optimal value for the steepness parameter a is searched for. It is expected that as in Alaya Cheikh et al [4], values in the neighborhood of 1 will be found to be optimal. As a second extension, we use the Teager energy E, instead of the squared gradient, as activity image: