Active contours without edges and without reinitialisation

This paper is concerned with the use of the level set methods in image segmentation. It is known that the reinitialisation is sometimes needed for the correct function of these methods. This step, however, is problematic both from the theoretical and from the practical point of view. In this paper, we present a modification of the well known Chan and Vese method that does not require the reinitialisation. It means that, during the iterative process, it is not necessary to switch between the usual and reinitialisation steps. The method is based on formulating the image segmentation problem as a problem of minimising a functional with a constraint. The solution is done by making use of the Lagrange multipliers method. We present the theory needed for implementing as well as results of practical testing.