INITIALISATION AND TERMINATION OF ACTIVE CONTOUR LEVEL-SET EVOLUTIONS

M. Weber, A. Blake and R. Cipolla

October 2003

This paper deals with the evolution control of level-sets in the context of contour detection. There is a considerable amount of existing work on PDEs for geodesic contour detection and the investigation of level-set implementations has recently resulted in efficient and stable numerical realisations of the differential evolution. This paper is based on a finite element implementation for signed distance level-set evolutions and focuses the attention to the initialisation and termination of level-set evolutions.

An initialisation consists of an initial signed distance function which corresponds to some implicit curve. We discuss two types of initialisation. We generalise the commonly used a priori type, which can be a rectangle the size of the image, to include more general initial shapes. We show that the initial shape does not have to be closed and can for instance be a single line.

The second type of initialisations is not specified by the user but a result of previous level-set evolutions. This type of initialisation is useful when different evolution equations are to be alternated and can be used for instance to detect nested contours or in multi-resolution techniques. For the termination of a geodesic evolution, we introduce an automatic stopping condition by looking at the Riemannian length of the implicit curve as the quantity that is subject to the minimisation. It turns out that the length can be computed efficiently from the employed finite element representation and used to terminate the gradient descent.

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