Distance-based Speed Functions for Level Set Methods in Image Segmentation

Abstract

Level set methods are a well-known means for the segmentation of objects in image data. In this paper, we discuss a class of easy to calculate terms based on distance measures for integration into the level set speed function. We will give examples for the use of these distance-based terms as a stopping criterion in the absence of reliable image features and as an acceleration force for the propagating front to connect parts of a single object. A comparison of the results with a level set segmentation not using any distance measures will be given to demonstrate the improvement of segmentation results. 1 Level Set Speed Functions Level set methods have become popular for many domains of science as diverse as computer graphics, simulation of crystal growth or fluid mechanics. In image processing they are often used for segmentation. Because of their implicit definition level sets are independent of the number of degrees of freedom of the object of interest as well as the number of dimensions of the underlying data. Level Sets describe the propagation process of a closed curve C ∈Rn. This curve C is represented as the zero level set of a higher dimensional function Φ ∈Rn+1 given by