Restoration of dendrites and spines with the objective of topologically correct segmentation

In many biomedical applications, typically a specimen marked with a coloring is to be segmented from its environment which is unmarked. Although this is a binary mapping in nature, it is not an easy task if the size of the specimen lies in the range of the optical resolution of the sampling equipment, because intermediate signal values can be caused by the distance to an object as well as by the size of the object itself. This ambiguity can cause topological errors in the segmentation result. We study operators designed to segment thin objects from their background. These operators decide on the basis of the differential geometric properties of the 3D grayscale image function. Their capabilities and drawbacks are discussed by the example of the observation of neural dendrites and spines by confocal laser scan microscopy