Abstract: Automated three-dimensional ~3-D! image analysis methods are presented for tracing of dye-injected neurons imaged by fluorescence confocal microscopy and HRP-stained neurons imaged by transmitted-light brightfield microscopy. An improved algorithm for adaptive 3-D skeletonization of noisy images enables the tracing. This algorithm operates by performing connectivity testing over large N � N � N voxel neighborhoods exploiting the sparseness of the structures of interest, robust surface detection that improves upon classical vacant neighbor schemes, improved handling of process ends or tips based on shape collapse prevention, and thickness-adaptive thinning. The confocal image stacks were skeletonized directly. The brightfield stacks required 3-D deconvolution. The results of skeletonization were analyzed to extract a graph representation. Topological and metric analyses can be carried out using this representation. A semiautomatic method was developed for reconnection of dendritic fragments that are disconnected due to insufficient dye penetration, an imaging deficiency, or skeletonization errors. Key words: automated neuron tracing, 3-D skeletonization, confocal microscopy, 3-D brightfield microscopy, deconvolution, reconnection

A simple point of an object is a point whose removal does not change the topology. However, the simultaneous deletion of simple points may change the topology. Through the notion of P-simple point, we give examples of algorithms, described by a two-steps procedure, which removes simple points in parallel and which are automatically ensured to preserve the topology. More particularly, a new symmetrical thinning algorithm is proposed. Furthermore, through the notion of P^x-simple point, we give a methodology which permits to produce an algorithm A' (described by a one-step procedure) from an existent one A, which is "faster" than A, in the sense that it usually 'deletes more points than A''.