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Abstract. We propose in this paper a new approach to segmentation of 3-D tomography of liver vessel system. The approach is based on a pointwise reconstruction with restriction to simple points manipulation to preserve the homotopy. We propose and compare two dual methods of the vessel system extraction. The efficiency of these methods is demonstrated on a raw X-ray tomography image. The desired level of detail in the vein ramification system is obtained by adjusting one parameter controlling the admitted level of light intensity. The paper is organized as follows: In the introductory section we present the main principles of the approach using simple points. We explain the algorithm as well as the aspects of efficient computer implementation. Experiment results for different parameter values are given together with discussion and conclusions.

Contrary to the 2D case, a 3D hole is not a subset of the 3D space. It is therefore not possible to use connected component search algorithms for detecting and suppressing 3D holes. In this paper, we propose an algorithm for closing 3D holes. It is based on properties of the previously introduced notion of topological numbers. Our algorithm is linear in time and it allows to control the size of the holes which are closed. As far as we know, this is the first 3D-hole closing algorithm.