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We propose the use of eigenvectors for automated multidimensional image segmentation. The approach of Shi and Malik (1997) has been extended in three dimensions and applied on biomedical data from electron microscopy and electron beam computed tomography. The approach exploits different similarity criteria, e.g. proximity and gray level similarity. Theory, implementation, parameter setting and results are discussed in detail. The method turns out be a powerful tool for visualization, with the potential for developing further affinity measurements adapted to specific applications.