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Nowadays volume images are frequently used in many applications. Volume images of paper can be analyzed to increase the understanding of the complexity of the fiber network in paper and its effect on the optical and mechanical properties of paper. We show how curve and surface representations of the fiber, the fiber wall, and the fiber lumen can be computed using distance transform based algorithms. These representations are used for easy computation of wall thickness, degree of collapse, fiber length, slenderness ratio, fiber curl, and torsional resistance for the fibers. Free-fiber segments are identified, again using a distance transform based algorithm. Finally, we show tools for qualitative visual inspection of the fibers. The methods are evaluated and illustrated using both sets of synthetic and of real data. In addition to the analysis of the fiber network in paper, they can be used in many other applications where shape analysis of elongated objects is to be performed.