The study of the filamentous objects in wastewater has recently gained momentum due to its significant effect in environmental pollution. This paper describes a neural network based skeleton extraction technique for volumetric images of these bio-film objects. These objects require huge computer storage space. One way to economize the storage space is to represent such images in the form of a vector skeleton (a piecewise linear approximation). Such a skeleton preserves the essential structure of the object. The proposed neural network does not start with a predefined net topology. The topology evolves during the learning process based on the input. The present technique has certain advantages over the conventional 3-D thinning techniques. It achieves data reduction at a higher rate. In addition, the proposed technique is highly robust to noise and arbitrary rotations of an image.