A skeleton provides a synthetic and thin representation of three dimensional objects, and is useful for shape description and recognition. In this paper, a novel 3D skeleton algorithm is proposed based on neutrosophic cost function. Firstly, the distance transform is used to a 3D volume, and the distance matrix is obtained for each voxel in the volume. The ridge points are identified based on their distance transform values and are used as the candidates for the skeleton. Then, a novel cost function, namely neutrosophic cost function (NCF) is proposed based on neutrosophic set, and is utilized to define the cost between each ridge points. Finally, a shortest path finding algorithm is used to identify the optimum path in the 3D volume with least cost, in which the costs of paths are calculated using the new defined eutrosophic set istance transform ath finding algorithm NCF. The optimum path is treated as the skeleton of the 3D volume. A variety of experiments have been conducted on different 3D volume. The experimental results demonstrate the better performance of the proposed method. It can identify the skeleton for different volumes with high accuracy. In addition, the proposed method is robust to the noise on the volume. This advantage will lead it to wide application in the skeleton detection applications in the real world. © 2015 Elsevier B.V. All rights reserved.