This paper considers the problem of image segmentation using the random walker algorithm. In the case of 3D images, the method uses an extreme amount of memory and time resources. These are required in order to represent the corresponding enormous image graph and to solve the resulting sparse linear system. Having in mind these limitations, this paper proposes techniques for the optimization of the random walker approach. The optimization is obtained by processing supervoxels representing homogeneous image regions rather than single voxels. A fast and efficient method for supervoxel determination is introduced. A method for the creation of an image adjacency graph from an irregular grid of supervoxels is also proposed. The results of applying the introduced approach to segmentation of 3D CT data sets are presented and compared with the results of the original random walker approach and other state-of-the-art methods. The accuracy and the computational overhead is regarded in the comparison. The analysis of results shows that the modified method can be successfully applied for the segmentation of volumetric images and provides results in a reasonable time without a significant loss in the image segmentation accuracy. It also outperforms the state-of-the-art methods considered in the comparison.