Traditional interpolation techniques consist of direct interpolation of the grey values. When user interaction is called for in image segmentation, as a consequence of these interpolation methods, the user needs to segment a much greater amount of data. To mitigate this problem, a method called shape-based interpolation of dimension that generalized the shape-based method from binary to grey data. We showed preliminary evidence that it produced more accurate results than conventional grey-level interpolation methods. In this paper, concentration on the 3D interpolation problem, we compare statistically the accuracy of eight different methods: nearest-neighbor, linear grey- level cubic spline, grey-level modified cubic spline, Goshtasby et al., and three methods from the grey-level shape-based class. A population of patient MR and CT 3D images are utilized for comparison. Each slice in these data sets is estimated by each interpolation method and compared to the original slice at the same location suing three measures: mean-squared difference, number of sites of disagreement, and largest difference. The methods are statistically compared pairwise based on these measures. The shape-based methods statistically outperformed other methods in all measures in all applications considered here.