An objective comparison of 3-D image interpolation methods

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Abstract
To aid in the display, manipulation, and analysis of biomedical image data, they usually need to he converted to data of isotropic discretization through the process of interpolation. Traditional 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 (typically 4-10x) amount of data. To mitigate this problem, a method called shape-based interpolation of binary data was developed 121. Besides significantly reducing user time, this method has been shown to provide more accurate results than grey-level interpolation. We proposed an approach for the interpolation of grey data of arbitrary dimensionality that generalized the shape-based method from binary to grey data. This method has characteristics similar to those of the binary shape-based method. In particular, we showed preliminary evidence that it produced more accurate results than conventional grey-level interpolation methods. In this paper, concentrating on the three-dimensional (3-D) interpolation problem, we compare statistically the accuracy of eight different methods: nearest-neighbor, linear grey-level, 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 magnetic resonance and computed tomography images, corresponding to different parts of the human anatomy, coming from different three-dimensional imaging applications, 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 using 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 significantly outperformed all other methods in all measures in all applications considered here with a statistical relevance ranging from 10% to 32% (mean = 15%) for mean-squared difference.

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