Grevera G J, Udupa J K
Department of Radiology, University of Pennsylvania, Philadelphia 19104-6021, USA.
IEEE Trans Med Imaging. 1998 Aug;17(4):642-52. doi: 10.1109/42.730408.
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.
为了便于生物医学图像数据的显示、操作和分析，通常需要通过插值过程将其转换为各向同性离散化的数据。传统技术包括对灰度值进行直接插值。当在图像分割中需要用户交互时，由于这些插值方法，用户需要分割的数据量要大得多（通常为4到10倍）。为了缓解这个问题，开发了一种称为基于形状的二进制数据插值的方法[121]。除了显著减少用户时间外，该方法还被证明比灰度插值能提供更准确的结果。我们提出了一种用于任意维度灰度数据插值的方法，该方法将基于形状的方法从二进制数据推广到灰度数据。该方法具有与基于二进制形状的方法类似的特性。特别是，我们展示了初步证据，表明它比传统的灰度插值方法产生的结果更准确。在本文中，我们专注于三维（3-D）插值问题，对八种不同方法的准确性进行了统计比较：最近邻法、线性灰度法、灰度三次样条法、灰度修正三次样条法、戈什塔斯比等人的方法，以及基于灰度形状类别的三种方法。利用来自不同三维成像应用的、对应于人体解剖不同部位的患者磁共振和计算机断层扫描图像群体进行比较。这些数据集中的每个切片都通过每种插值方法进行估计，并使用三种度量与相同位置的原始切片进行比较：均方误差、不一致位点数量和最大差异。基于这些度量对方法进行成对的统计比较。在这里考虑的所有应用中，基于形状的方法在所有度量上在统计上都显著优于所有其他方法，均方误差的统计相关性范围为10%至32%（平均值 = 15%）。
