An objective comparison of 3-D image interpolation methods

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.

Quantitative evaluation of convolution-based methods for medical image interpolation

“…However, given an image processing task, the most useful evaluation is obtained by applying the kernels to perform that task and to compare the results to what is considered the gold standard. In a recently published paper by Grevera & Udupa [11], an elaborate comparison of a number of well-known scene-based and object-based interpolation methods was presented. In the evaluation, 3D medical images from different modalities were first subsampled in the slice-direction with a factor of two.…”

“…As can be concluded from recent literature, the latter is still the most frequently used kernel in a wide variety of application areas [11].…”

“…However, that study did not include images from other modalities. Grevera & Udupa [11] described the results of an elaborate quantitative evaluation of a number of both convolution-and shape-based interpolation methods for the purpose of slice doubling in MR and CT images. However, the effects of these techniques on the geometrical transformation of images from these and other medical image modalities were not investigated.…”

Structural flow smoothing for shape interpolation

“…Hessians have been used as kernels for diffusion based smoothing in various applications [3,9]. In this study we employ the Hessian of the local data as the covariance matrix in the Heat kernel from (4). In this case we achieve anisotropic diffusion for smoothing structural flows associated with internal object variation while preserving the boundaries and its internal structure.…”

“…Volumetric image reconstruction by interpolation has received increased attention, particularly due to its application in medical visualization and analysis [2,4,6]. This is inherently a difficult problem due to the sparseness of the information available and the missing data.…”