Survey: interpolation methods in medical image processing

Abstract

Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sinc; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1 x 1 up to 8 x 8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced and fundamental properties of interpolators are derived. Successful methods should be direct current (DC)-constant and interpolators rather than DC-inconstant or approximators. Each method's parameters are tuned with respect to those properties. This results in three novel kernels, which are introduced in this paper and proven to be within the best choices for medical image interpolation: the 6 x 6 Blackman-Harris windowed sinc interpolator, and the C2-continuous cubic kernels with N = 6 and N = 8 supporting points. For quantitative error evaluations, a set of 50 direct digital X rays was used. They have been selected arbitrarily from clinical routine. In general, large kernel sizes were found to be superior to small interpolation masks. Except for truncated sinc interpolators, all kernels with N = 6 or larger sizes perform significantly better than N = 2 or N = 3 point methods (p << 0.005). However, the differences within the group of large-sized kernels were not significant. Summarizing the results, the cubic 6 x 6 interpolator with continuous second derivatives, as defined in (24), can be recommended for most common interpolation tasks. It appears to be the fastest six-point kernel to implement computationally. It provides eminent local and Fourier properties, is easy to implement, and has only small errors. The same characteristics apply to B-spline interpolation, but the 6 x 6 cubic avoids the intrinsic border effects produced by the B-spline technique. However, the goal of this study was not to determine an overall best method, but to present a comprehensive catalogue of methods in a uniform terminology, to define general properties and requirements of local techniques, and to enable the reader to select that method which is optimal for his specific application in medical imaging.

Tensor Field Interpolation with PDEs

“…Classical methods to achieve this goal are linear interpolation, cubic or quintic splines, radial basis functions and sinc-based interpolation techniques; see e.g. [10,13]. If the data are not available on a regular grid, scattered data interpolation techniques have been proposed [7,15].…”

Simulation of Ground-Truth Validation Data Via Physically- and Statistically-Based Warps

“…We interpolate the spatial displacements of the gray-level and segmentation image domains, and of landmark coordinates using bi-cubic interpolation. There are several possible interpolation methods for interpolating the pixel intensities from the original spatially un-warped intensity image [19]. To generate the results in this paper, we used bi-linear intensity interpolation in 2D and thin plate splines in 3D.…”

Comparative Calibration of Corrosion Measurements Using K-Nearest Neighbour Based Techniques

“…Different techniques can be applied as interpolators; Polynomial interpolation, Multivariate interpolation, Bilinear interpolation, Bi-cubic spline interpolation, K-Nearest-neighbor interpolation (KNN), Inverse distance weighting (IDW) Interpolation, quadratic interpolation, B-spline interpolation, Lagrange interpolation, Gaussian interpolation, among other techniques [5][6][7]. Interpolation techniques are well expressed in the application of image processing, data mining, artificial neural networks, as well as other variant applications.…”