Volume 18, Issue 11

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 sine; 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/spl times/1 up to 8/spl times/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/spl times/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 sine interpolators, all kernels with N=6 or larger sizes perform significantly better than N=2 or N=3 point methods (p/spl Lt/0.005). However, the differences within the group of large-sized kernels were not significant. Summarizing the results, the cubic 6/spl times/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/spl times/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.

图像插值技术在医学成像中常用于图像生成（例如，用于逆拉东变换的离散反投影）以及处理如压缩或重采样。由于理想插值函数在空间上是无限的，因此引入了多种有限大小的插值核。本文比较了：1）截断和加窗sinc；2）最近邻；3）线性；4）二次；5）三次B样条；6）三次；7）拉格朗日；以及8）高斯插值和近似技术，核大小从1×1到8×8。比较通过以下方式进行：1）空间和傅里叶分析；2）计算复杂度及运行时间评估；以及3）针对医学图像处理中常见情况的特定插值任务的定性和定量插值误差确定。对于局部和傅里叶分析，引入了标准化符号并推导了插值器的基本属性。成功的方法应为直流（DC）恒定且为插值器，而非DC不恒定或近似器。每种方法的参数根据这些属性进行调整。这产生了三个新颖的核，在本文中介绍并证明是医学图像插值的最佳选择之一：6×6 Blackman-Harris窗sinc插值器，以及具有N=6和N=8支撑点的C2连续三次核。对于定量误差评估，使用了50张直接数字X光片。这些X光片是从临床常规中任意选取的。总的来说，大核尺寸优于小插值掩模。除截断sinc插值器外，所有N=6或更大尺寸的核性能显著优于N=2或N=3点方法（p<<0.005）。然而，大尺寸核组内的差异并不显著。总结结果，如（24）中定义的具有连续二阶导数的三次6×6插值器可推荐用于大多数常见插值任务。它似乎是计算上最快的六点核。它提供了卓越的局部和傅里叶特性，易于实现，且误差很小。相同的特性也适用于B样条插值，但6×6三次插值避免了B样条技术产生的固有边界效应。然而，本研究的目标并非确定总体最佳方法，而是以统一的术语提供方法的全面目录，定义局部技术的一般属性和要求，并使读者能够选择最适合其特定医学成像应用的方法。

With the increased interest in computer-aided image analysis methods, there is a greater need for objective methods of algorithm evaluation. Validation of in vivo MRI studies is complicated by a lack of reference data and the difficulty of constructing anatomically realistic physical phantoms. The authors present here an extensible MRI simulator that efficiently generates realistic three-dimensional (3-D) brain images using a hybrid Bloch equation and tissue template simulation that accounts for image contrast, partial volume, and noise. This allows image analysis methods to be evaluated with controlled degradations of image data.

随着对计算机辅助图像分析方法的兴趣增加，对算法评估的客观方法的需求也更大。体内MRI研究的验证因缺乏参考数据和构建解剖学逼真的物理体模的困难而变得复杂。作者在此介绍一种可扩展的MRI模拟器，能够高效生成逼真的三维...

A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scattering problem, which is solved by applying the finite-element method (FEM). Given a set of scattered field measurements, the objective is to minimize a cost function which cons...

提出了一种从散射场测量中重建二维可穿透散射体本构参数的方法。该方法基于前向散射问题的微分形式，通过应用有限元法（FEM）求解。给定一组散射场测量值，目标是使代价函数最小化，该函数...

The authors study the application of Fourier rebinning methods to dual-planar cone-beam SPECT. Dual-planar cone-beam SPECT involves the use of a pair of dissimilar cone-beam collimators on a dual-camera SPECT system. Each collimator has its focus in a different axial plane. While dual-planar data is best reconstructed with fully three-dimensional (3-D) iterative methods, these methods are slow and...

作者研究了傅里叶重排方法在双平面锥束SPECT中的应用。双平面锥束SPECT涉及在双相机SPECT系统上使用一对不同的锥束准直器。每个准直器在不同轴向平面聚焦。虽然双平面数据最好使用全三维迭代方法重建，但这些方法速度慢且计算量大。

While the equivalence of different filter materials commonly considered useful in diagnostic radiology can be obtained in terms of the overall transmitted primary photons, the scattering characteristics are not the same. In this work, comparative models that relate the scattered photons produced from one filter material with those from another have been developed. The comparison of the results of ...

虽然在诊断放射学中通常认为有用的不同滤片材料在整体透射初级光子方面可以获得等效性，但散射特性并不相同。在这项工作中，开发了比较模型，将一个滤片材料产生的散射光子与另一个滤片材料产生的散射光子联系起来。比较结果...