Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129, USA.
IEEE Trans Image Process. 2013 Feb;22(2):816-27. doi: 10.1109/TIP.2012.2224356. Epub 2012 Oct 11.
We show that image registration using conventional interpolation and summation approximations of continuous integrals can generally fail because of resampling artifacts. These artifacts negatively affect the accuracy of registration by producing local optima, altering the gradient, shifting the global optimum, and making rigid registration asymmetric. In this paper, after an extensive literature review, we demonstrate the causes of the artifacts by comparing inclusion and avoidance of resampling analytically. We show the sum-of-squared-differences cost function formulated as an integral to be more accurate compared with its traditional sum form in a simple case of image registration. We then discuss aliasing that occurs in rotation, which is due to the fact that an image represented in the Cartesian grid is sampled with different rates in different directions, and propose the use of oscillatory isotropic interpolation kernels, which allow better recovery of true global optima by overcoming this type of aliasing. Through our experiments on brain, fingerprint, and white noise images, we illustrate the superior performance of the integral registration cost function in both the Cartesian and spherical coordinates, and also validate the introduced radial interpolation kernel by demonstrating the improvement in registration.
我们表明，由于重采样伪影，使用传统插值和连续积分求和近似的图像配准通常会失败。这些伪影通过产生局部最优、改变梯度、移动全局最优和使刚体配准不对称，对配准的准确性产生负面影响。在本文中，经过广泛的文献回顾，我们通过分析比较包含和避免重采样来展示伪影的原因。我们展示了平方和差代价函数作为积分的形式比其在图像配准的简单情况下的传统求和形式更准确。然后，我们讨论了由于笛卡尔网格中表示的图像在不同方向上以不同的速率采样而导致的旋转中的混叠，并提出使用振荡各向同性插值核，通过克服这种类型的混叠，允许更好地恢复真正的全局最优。通过对脑、指纹和白噪声图像的实验，我们说明了积分配准代价函数在笛卡尔和球坐标中的优越性能，并且通过证明配准的改进，验证了所引入的径向插值核的有效性。
