Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method. 1. Introduction 1.1. Interpolation One of the most important parts of designing a registration algorithm is choosing a good interpolation function in order to increase the accuracy of registration. Also, Interpolation is required if the fractional unit of the motion is not matched and located on high resolution (HR) grid. One of the ways by which we can help physicians in coming up with a better diagnosis and treatment is improving the resolution of images. One scheme for the interpolation step is shown in Figure 1. Here, a circle shows the reference HR image, and a diamond and a triangle represent a shifted HR pixel. For instance, if the image is downsampled by a factor of 4, a diamond has (0.25, 0.25) subpixel shift for the vertical and horizontal directions and a triangle has a shift that is less than (0.25, 0.25). In Figure 1, a triangle is not placed on the HR grid and it needs interpolation, but a diamond does not need interpolation. Figure 1: Scheme for interpolation. Straight line shows the original HR grid, circle shows the reference HR pixels, and a diamond and a triangle are shifted version of HR pixels. Therefore, some interpolation approaches are proposed to overcome the
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