This paper compares various interpolation techniques used in medical image processing, including truncated and windowed sine, nearest neighbor, linear, quadratic, cubic B-spline, cubic, Lagrange, and Gaussian methods. The comparison is conducted through spatial and Fourier analyses, computational complexity evaluations, and qualitative and quantitative error determinations. The study introduces a standardized notation for local and Fourier analyses and derives fundamental properties of interpolators, emphasizing the importance of direct current (DC) constancy. Three novel kernels are proposed: the $6 \times 6$ Blackman–Harris windowed sine interpolator and C2-continuous cubic kernels with $N = 6$ and $N = 8$ supporting points. The results show that large kernel sizes generally outperform smaller ones, with the $6 \times 6$ cubic kernel being the most effective for most common tasks due to its computational efficiency, local and Fourier properties, and minimal errors. The paper aims to provide a comprehensive catalog of methods, define general properties, and enable readers to select the most suitable method for specific medical imaging applications.This paper compares various interpolation techniques used in medical image processing, including truncated and windowed sine, nearest neighbor, linear, quadratic, cubic B-spline, cubic, Lagrange, and Gaussian methods. The comparison is conducted through spatial and Fourier analyses, computational complexity evaluations, and qualitative and quantitative error determinations. The study introduces a standardized notation for local and Fourier analyses and derives fundamental properties of interpolators, emphasizing the importance of direct current (DC) constancy. Three novel kernels are proposed: the $6 \times 6$ Blackman–Harris windowed sine interpolator and C2-continuous cubic kernels with $N = 6$ and $N = 8$ supporting points. The results show that large kernel sizes generally outperform smaller ones, with the $6 \times 6$ cubic kernel being the most effective for most common tasks due to its computational efficiency, local and Fourier properties, and minimal errors. The paper aims to provide a comprehensive catalog of methods, define general properties, and enable readers to select the most suitable method for specific medical imaging applications.