Cubic convolution interpolation is a technique for resampling discrete data, particularly useful in digital image processing. The method is efficient and can be performed on digital computers. The cubic convolution interpolation function converges uniformly to the function being interpolated as the sampling increment approaches zero, with an accuracy between linear interpolation and cubic splines. The paper derives a one-dimensional cubic convolution interpolation function and extends it to two dimensions for image data. The cubic convolution interpolation kernel is composed of piecewise cubic polynomials defined on subintervals between -2 and +2, with specific conditions for symmetry, continuity, and boundary values. The kernel is zero outside these intervals, reducing the number of data samples used. The interpolation coefficients are derived from these conditions, resulting in a third-order approximation. The paper compares the cubic convolution method with other interpolation methods, such as nearest-neighbor, linear, and cubic spline interpolation. It shows that the cubic convolution method is more accurate and efficient, especially for large data sets. The cubic convolution method uses four sample points for each interpolation point, requiring nine additions and eight multiplications per interpolated point, compared to fewer operations for linear and cubic spline methods. The paper also discusses fourth-order algorithms, which achieve higher accuracy by increasing the length of the interval over which the interpolation kernel is not zero. However, fourth-order accuracy is the highest possible with piecewise cubic polynomials. In conclusion, the cubic convolution interpolation function is a robust and efficient method for image processing, offering better accuracy and computational efficiency compared to other interpolation techniques.Cubic convolution interpolation is a technique for resampling discrete data, particularly useful in digital image processing. The method is efficient and can be performed on digital computers. The cubic convolution interpolation function converges uniformly to the function being interpolated as the sampling increment approaches zero, with an accuracy between linear interpolation and cubic splines. The paper derives a one-dimensional cubic convolution interpolation function and extends it to two dimensions for image data. The cubic convolution interpolation kernel is composed of piecewise cubic polynomials defined on subintervals between -2 and +2, with specific conditions for symmetry, continuity, and boundary values. The kernel is zero outside these intervals, reducing the number of data samples used. The interpolation coefficients are derived from these conditions, resulting in a third-order approximation. The paper compares the cubic convolution method with other interpolation methods, such as nearest-neighbor, linear, and cubic spline interpolation. It shows that the cubic convolution method is more accurate and efficient, especially for large data sets. The cubic convolution method uses four sample points for each interpolation point, requiring nine additions and eight multiplications per interpolated point, compared to fewer operations for linear and cubic spline methods. The paper also discusses fourth-order algorithms, which achieve higher accuracy by increasing the length of the interval over which the interpolation kernel is not zero. However, fourth-order accuracy is the highest possible with piecewise cubic polynomials. In conclusion, the cubic convolution interpolation function is a robust and efficient method for image processing, offering better accuracy and computational efficiency compared to other interpolation techniques.