In order to obtain an interpolated image with a superior quality, a new C\+2 cubic many-knot spline interpolation kernel function with compact support (-2,2) is presented. The cubic many-knot spline interpolation formula is constructed via degrees of freedom from inserting knots. The approximation order of the interpolation with the appropriate boundary conditions and constraints is analyzed. The one-dimensional many-knot splines interpolation algorithm is extended to that of two dimensions, which is applied to image processing. In general, images interpolated by the bicubic many-knot spline interpolation are blurred in the edge regions as a result of ignoring the local features of the images. In order to solve the problem of blurring in the edge regions, an adaptive interpolation method is presented based on applying an inverse gradient to the above bicubic many-knot spline interpolation formula. The experiment results are presented to show that the adaptive interpolation algorithm produces a reconstructed image with a superior quality than the conventional bicubic convolution method and the adaptive bicubic convolution method in terms of error and PSNR.