Definition of Kernels for the N-Dimensional Hermite Coordinate Interpolation: Application to Image Zooming
Konstantinos K. Delibasis, Aristides I. Kechriniotis, Iro Oikonomou, G. Tsigaridas · 2025
Image interpolation is a fundamental image processing task. In this work we utilize the multidimensional coordinate Hermite spline interpolation defined on non-equal spaced, rectilinear grids. Since Hermite interpolation utilizes function values, as well as partial derivative values, it is well suited for image processing tasks as a special case of equi-spaced grid, using numerical approximations of the image partial derivatives at each pixel. The novelty of this work is the construction of Hermite kernels according to the n-dimensional interpolant of Theorem 2, derived in [1], of any spatial dimension and any degree of partial derivatives. We show that despite the increased complexity of the interpolant, once the kernels are constructed, the Hermite spline interpolation can be applied to images as efficiently as any other convolution-based method. Finally, we perform illustrative numerical examples to showcase the applicability and high accuracy of the proposed Hermite kernels for image zooming, compared to other interpolation methods, both traditional convolution-based, as well as employing deep learning, in terms of PSNR and SSIM error metrics. The proposed Hermite spline kernels outperform all other methods in the majority of the test images, in experiments using many cascaded repetitions of the zoom operation. Source code available in: https://github.com/kdelimpasis/Image-2x-zooming-kernels.git