A number of basic image processing tasks, such as any geometric
transformation require interpolation at subpixel image values. In this work we
utilize the multidimensional coordinate Hermite spline interpolation defined on
non-equal spaced, rectilinear grids and apply it to a very common image
processing task, image zooming. Since Hermite interpolation utilizes function
values, as well as partial derivative values, it is natural to apply it to
image processing tasks as a special case of equi-spaced grid, using numerical
approximations of the image partial derivatives at each pixel. Furthermore, the
task of image interpolation requires the calculation of image values at
positions with nono-zero fractional part. Thus, any spline interpolation can be
written as convolution with an appropriate kernel. In this context we generate
the Hermite kernels according to the derived $n-$dimensional interpolant of
Theorem 2 in [1]. 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 less complicated 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, as
well as 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. Interesting conclusions can be
drawn considering all methods under comparison.

基于 Hermite 样条插值的图像缩放方法在 PSNR 和 SSIM 误差度量方面优于传统卷积和深度学习方法，适用于多数测试图像和级联重复的缩放操作。