Construction and optimization of the fourth-order polynomial convolution 1P kernel

The paper describes the construction of two the fourth-order polynomial interpolation convolution kernels. The first kernel is without parameterization, while the second kernel is with parameterization. The parameterized kernel was optimized with the aim of approximating the ideal interpolation kernel sinc. The optimizations were performed according to two interpolation criteria. The first criterion implies the equation of the slope of the amplitude characteristic of the kernel in the node x = 1. The second criterion refers to the continuity of the third-order derivative of the amplitude characteristic in the node x = 1. The precision of the interpolation was tested by an experiment, in which some test images were interpolated. The results of the experiment showed that the precision of interpolation when applying the kernel, which is optimized by equalizing the slope, is higher in relation to the precision of the kernel with the optimization of the continuity of the third-order derivative of the amplitude characteristic. In addition, it was shown that the optimized kernel has a higher interpolation precision compared to the kernel without optimization.