Gaussian Filter Kernel Function Generation

The Gaussian filter kernel function is a generation function that creates corresponding Gaussian kernels based on a given K value. This function implements a fundamental image processing technique where Gaussian filtering effectively removes noise, smoothes images, and enhances overall image quality. The kernel generation process utilizes a mathematical algorithm based on the Gaussian distribution formula: G(x,y) = (1/(2πσ²)) * exp(-(x²+y²)/(2σ²)), where σ (sigma) is derived from the K parameter. The implementation typically involves creating a 2D grid of values calculated using this formula, then normalizing the kernel to ensure the sum of all elements equals 1. By adjusting the K value, which directly influences the standard deviation (σ) of the Gaussian distribution, developers can control the kernel's spread and achieve varying degrees of smoothing效果. This parameter adjustment allows customization for different image processing requirements, with larger K values producing broader smoothing effects while smaller values preserve more image details. The function can be efficiently implemented using numerical computing libraries like NumPy with vectorized operations for optimal performance.