Short answers, pulled from the story.
A kernel in image processing is a small matrix used to transform an image through a process called convolution. By positioning the kernel over each pixel and computing a weighted sum of the pixel and its neighbors, a kernel can blur, sharpen, detect edges, emboss, or perform other visual effects.
Convolution positions the kernel over each pixel in the image, multiplies each kernel value by the corresponding pixel value beneath it, and sums the products into a single output value for that pixel. If the kernel is not symmetric, it must be flipped around both its horizontal and vertical axes before the multiplication step.
A symmetric kernel has its origin at the center element and can be applied directly to a pixel without additional preparation. An asymmetric kernel must be flipped around both its horizontal and vertical axes before convolution is calculated.
There are six main approaches: extend (stretching border pixels outward), wrap (tiling the image), mirror (reflecting it at the boundary), crop or avoid overlap (skipping output pixels that need out-of-bounds values), kernel crop (trimming the kernel and adjusting normalization), and constant (filling out-of-bounds positions with a fixed value like black).
Normalization divides each element in the kernel by the sum of all kernel elements so that the elements total exactly one. This ensures the average brightness of the output image matches the average brightness of the original.
Separable convolution decomposes a two-dimensional kernel into two one-dimensional kernels applied in sequence. This reduces the number of multiplications per pixel from M times N (for an M-by-N kernel) down to M plus N, significantly lowering the computational cost on large images.