Convolutionkernels

Convolution kernels are small arrays of numbers used to filter signals or images by convolution. In discrete signal processing, a kernel operates on an input by sliding a window across the data and computing a weighted sum of nearby samples. The result is a transformed output that emphasizes or suppresses certain features.

In two-dimensional image processing, a kernel is typically a small matrix, such as 3x3 or 5x5, applied to each pixel by centering the kernel on the pixel and summing the products of the kernel weights and the corresponding neighborhood pixels. The process may require padding at the borders and a stride that determines how far the kernel moves between positions. The term convolution is sometimes implemented as cross-correlation in practice, which means the kernel is not flipped.

Kernels serve common tasks: smoothing or blurring (box blur, Gaussian), sharpening, and various edge detectors (Sobel, Scharr, Laplacian). Other effects such as embossing or bump mapping can be achieved by specific kernels. The choice of weights determines the frequency response and the visual effect.

In deep learning, convolutional neural networks use learnable kernels or filters. Here, a kernel is a small tensor whose values are learned during training and applied across input channels to produce output feature maps. Multiple kernels produce multiple channels of output; stacking kernels increases expressive power. Padding, stride, and dilation influence spatial size and receptive field.

Related concepts include separable kernels, which can be broken into two one-dimensional kernels to reduce computation, and frequency-domain convolution via the Fourier transform, which can speed up large-kernel filtering. Convolution kernels thus provide a compact, flexible framework for modifying or extracting structure from signals and images.