BlurringFunktion

BlurringFunktion is a concept in digital image processing that describes the transformation of a sharp image into a blurred version by reducing high-frequency content. It is typically modeled as a convolution of the original image with a blur kernel, also known as a point spread function (PSF). In continuous form, B(x,y) = I(x,y) * h(x,y); in discrete form, B[i,j] = sum_m sum_n I[i−m, j−n] h[m,n], with the kernel normalized so its sum equals one.

Common blur types include Gaussian blur, which uses a Gaussian PSF and yields isotropic smoothing; motion blur, caused by camera or subject motion, resulting in a directional smear; and defocus blur, which mimics out-of-focus lens effects. Non-uniform or space-variant blur can occur when PSF varies across the image.

Implementation often relies on convolution, with optimizations such as separable kernels for Gaussians or FFT-based methods for large kernels. Blurring is used deliberately in photography for aesthetic effect, in privacy-preserving applications to obscure faces or license plates, and as a preprocessing step to reduce noise or simulate imaging conditions.

The inverse problem—deblurring or deconvolution—seeks to recover the original image from the blurred observation. This is typically ill-posed and requires regularization or prior information; common methods include Wiener filtering and iterative algorithms such as Richardson–Lucy deconvolution.

Limitations include artifacts like ringing near edges, sensitivity to the PSF estimate, and boundary effects. See also: point spread function, convolution, deconvolution, Gaussian blur, Wiener filter, Richardson–Lucy.