Гаусс бұлғылауы: сурет өңдеудегі Gaussian функциясының қолданылуы

Type of image blur produced by a Gaussian function

In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician and scientist Carl Friedrich Gauss). It is a widely used effect in graphics software, typically to reduce image noise and reduce detail. The visual effect of this blurring technique is a smooth blur resembling that of viewing the image through a translucent screen, distinctly different from the bokeh effect produced by an out of focus lens or the shadow of an object under usual illumination. Gaussian smoothing is also used as a pre processing stage in computer vision algorithms in order to enhance image structures at different scales—see scale space representation and scale space implementation.

Gaussian blur is a low pass filter, attenuating high frequency signals. Its amplitude Bode plot (the log scale in the frequency domain) is a parabola.

This sample matrix is produced by sampling the Gaussian filter kernel (with σ = 0.84089642) at the midpoints of each pixel and then normalizing. The center element (at [0, 0]) has the largest value, decreasing symmetrically as distance from the center increases. Since the filter kernel's origin is at the center, the matrix starts at and ends at where R equals the kernel radius. The element 0.22508352 (the central one) is 1177 times larger than 0.00019117 which is just outside 3σ.

A Gaussian blur effect is typically generated by convolving an image with an FIR kernel of Gaussian values. In practice, it is best to take advantage of the Gaussian blur’s separable property by dividing the process into two passes. In the first pass, a one dimensional kernel is used to blur the image in only the horizontal or vertical direction. In the second pass, the same one dimensional kernel is used to blur in the remaining direction. The resulting effect is the same as convolving with a two dimensional kernel in a single pass, but requires fewer calculations. Discretization is typically achieved by sampling the Gaussian filter kernel at discrete points, normally at positions corresponding to the midpoints of each pixel. This reduces the computational cost but, for very small filter kernels, point sampling the Gaussian function with very few samples leads to a large error. In these cases, accuracy is maintained (at a slight computational cost) by integration of the Gaussian function over each pixel's area. When converting the Gaussian’s continuous values into the discrete values needed for a kernel, the sum of the values will be different from 1. This will cause a darkening or brightening of the image. To remedy this, the values can be normalized by dividing each term in the kernel by the sum of all terms in the kernel. A much better and theoretically more well founded approach is to instead perform the smoothing with the discrete analogue of the Gaussian kernel, which possesses similar properties over a discrete domain as makes the continuous Gaussian kernel special over a continuous domain, for example, the kernel corresponding to the solution of a diffusion equation describing a spatial smoothing process, obeying a semi group property over additions of the variance of the kernel, or describing the effect of Brownian motion over a spatial domain, and with the sum of its values being exactly equal to 1. For a more detailed description about the discrete analogue of the Gaussian kernel, see the article on scale space implementation and.

For processing pre recorded temporal signals or video, the Gaussian kernel can also be used for smoothing over the temporal domain, since the data are pre recorded and available in all directions. When processing temporal signals or video in real time situations, the Gaussian kernel cannot, however, be used for temporal smoothing, since it would access data from the future, which obviously cannot be available. For temporal smoothing in real time situations, one can instead use the temporal kernel referred to as the time causal limit kernel, which possesses similar properties in a time causal situation (non creation of new structures towards increasing scale and temporal scale covariance) as the Gaussian kernel obeys in the non causal case. The time causal limit kernel corresponds to convolution with an infinite number of truncated exponential kernels coupled in cascade, with specifically chosen time constants. For discrete data, this kernel can often be numerically well approximated by a small set of first order recursive filters coupled in cascade, see

Lower end digital cameras, including many mobile phone cameras, commonly use gaussian blurring to obscure image noise caused by higher ISO light sensitivities. Gaussian blur is automatically applied as part of the image post processing of the photo by the camera software, leading to an irreversible loss of detail.