Gaussian Filtering - Computer Vision Website Header (2024)

FAQs

What is the Gaussian filter in computer vision? ›

The Gaussian Smoothing Operator performs a weighted average of surrounding pixels based on the Gaussian distribution. It is used to remove Gaussian noise and is a realistic model of defocused lens.

1-dimensional Gaussian Filter

The univariate Gauss-function is defined as follows: gσ,μ(x)=1√2πσexp(−(x−μ)22σ2), where σ is the standard deviation and μ is the mean. In the context of filtering, the mean is always μ=0, the standard deviation σ is a parameter, which determines the width of the filter.

A Gaussian filter typically yields the smoothest image, whereas a similarly sized mean or median filter typically leaves blocky traces.

TLDR: A Gaussian blur is applied by convolving the image with a Gaussian function. In English, this means that we'll take the Gaussian function and we'll generate an n x m matrix. Using this matrix and the height of the Gaussian distribution at that pixel location, we'll compute new RGB values for the blurred image.

Smoothing and Noise Reduction: The Gaussian filter effectively smooths an image by reducing high-frequency noise. It convolves the image with a Gaussian function, which has a bell-shaped curve that provides a weighted average of neighboring pixels.

The Lowpass Gaussian Filter eliminates high frequency (sharp) features oriented along either the X or Y axis of the scan. The practical effect upon the image is a loss of detail or "blurring" effect.

In general, Gaussian filtering is a process of weighted averaging of the entire image. The value of each pixel is obtained by weighted averaging of other pixel values in itself and in the neighborhood.

One cut-off at each end of the profile is removed, to minimise the distortion at the ends of the profile. The minimum number of cut-offs in the measured profile (evaluation length) is three, to minimise the distortion of the profile due to the finite length of the profile.

A continuous random variable Z is said to be a standard normal (standard Gaussian) random variable, shown as Z∼N(0,1), if its PDF is given by fZ(z)=1√2πexp{−z22},for all z∈R. The 1√2π is there to make sure that the area under the PDF is equal to one.

It replaces every element of the input signal with a weighted average of its neighborhood. This causes blurring in time/space, which is the same as attenuating high-frequency components in the frequency domain. The Gaussian filter is a low-pass filter, that is broadly used in image and signal processing.

Which is better Gaussian filter or Wiener filter? ›

The Wiener filter shows poor performance using the smallest kernel size (3x3) while the Gaussian filter shows the best results in such case. With the Gaussian filter being used, similar results of those obtained with low noise could be obtained in the case of high noise variance but with a higher kernel size.

Introduction to Gaussian filter, or Gaussian blur

Another name for this filter is Gaussian blur. To get acquainted with filter window idea in signal and image processing read our “Filter window, or filter mask” article.

The effect of Gaussian smoothing is to blur an image, in a similar fashion to the mean filter. The degree of smoothing is determined by the standard deviation of the Gaussian. (Larger standard deviation Gaussians, of course, require larger convolution kernels in order to be accurately represented.)

Because a photograph is two-dimensional, Gaussian blur uses two mathematical functions (one for the x-axis and one for the y) to create a third function, also known as a convolution. This third function creates a normal distribution of those pixel values, smoothing out some of the randomness.

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 filter is one of the linear filters that serves to smooth and eliminate noise in an image. Mean Filter is very simple and easy to implement and is very useful for reducing the variation in value of a pixel with the next pixel.

As you can see, Gaussian is perfectly radial and isotropic, while a binomial filter has more “rectangular” response, filtering less of the diagonals.

Gaussian filter is used for blurring the images and removing the noise and detail. Gaussian filters have the properties of having no overshoot to the step function input while limiting the rise and fall time. This conduct is firmly associated with the way that the Gaussian filters has the base possible gathering delay.

Difference of gaussians is a grayscale image enhancement algorithm that involves the subtraction of one blurred version of an original grayscale image from another, less blurred version of the original.