In other words, for each pixel calculation, we will need the entire image. Here comes the problem.īecause the Gaussian function has infinite support (meaning it is non-zero everywhere), the approximation would require an infinitely large convolution kernel. But for that, we need to produce a discrete approximation to the Gaussian function. Now, just convolve the 2-d Gaussian function with the image to get the output. This is the motivation for using Gaussian distribution.Ī 2-d Gaussian function is obtained by multiplying two 1-d Gaussian functions (one for each direction) as shown belowĢ-d Gaussian function with mean=0 and std. So, we should look for a distribution/function that assigns more weights to the nearest pixels as compared to the distant pixels. Similarly while smoothing an image, it makes more sense to take the weighted average instead of just averaging the values under the mask (like we did in Averaging). Thus if we were to interpolate a pixel value, more chances are that it resembles that of the neighborhood pixels and less on the distant pixels. We already know that a digital image is obtained by sampling and quantizing the continuous signal. So, let’s get started with a basic background introduction. We will also discuss various properties of the Gaussian filter that makes the algorithm more efficient.

This is perhaps the most frequently used low pass filter in computer vision applications. In this article, we will discuss another smoothing technique known as Gaussian Blurring, that uses a low pass filter whose weights are derived from a Gaussian function. In the previous blog, we discussed smoothing filters.

Gaussian kernel