Gaussian Blur - Implementation

Implementation

A Gaussian blur effect is typically generated by convolving an image with a 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, another 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.

Discretisation 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.