Gaussian blur and convolution kernels

Question

I do not understand what a convolution kernel is and how I would apply a convolution matrix to pixels in an image (I am talking about doing a Gaussian Blur operation on an image).

Also could I get an explanation on how to create a kernel for a Gaussian Blur operation?

I am reading this article (http://en.wikipedia.org/wiki/Gaussian_blur) but I cannot seem to understand how things are done...

Thanks to anyone who takes time to explain this to me :),

ExtremeCoder

Answer 1

The basic idea is that the new pixels of the image are created by an weighted average of the pixels close to it (imagine drawing a circle around the pixel).

For each pixel in the image you are going to create a little square around the pixel. Lets say you take the 8 neighbors next to a pixel (including diagonals even though do not matter here), and we perform a weighted average to get the middle pixel.

In the Gaussian blur case it breaks down to two one dimensional operations. For each pixel take the some amount of pixels next to a pixel in the row direction only. Multiply the pixel values time the weights computed from the Gaussian distribution (or if you are doing this for an visual effect and not for a scientific reason, the weights can anything that looks good) and sum them up. Another way to look at it is the pixel make a vector and the weights make a vector and your are taking the dot product. Repeat this process in the column direction as a separate pass.

Answer 2

A convolution kernel is a matrix of values that specify how the neighborhood of a pixel contribute to that pixel's state in the final image. There's a fair description of the basics here. A gaussian blur is a convolution function that uses a really ugly (you've seen the wikipedia page) function to compute a convolution kernel to pass over the image. You'll find an example kernel for a gaussian in that wikipedia page.

The point of all the math in there is to produce a soft blur that resembles the scatter pattern produced by a mesh screen placed between the viewer and the image. You can think of the 'size' (the standard deviation) of the gaussian as being related to the distance between the image and the screen.