What are filters

Today we will investigate the use of blurring filters on images. This is just one of many applications of filters in image processing, and in the next session we will use the same basic techniques for feature detection.

Blurring filters do exactly what it says on the tin. They blur the image. This has the effect of smoothing out noise, so it is a useful technique for noise removal.

One of the groups using machine vision in the final year project last year had problems with the camera failing to return a value in some pixel. The result was black pixels, so-called pepper noise. A blurring filter solves this problem very effectively.

If you have read signal processing or image processing previously, all of this may be familiar to you already.

Conceptual Application

• Recalculate pixels using a neighbourhood
• Use a matrix of coefficients for a weighted average

Convolution

\[(f*g)[x] = \sum_{k=-\infty}^{\infty} f[k]g[x-k]\]

• Note the convolution of a sampled signal and a continuous one
• Demo

Note OpenCV uses correlation instead of convolution. Conceptually this is different, but in practice, the only effect is to mirror the filter.

\[(f\star g)[x] = \sum_{k=-\infty}^{\infty} f[k]g(k+x)\]