larger sobel operators are more stable in noise. why?

heya! i recently came across this statement larger sobel operators are more stable 开发者_运维技巧in noise. which got me thinking- why?

its probably because the gradient differences are less pronounced, so that noise is ignored. am i correct? thanks!

Of course, this depends on a lot of things, one being the frequency of the noise you are facing. If the noise changes with much higher frequency (e.g. with every pixel) than the patterns you are trying to find, then you are correct.

In general, however, sobel operators are a sort of finite-differencing, and as such work best the smaller the differences are.

If you use a larger sobel operator, what you are actually doing is using a sobel operator + a low pass filter. The low pass filter might not be the best way to deal with the noise in your image - sometimes it might be more favorable to use the smallest sobel filter and some other (machine-learning) algorithm for noise rejection.