Editing Edge detection (section)

== A simple edge model ==
Although certain literature has considered the detection of ideal step edges, the edges obtained from natural images are usually not at all ideal step edges. Instead they are normally affected by one or several of the following effects:
* focal blur caused by a finite [[depth-of-field]] and finite [[point spread function]].
* [[penumbra|penumbral blur]] caused by shadows created by light sources of non-zero radius.
* [[shading]] at a smooth object
A number of researchers have used a Gaussian smoothed step edge (an [[error function]]) as the simplest extension of the ideal step edge model for modeling the effects of edge blur in practical applications.<ref name=lin98/><ref>W. Zhang and F. Bergholm (1997) "[https://link.springer.com/article/10.1023/A:1007923307644 Multi-scale blur estimation and edge type classification for scene analysis]", International Journal of Computer Vision, vol 24, issue 3, Pages: 219–250.</ref>
Thus, a one-dimensional image <math>f</math> that has exactly one edge placed at <math>x = 0</math> may be modeled as:

:<math>f(x) = \frac{I_r - I_\ell}{2} \left( \operatorname{erf}\left(\frac{x}{\sqrt{2}\sigma}\right) + 1\right) + I_\ell.</math>

At the left side of the edge, the intensity is <math>I_\ell = \lim_{x \rightarrow -\infty} f(x)</math>, and right of the edge it is
<math>I_r = \lim_{x \rightarrow \infty} f(x)</math>. The scale parameter <math>\sigma</math> is called the blur scale of the edge. Ideally this scale parameter should be adjusted based on the quality of image to avoid destroying true edges of the image.{{citation needed|date=September 2015}}