Edge Detection by Supertask x Seeded Viison

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.
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.[4][5] Thus, a one-dimensional image
𝑓
{\displaystyle f} that has exactly one edge placed at
𝑥
=
0
{\displaystyle x=0} may be modeled as:

𝑓
(
𝑥
)
=
𝐼
𝑟
−
𝐼
ℓ
2
(
erf
⁡
(
𝑥
2
𝜎
)
+
1
)
+
𝐼
ℓ
.
{\displaystyle f(x)={\frac {I_{r}-I_{\ell }}{2}}\left(\operatorname {erf} \left({\frac {x}{{\sqrt {2}}\sigma }}\right)+1\right)+I_{\ell }.}

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