# Removing fish-eye effect

The DNG specification (page 87) describes a simple algorithm for converting a "fish-eye" photo into a regular photo (just several lines of basic geometry).

The transformation is configured using six numbers: $$k_0, k_1, k_2, k_3, c_x,c_y$$. Does it allow to represent identity (i.e. not changing the photo at all)? In order to get identity, the $$f$$ should be always one, so the bracket $$(k_0\theta + k_1\theta^3+ k_2\theta^5+ k_3\theta^7)$$ should be alwqys $$r$$.

In other words:

$$w(r) = k_0\theta + k_1\theta^3+ k_2\theta^5+ k_3\theta^7$$, where $$\theta=arctan(r)$$

What should be $$k$$s, so that $$w$$ is the identity for $$r\in[0,1]$$?