## August 21, 2018

# NCH: closing the gap

Introduction Following up with my last post on NCH being roto-translation invariant, the idea of this one is to cover what I consider the most important gaps left by the original brief paper. My expectation is that doing this will help understand better why NCH works, and hopefully gain some insight into how to improve it.
Equivalence of formulations Equation (4) in the paper says:
$$f_i^{r_i} (x) = \frac{1}{2 r_i} (r_i^2 - || x - (p_i + r_i n_i) ||^2)$$

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