## September 9, 2018

# NCH: finding a metric for point removal

Introduction The objective of my thesis is to find ways to remove points from the input point cloud to NCH, while managing to guarantee that the error incurred is not too big. Clearly, the last sentence is far from specific: I haven’t defined a metric, nor said what “too big” means.
Before we begin, let’s recap on what the definition of the NCH function looks like:
$$ f(x) = \max_{1 \leq i \leq N} f_i(x) $$
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