  Existing position based point cloud filtering methods can hardly preserve
sharp geometric features. In this paper, we rethink point cloud filtering from
a non-learning non-local non-normal perspective, and propose a novel position
based approach for feature-preserving point cloud filtering. Unlike normal
based techniques, our method does not require the normal information. The core
idea is to first design a similarity metric to search the non-local similar
patches of a queried local patch. We then map the non-local similar patches
into a canonical space and aggregate the non-local information. The aggregated
outcome (i.e. coordinate) will be inversely mapped into the original space. Our
method is simple yet effective. Extensive experiments validate our method, and
show that it generally outperforms position based methods (deep learning and
non-learning), and generates better or comparable outcomes to normal based
techniques (deep learning and non-learning).
