Page Author: [Shubodh Sai](mailto:[email protected]?Subject=The%20Notion%20Note-taking%20Project%20|%20ICP)

Using this Notion page

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Resources

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Introduction

Given two corresponding point sets:

$$ \begin{array}{l} X=\left\{x_{1}, \ldots, x_{N_{x}}\right\} \\ P=\left\{p_{1}, \ldots, p_{N_{p}}\right\} \end{array} $$

$$ E(R, t)=\frac{1}{N_{p}} \sum_{i=1}^{N_{p}}\left\|x_{i}-R p_{i}-t\right\|^{2}  $$

If the correct correspondences are known, the correct relative rotation/translation can be calculated in closed form.

ICP: Known Correspondences

Center of Mass

$$ \mu_{x}=\frac{1}{N_{x}} \sum_{i=1}^{N_{x}} x_{i} \text { and } \mu_{p}=\frac{1}{N_{p}} \sum_{i=1}^{N_{p}} p_{i} $$