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Merge pull request #96 from augusto-de-freitas-isi/patch-1
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Update shape_metrics.md
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fwilliams authored Sep 8, 2024
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Expand Up @@ -5,7 +5,7 @@ Point Cloud Utils has functions to compute a number of commonly used metrics bet
## Chamfer Distance
The Chamfer distance between two point clouds $P_1 = \{x_i \in \mathbb{R}^3\}_{i=1}^n$ and $P_2 = \{x_j \in \mathbb{R}^3\}_{j=1}^m$ is defined as the average distance between pairs of nearest neighbors between $P_1$ and $P_2$ *i.e.*
$$
\text{chamfer}(P_1, P_2) = \frac{1}{2n} \sum_{x \in P_1} \|x - \text{NN}(x, P_2)\| + \frac{1}{2m} \sum_{x \in P_2} \|x - \text{NN}(x, P_1)\|
\text{chamfer}(P_1, P_2) = \frac{1}{2n} \sum_{x \in P_1}^{n} \|x - \text{NN}(x, P_2)\| + \frac{1}{2m} \sum_{x \in P_2}^{m} \|x - \text{NN}(x, P_1)\|
$$
and $\text{NN}(x, P) = \text{argmin}_{x' \in P} \|x - x'\|$ is the nearest neighbor function.

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