diff --git a/docs/docs/sections/shape_metrics.md b/docs/docs/sections/shape_metrics.md index 54a4860..e3b4966 100644 --- a/docs/docs/sections/shape_metrics.md +++ b/docs/docs/sections/shape_metrics.md @@ -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.