【Furthest Sampling Point FPS】Principle Introduction

The farthest point sampling (FPS) is a commonly used sampling algorithm. The sampling point algorithm used in PointNet++ is this. Let me explain the algorithm principle of FPS based on other people's introduction and my own understanding. 1. Let P={P0, P1,...,Pn} be the input point cloud collection
. Take the first point cloud P0 as the starting query point to obtain the sampling point set S = {P0}
2. Construct an N-dimensional array L, where L represents the distance from all points to P0 (L={d(P0,P0),d(P1,P0),…,d(Pn,P0)}), and select the maximum value P1 in L as the new query point, and update the sampling point set S={P0,P1} at this time. Since the number of extracted points is greater than 1, each point in the selected point set needs to be considered when selecting a sampling point. The specific idea is as follows: (1) Calculate the distance between all points and P1 (d(P0,P1),d(P1,P1),...,d(Pm,P1)), if d(Pi,P1) is less than L[i], then update L[i] = d(Pi,P1) (the distance from yourself to yourself is 0, and the value of the point with the largest distance before can be replaced by this step), so the value stored in the array L is always the point with the shortest distance from each point to the sampling point set (2) Select the maximum value P2 in L as the new sampling point (3) Update the sampling point set S = {P0, P1, P2} 3. Repeat step 2 until the number of selected sampling
points
reaches
M.

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