高效计算 3d 点云中基于网格的点密度

Question

我有一个 3d 点云矩阵，我正在尝试计算矩阵内较小体积内的最大点密度。 我目前正在使用 3D 网格直方图系统，我循环遍历矩阵中的每个点并增加相应网格正方形的值。 然后，我可以简单地找到网格矩阵的最大值。

我已经编写了有效的代码，但是对于我正在尝试做的事情来说速度非常慢

import numpy as np

def densityPointCloud(points, gridCount, gridSize):
    hist = np.zeros((gridCount, gridCount, gridCount), np.uint16)

    rndPoints = np.rint(points/gridSize) + int(gridCount/2)
    rndPoints = rndPoints.astype(int)


    for point in rndPoints:
        if np.amax(point) < gridCount and np.amin(point) >= 0:
            hist[point[0]][point[1]][point[2]] += 1

    return hist


cloud = (np.random.rand(100000, 3)*10)-5
histogram = densityPointCloud(cloud , 50, 0.2)
print(np.amax(histogram))

有什么捷径可以让我更有效地做到这一点吗？

Answer 1

这是一个开始：

import numpy as np
import time
from collections import Counter

# if you need the whole histogram object
def dpc2(points, gridCount, gridSize):

    hist = np.zeros((gridCount, gridCount, gridCount), np.uint16)
    rndPoints = np.rint(points/gridSize) + int(gridCount/2)
    rndPoints = rndPoints.astype(int)
    inbounds = np.logical_and(np.amax(rndPoints,axis = 1) < gridCount, np.amin(rndPoints,axis = 1) >= 0)

    for point in rndPoints[inbounds,:]:
        hist[point[0]][point[1]][point[2]] += 1

    return hist

# just care about a max point
def dpc3(points, gridCount, gridSize):

    rndPoints = np.rint(points/gridSize) + int(gridCount/2)
    rndPoints = rndPoints.astype(int)
    inbounds = np.logical_and(np.amax(rndPoints,axis = 1) < gridCount,
        np.amin(rndPoints,axis = 1) >= 0)
    # cheap hashing
    phashes = gridCount*gridCount*rndPoints[inbounds,0] + gridCount*rndPoints[inbounds,1] + rndPoints[inbounds,2]
    max_h, max_v = Counter(phashes).most_common(1)[0]

    max_coord = [(max_h // (gridCount*gridCount)) % gridCount,(max_h // gridCount) % gridCount,max_h % gridCount]
    return (max_coord, max_v)

# TESTING
cloud = (np.random.rand(200000, 3)*10)-5
t1 = time.perf_counter()
hist1 = densityPointCloud(cloud , 50, 0.2)
t2 = time.perf_counter()
hist2 = dpc2(cloud,50,0.2)
t3 = time.perf_counter()
hist3 = dpc3(cloud,50,0.2)
t4 = time.perf_counter()
print(f"task 1: {round(1000*(t2-t1))}ms\ntask 2: {round(1000*(t3-t2))}ms\ntask 3: {round(1000*(t4-t3))}ms")
print(f"max value is {hist3[1]}, achieved at {hist3[0]}")
np.all(np.equal(hist1,hist2)) # check that results are identical
# check for equal max - histogram may be multi-modal so the point won't
# necessarily match
np.unravel_index(np.argmax(hist2, axis=None), hist2.shape)

这个想法是做一次所有的 if/and 比较：让 numpy 做它们（在 C 中有效），而不是在 Python 循环中“手动”做它们。 这也让我们只迭代将导致hist递增的点。

如果您认为您的云将有大量空白空间，您也可以考虑为hist使用稀疏数据结构 - memory 分配可能成为非常大数据的瓶颈。

没有科学地对此进行基准测试，但似乎运行速度快了 2-3 倍（v2）和 6-8 倍（v3）！ 如果您想要所有与最大值相关的点。 密度，很容易从Counter object 中提取那些。