加速 3D 点云中的 RANSAC 平面检测

Question

现在我正在使用 RANSAC 对 3D 点云数据进行平面分割。我的代码的基本流程图是：

Select 3个随机点然后创建一个候选平面
检查到平面一定距离阈值内的所有其他点。如果阈值以下有很多点，那么我会保存飞机。
如果覆盖点低于阈值，则select另一个RANSAC点（回到第1个）

让我沮丧的是，如何加快这个过程？想象一下，如果我有 1 个 mio 点，那么我必须检查所有点到我的候选平面，如果不符合阈值，那么我 select 另一个随机点并一遍又一遍地检查 1 个 mio 点。对于我的代码的任何建议甚至更正，我将非常感激

这是我的代码，数据集可以下载here。对于这个示例，我使用了一小部分真实数据。

import numpy as np
import pandas as pd
import math
from scipy.spatial import cKDTree
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import random

data = pd.read_csv('data_sample.txt', usecols=[0,1,2], header=None, delimiter=' ')
df_points = pd.DataFrame(data)

%matplotlib qt


#Change parameter
distance_threshold = 0.06
minimum_point_threshold = 400
sampling_resolution = 0.06

#search nearest neighbor
kdtree = cKDTree(df_points)

temp_pair_point = []
list_pair_point = []
list_candidates = []

#Select random points
for h in df_points.index:
    pair_point = kdtree.query_ball_point(np.array(df_points.iloc[h]),r=sampling_resolution, return_sorted=False)
    temp_pair_point.append(pair_point)


for k in range(0,len(temp_pair_point)):
    pairsize = len(temp_pair_point[k])
    if pairsize > 10:
        list_pair_point.append(temp_pair_point[k])

for m in range(0,len(list_pair_point)):
    candidates = random.choices(list_pair_point[m], k=3)
    list_candidates.append(candidates)




#select random point from nearest neighbor
list_sample_point = []

for i in range(0,len(list_candidates)):
    list_test_distance = []


    p1 = np.array(data.iloc[list_candidates[i][0]])
    p2 = np.array(data.iloc[list_candidates[i][1]])
    p3 = np.array(data.iloc[list_candidates[i][2]])
    sample = [p1,p2,p3]

    #create plane
    x1,y1,z1 =np.ravel(p1)
    x2,y2,z2 =np.ravel(p2)
    x3,y3,z3 =np.ravel(p3)

    m_u = [x2-x1,y2-y1,z2-z1]
    m_v = [x3-x2,y3-y2,z3-z2]

    m_normal = np.cross(m_u,m_v)
    m_pos = p1
    m_dist = np.dot(-m_normal, m_pos)

    for j in data.index:
        test_point = np.array(data.iloc[j])
        test_distance = np.dot(-m_normal,test_point)
        #print('Distance ={}'.format(test_distance))
        if abs(test_distance) < distance_threshold:
            list_test_distance.append(test_distance)

    if len(list_test_distance) > minimum_point_threshold:
        list_sample_point.append(sample)



#Check candidate plane
list_u = []
list_v = []
list_normal = []
list_distance = []
list_min_max = []

for i in range(0,len(list_sample_point)):
    psample = list_sample_point[i]
    psample1 = np.array(psample[0])
    psample2 = np.array(psample[1])
    psample3 = np.array(psample[2])
    min_max = [float(min(np.transpose(psample)[0])), float(max(np.transpose(psample)[0])),float(min(np.transpose(psample)[1])), float(max(np.transpose(psample)[1])),float(min(np.transpose(psample)[2])), float(max(np.transpose(psample)[2]))]
    list_min_max.append(min_max)

    u = [psample2[0]-psample1[0], psample2[1]-psample1[1], psample2[2]-psample1[2]]
    v = [psample3[0]-psample2[0], psample3[1]-psample2[1], psample3[2]-psample2[2]]
    normal = np.cross(u,v)
    d = np.dot(-normal,psample1)

    list_u.append(u)
    list_v.append(v)
    list_normal.append(normal)
    list_distance.append(d)




#Plot candidate plane  
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
#ax.scatter3D(xs=plot_x, ys=plot_y, zs=plot_z, s=30, c='red')
ax.set_xlim3d(-25,-20)
ax.set_ylim3d(5,10)
ax.set_xlim3d(5,10)
ax.scatter3D(xs=df_points[0], ys=df_points[1], zs=df_points[2], s=1, c='green')

for j in range(0,len(list_normal)):
    if list_normal[j][2] != 0:
        print('Normal plane to Z axis')
        xx, yy = np.meshgrid(np.arange(list_min_max[j][0],list_min_max[j][1]+(list_min_max[j][1]-list_min_max[j][0]),(list_min_max[j][1]-list_min_max[j][0])), np.arange(list_min_max[j][2],list_min_max[j][3]+(list_min_max[j][3]-list_min_max[j][2]),(list_min_max[j][3]-list_min_max[j][2])), sparse=True)
        z = (-list_normal[j][0] * xx - list_normal[j][1] * yy -list_distance[j]) / list_normal[j][2]    
        ax.plot_surface(xx, yy, z, color=np.random.rand(3,), alpha=0.5)

    elif list_normal[j][0] != 0:
        print('Normal plane to X axis')
        yy, zz, = np.meshgrid(np.arange(list_min_max[j][2],list_min_max[j][3]+(list_min_max[j][3]-list_min_max[j][2]),(list_min_max[j][3]-list_min_max[j][2])), np.arange(list_min_max[j][4],list_min_max[j][5]+(list_min_max[j][5]-list_min_max[j][4]),(list_min_max[j][5]-list_min_max[j][4])), sparse=True)
        x = (-list_normal[j][1] * yy - list_normal[j][2] * zz -list_distance[j]) / list_normal[j][0]
        ax.plot_surface(x, yy, zz,  color=np.random.rand(3,), alpha=0.5)

    elif list_normal[j][1] !=0:
        print('Normal plane to Y axis')
        xx, zz, = np.meshgrid(np.arange(list_min_max[j][0],list_min_max[j][1]+(list_min_max[j][1]-list_min_max[j][0]),(list_min_max[j][1]-list_min_max[j][0])), np.arange(list_min_max[j][4],list_min_max[j][5]+(list_min_max[j][5]-list_min_max[j][4]),(list_min_max[j][5]-list_min_max[j][4])), sparse=True)
        y = (-list_normal[j][0] * xx - list_normal[j][2] * zz -list_distance[j]) / list_normal[j][1]
        ax.plot_surface(xx, y, zz, color=np.random.rand(3,), alpha=0.5)

Answer 1

首先，RANSAC 并不是每个点都运行。使用您的代码，它可以从您拥有的 1945 个点中计算出 1729 个平面。通常你会在开始之前计算你想要运行 RANSAC 的迭代次数。这取决于预期平面的离群值和离群值的数量：

k = log(1-p)/log(1-(1-e)^s)

p 是您期望的概率，即 RANSAC 导致异常值自由平面，例如 99.99% 的概率。 e 是异常值的百分比，例如对于 80% 的离群值 e = 0.8。这导致 1147 次迭代。但是通常你应该能够假设一个较低的异常值概率，假设 20% 由于选择邻居（就像你所做的那样）现在突然只有 13 次迭代来检测一个概率为 99.99% 的平面，所以只有 13（！ ) 而不是 1729(!)。如果您想找到 100 个平面，它仍然会减少大约 25% 的迭代次数。

其次，如果您仍想运行每一点，您可以加强代码的某些部分：首先，您使用两个 for 循环来处理可以写在一个循环中的内容，并且即使 len(list_test_distance) > minimum_point_threshold 可能已经为真，您仍在继续计算 test_distance。通过将代码更改为：

#select random point from nearest neighbor
list_sample_point = []
list_u = []
list_v = []
list_normal = []
list_distance = []
list_min_max = []


for i in range(0,len(list_candidates)):
    list_test_distance = []


    p1 = np.array(data.iloc[list_candidates[i][0]])
    p2 = np.array(data.iloc[list_candidates[i][1]])
    p3 = np.array(data.iloc[list_candidates[i][2]])
    sample = [p1,p2,p3]

    #create plane
    x1,y1,z1 =np.ravel(p1)
    x2,y2,z2 =np.ravel(p2)
    x3,y3,z3 =np.ravel(p3)

    m_u = [x2-x1,y2-y1,z2-z1]
    m_v = [x3-x2,y3-y2,z3-z2]

    m_normal = np.cross(m_u,m_v)
    m_pos = p1
    m_dist = np.dot(-m_normal, m_pos)

    for j in data.index:
        test_point = np.array(data.iloc[j])
        test_distance = np.dot(-m_normal,test_point)
        #print('Distance ={}'.format(test_distance))
        if abs(test_distance) < distance_threshold:
            list_test_distance.append(test_distance)

        if len(list_test_distance) > minimum_point_threshold:
            #list_sample_point.append(sample) I think you don't need this one any more as well
            psample = sample
            psample1 = np.array(psample[0])
            psample2 = np.array(psample[1])
            psample3 = np.array(psample[2])
            min_max = [float(min(np.transpose(psample)[0])), float(max(np.transpose(psample)[0])),float(min(np.transpose(psample)[1])), float(max(np.transpose(psample)[1])),float(min(np.transpose(psample)[2])), float(max(np.transpose(psample)[2]))]
            list_min_max.append(min_max)

            u = [psample2[0]-psample1[0], psample2[1]-psample1[1], psample2[2]-psample1[2]]
            v = [psample3[0]-psample2[0], psample3[1]-psample2[1], psample3[2]-psample2[2]]
            normal = np.cross(u,v)
            d = np.dot(-normal,psample1)

            list_u.append(u)
            list_v.append(v)
            list_normal.append(normal)
            list_distance.append(d)
            break

我将笔记本电脑上的运行时间从 7 分 11 秒缩短为 2 分 35 秒，使其速度提高了 2.5 倍多。结果应该还是一样的（如果我错了请纠正我）

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