（slam工具）4 3D点集配准相似变换sRt计算

 

 

 

 

https://github.com/Dongvdong/v1_1_slam_tool

 

链接：https://pan.baidu.com/s/1ntXJch2t3GcLJhFBXFrBdw?pwd=kles
提取码：kles

 

 注意事项

R的行列式算出来如果是-1 需要给R的第三列取符号，不然会导致两个平面（RTK采集数据厘米级别精度平面飞行， 非三维空间上下而是退化到二维平面计算srt）计算的t是反着的

 

 

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import random import math   import numpy as np import os               def API_pose_estimation_3dTo3d_ransac(points_src, points_dst): #NED -> slam     p = np.array(points_src, dtype=float)     q = np.array(points_dst, dtype=float)     print("匹配点数: ", len(points_src), " ", len(points_dst))     # 1.计算s并去质心     mean_p = np.mean(p, axis=0)     mean_q = np.mean(q, axis=0)       p_norm = p - mean_p     q_norm = q - mean_q       # 计算距离比     iter_num = 0     _s = 0     inliner_num = 0     ransac_time=2000 # ransac随机抽取验证次数     while iter_num < ransac_time:         # 随机挑选两个元素         _list = []         # print("len(points_src): ",len(points_src))         # if len(points_src) < 2:         #     break         inx_1, inx_2 = random.sample(range(len(points_src)), 2)         #print("inx_1: ",inx_1,"inx_2: ",inx_2)         # print("inx_2: ",inx_2)         p_r = np.array([points_src[inx_1], points_src[inx_2]], dtype=float)         q_r = np.array([points_dst[inx_1], points_dst[inx_2]], dtype=float)         _list.append(inx_1)         _list.append(inx_2)         # 计算s           p_norm_r = p_r - mean_p         q_norm_r = q_r - mean_q           # 所有点的xyz平方求和         d1_list = []         d2_list = []         for i in range(len(q_norm_r)):             d1 = q_norm_r[i]             d2 = p_norm_r[i]             dist1 = math.sqrt(np.sum(d1**2))             dist2 = math.sqrt(np.sum(d2**2))             d1_list.append(dist1)             d2_list.append(dist2)         s_r = np.sum(d1_list) / np.sum(d2_list)           # 计算其他点s的误差值         inliner_p = [points_src[inx_1], points_src[inx_2]]         inliner_q = [points_dst[inx_1], points_dst[inx_2]]           for inx in range(len(points_src)):             # 计算点不参与验证             if inx == inx_1 or inx == inx_2:                 continue             p_src = np.array(points_src[inx])             q_dst = np.array(points_dst[inx])             # 分别计算到质心距离             p_src_norm = p_src - mean_p             q_dst_norm = q_dst - mean_q             p_src_norm_dist = math.sqrt(np.sum(p_src_norm**2))             q_dst_norm_dist = math.sqrt(np.sum(q_dst_norm**2))             # 计算误差             cal_dist = p_src_norm_dist * s_r             error = cal_dist - q_dst_norm_dist             if abs(error) < 3:                 inliner_p.append(points_src[inx])                 inliner_q.append(points_dst[inx])                 _list.append(inx)           # 利用所有内点计算新的s         p_r = np.array(inliner_p)         q_r = np.array(inliner_q)         p_norm_f = p_r - mean_p         q_norm_f = q_r - mean_q           d1_list = []         d2_list = []         for i in range(len(q_norm_f)):             d1 = q_norm_f[i]             d2 = p_norm_f[i]             dist1 = math.sqrt(np.sum(d1**2))             dist2 = math.sqrt(np.sum(d2**2))             d1_list.append(dist1)             d2_list.append(dist2)           s_final = np.sum(d1_list) / np.sum(d2_list)         # 记录内点数最高的模型         if inliner_num < len(inliner_p):             _s = s_final             inliner_num = len(inliner_p)             inx_list = _list         iter_num += 1       s = _s       # 2.用s缩放src到dst尺度下     p = s * p     mean_p = np.mean(p, axis=0)     p_norm = p - mean_p       # 2.计算q1*q2^T(注意顺序：q2->q1，x是dst,y是src)     N = len(p)       W = np.zeros((3, 3))     for i in range(N):         x = q_norm[i, :]     # 每一行数据         x = x.reshape(3, 1)  # 3行1列格式 一维数组借助reshape转置         y = p_norm[i, :]         y = y.reshape(1, 3)         W += np.matmul(x, y)       # 3.SVD分解W     # python 线性代数库中svd求出的V与C++ Eigen库中求的V是转置关系     U, sigma, VT = np.linalg.svd(W, full_matrices=True)     # 旋转矩阵R     R = np.matmul(U, VT)    # 这里无需再对V转置     # 在寻找旋转矩阵时，有一种特殊情况需要注意。有时SVD会返回一个“反射”矩阵，这在数值上是正确的，但在现实生活中实际上是无意义的。     # 通过检查R的行列式（来自上面的SVD）并查看它是否为负（-1）来解决。如果是，则V的第三列乘以-1。     # 验证R行列式是否为负数   参考链接:https://blog.csdn.net/sinat_29886521/article/details/77506426     # R为-1 会导致两个平面计算方向相反 导致T方向相反 所以要吧R取符号     # 方案1 R=SD的逆=UV的逆 V第三列取负号     # 方案2 按照SLam14讲解R的第三行给负1     if np.linalg.det(R) < 0:         R_temp=np.matmul(U, VT) # R=SD=UV的转置         R_temp_det = np.linalg.det(R_temp) #其实就是-1         # VT 第三列给负号         VT_3col_to_fu1 = np.array([[1, 0, 0], [0, 1, 0], [0, 0, R_temp_det]])         VT_new= np.matmul(VT, VT_3col_to_fu1)         # 重新计算 R  等同于R的第三列直接取负号         R = np.matmul(U, VT_new)     # 平移向量     T = mean_q - np.matmul(R, mean_p)   # dst - src     T = T.reshape(3, 1)     sR = s*R     RT_34 = np.c_[sR, T]       # 4.计算误差值     p = np.array(points_src)     error_sum = 0     inx_list2 = []     error_ENU = []     for i in range(N):         src = p[i, :]         dst = q[i, :]         src = src.reshape(3, 1)         dst = dst.reshape(3, 1)         test_dst = np.matmul(sR, src) + T           error_Mat = test_dst - dst         error_Mat2 = error_Mat**2         error = math.sqrt(np.sum(error_Mat2))         error_ENU.append(error)         if error < 3:             inx_list2.append(i)         error_sum += error       print("mean error:", error_sum/N)     print("max error:", max(error_ENU))     print("RT_34:\n", RT_34)     print("缩放系数s:\n", s)     print("旋转矩阵R:\n", R)     print("通尺度下的T:\n", T)     return RT_34, sR, T     # 根据 srt 将单个目标点云变换到指定坐标系下 def API_src3D_sRt_dis3D_one(points_src,SR,T):                  points_src_ = [[points_src[0]], [points_src[1]], [points_src[2]]]     points_dis_ = np.matmul(SR,points_src_) + T     #points_dis_ = SR @ points_src_ + T     points_dis_t=[points_dis_[0][0],points_dis_[1][0],points_dis_[2][0]]       return points_dis_t   # 将1组3d点 根据 srt变换到另一个坐标系下 def API_src3D_sRt_dis3D_list(points_src,points_dst,SR,T):         points_dis_t_list=[]     error_sum=0 # 误差计算       for p_i in range(0,len(points_src)):         # 根据srt计算便函后的x y z平移点         points_dis_t=API_src3D_sRt_dis3D_one(points_src[p_i],SR,T)           print("原始点",points_src[p_i],"变换后的点",points_dis_t,"真值",points_dst[p_i])         points_dis_t_list.append(points_dis_t)                   # =========整体转换后的计算误差===============         points_dis_t = np.array(points_dis_t)         points_dst[p_i] = np.array(points_dst[p_i])         error_Mat = points_dis_t - points_dst[p_i]         error_Mat2 = error_Mat**2         error = np.sum(error_Mat2)         error_sum += error             error_sum=math.sqrt(error_sum)/len(points_src)     print("平均误差:",error_sum)     return points_dis_t_list         ''' if __name__ == "__main__":                 # points_src=[[1,1,1],[2,2,2],[3,3,3]]     # points_dst=[[11,11,11],[21,21,21],[31,31,31]]     # RT_34, SR, T = API_pose_estimation_3dTo3d_ransac(points_src, points_dst) #     # points_dis_t_list=API_src3D_sRt_dis3D_list(points_src,points_dst,SR, T)     # print("变换后的列表",points_dis_t_list)   '''   '''     # # 4 数据转化 为3D-3D计算相似变换准备  colmap enu 变换到 gnss enu坐标系上     # #ENU_List  :名字 e n u 转化为:  e n u     # 4-1 读取gnss enu     # 取出前400个数据计算     ENU_GNSS_List_4= API_read2txt("data/test/2ENU_from_GNSS.txt")     ENU_GNSS_List_4_400=[]     for i in range(160 , len(ENU_GNSS_List_4)):         ENU_GNSS_List_4_400.append(ENU_GNSS_List_4[i])     ENU_GNSS_List_3_400=API_data0123_to_data123(ENU_GNSS_List_4_400) # 去掉第一列名字           # 4-2 读取colmap enu     ENU_colmap_list_4= API_read2txt("data/test/colmap_images_t.txt")     ENU_colmap_list_3=API_data0123_to_data123(ENU_colmap_list_4) # 去掉第一列名字       # 4-4 计算变换关系 points_src 到 points_dst     points_src=ENU_colmap_list_3     points_dst=ENU_GNSS_List_3_400 #ENU_GNSS_List_3_400     RT_34, SR, T = API_pose_estimation_3dTo3d_ransac(points_src, points_dst) #          colmapenu_in_gnssenu_3=API_src3D_sRt_dis3D_list(points_src,points_dst,SR, T)           # 4-5 保存计算结果 colmap enu变换到gnss enu坐标系下的新坐标     colmapenu_in_gnssenu_4=[]     for i in range(0,len(ENU_GNSS_List_4_400)):         name=ENU_GNSS_List_4[i][0]         #保存数据 名字 e n u         li=[name,colmapenu_in_gnssenu_3[i][0],colmapenu_in_gnssenu_3[i][1],colmapenu_in_gnssenu_3[i][2]]         colmapenu_in_gnssenu_4.append(li)     # 保存数据     colmapeEnu_from_GnssEnu_txt_name="data/test/3colmapeEnu_from_GnssEnu.txt"     API_Save2txt(colmapeEnu_from_GnssEnu_txt_name,colmapenu_in_gnssenu_4) '''