立体像对空间前方交会-点投影系数法（python实现）

一、原理

 

二、步骤

a.用各自像片的角元素计算出左右像片的旋转矩阵R1和R2。

b.根据左右像片的外方位元素计算摄影基线分量Bx,By,Bz。

c.逐点计算像点的空间辅助坐标。

d.计算投影系数。

e.计算未知点的地面摄影测量坐标。

f.重复以上步骤完成所有点的地面坐标的计算。

三、示例代码

# -*- coding: utf-8 -*-
"""
Created on Mon Nov 25 08:18:30 2019

@author: L JL
"""

import numpy as np
import math as m

def r_mat(f,w,k):
   Rf = np.mat([[m.cos(f), 0, -m.sin(f)],
              [0,         1,          0],
              [m.sin(f), 0,  m.cos(f)]])

   Rw = np.mat([[1,         0,          0],
              [0, m.cos(w), -m.sin(w)],
              [0, m.sin(w),  m.cos(w)]])
    
   Rk = np.mat([[m.cos(k), -m.sin(k), 0],
              [m.sin(k),  m.cos(k), 0],
              [0,         0,          1]])
    
   R = Rf*Rw*Rk 
    
   return R

def SpatialAuxiliaryCoordinate(xy,f,R):
    coor1 = np.mat([[xy[0]],
                      [xy[1]],
                       [-f]])
    coor2 = R*coor1
    return coor2
def ProjectionCoefficient(SAC1,SAC2,B):
    N1 = (B[0,0]*SAC2[2,0]-B[2,0]*SAC2[0,0])/(SAC1[0,0]*SAC2[2,0]-SAC2[0,0]*SAC1[2,0])
    N2 = (B[0,0]*SAC1[2,0]-B[2,0]*SAC1[0,0])/(SAC1[0,0]*SAC2[2,0]-SAC2[0,0]*SAC1[2,0])
    return N1,N2




#main
left_HomonymousImagePoints = [0.153,91.798]    
right_HomonymousImagePoints = [-78.672,89.122]
    
left_In = np.mat([0,0,152.91])
left_Ex = np.mat([[970302.448784],
           [-1138644.971216],
           [3154.584941],
           [0.010425],
           [-0.012437],
           [0.003380]])     
right_In = np.mat([0,0,152.91])
right_Ex = np.mat([[971265.303768],
            [-1138634.245942],
            [3154.784258],
            [0.008870],
            [-0.005062],
            [-0.008703]])

R_L = np.mat(np.zeros((3,3)))
R_R = np.mat(np.zeros((3,3)))    
left_SACoordinate = np.mat(np.zeros((3,1)))
right_SACoordinate = np.mat(np.zeros((3,1)))
baselineComponent = np.mat(np.zeros((3,1)))

R_L = r_mat(left_Ex[3,0],left_Ex[4,0],left_Ex[5,0])
R_R = r_mat(right_Ex[3,0],right_Ex[4,0],right_Ex[5,0])

#left_SpatialAuxiliaryCoordinate = R_L*left_In.T
#right_SpatialAuxiliaryCoordinate = R_R*right_In.T
left_SACoordinate = SpatialAuxiliaryCoordinate(left_HomonymousImagePoints,left_In[0,2],R_L)
right_SACoordinate = SpatialAuxiliaryCoordinate(right_HomonymousImagePoints,right_In[0,2],R_R)

baselineComponent = right_Ex[0:3,0] - left_Ex[0:3,0]
N1,N2 = ProjectionCoefficient(left_SACoordinate,right_SACoordinate,baselineComponent)
#GPhotogrammetrCoordinates
GPCoordinates = np.mat(np.zeros((3,1)))
GPCoordinates = ((left_Ex[0:3,0]+N1*left_SACoordinate) + (right_Ex[0:3,0]+N2*right_SACoordinate))/2

print("左影像同名点：",left_HomonymousImagePoints)
print("左影像同名点：",right_HomonymousImagePoints)
print("地面点坐标：
         X=%f,
         Y=%f,
         Z=%f"
      %(GPCoordinates[0,0],GPCoordinates[1,0],GPCoordinates[2,0]))