Difference between Rigid3DTransform Euler3DTransform

1

Rigid3DTransform and Euler3DTransform
It is not clear, I appreciate if someone explains the difference.

Another question can someone check my computation bellow is correct:

import numpy as np
import sys, math 
print("******************************************************")
print ("   Points Transformation  ")
print("******************************************************")
np.set_printoptions(precision=2)
np.set_printoptions(suppress=True)
print("---------------------------------------------------")
print("   Define input ")
print("---------------------------------------------------")
# Input Points 
p=np.array([[-1.1499  , 4.96146 ,-3.73897  ],[ 1.12107 , 6.15124 ,-4.09615  ],   [ 2.56265 , 7.01562 ,-4.0416   ],   [ 4.1089  , 7.87024 ,-3.37502  ],   [ 5.23609 , 8.08297 ,-1.92341  ],   [ 5.37945 , 7.84559 , 0.0562932],   [ 4.72791 , 6.72648 , 1.12291  ],   [ 3.17306 , 5.88972 , 1.40773  ],   [ 2.09212 , 5.46035 , 0.298082],   [ 1.39364 , 5.93    ,-0.860716],   [ 1.80359 , 6.98823 ,-1.9811  ],   [ 2.79237 , 8.16489 ,-1.89504 ],   [ 3.54371 , 8.4603  ,-0.688138],   [ 3.18755 , 8.01944 , 0.458005],   [ 1.99834 , 7.59242 , 0.468096],   [ 1.50188 , 7.8538  ,-0.489043],   [ 2.28302 , 8.5749  ,-0.594259]])

print(p)
# 3DEuler parameters
ep=np.array([ -0.369236, -0.074973, 0.177428, -0.895437, -7.486193, -9.989277])
print("---------------------------------------------------")
print("   Parameters to Rotation Matrix ")
print("---------------------------------------------------")
[rx,ry,rz]=ep[0:3];
[tx,ty,tz]=ep[3:6];
Ms = []
cosx = math.cos(rx)
sinx = math.sin(rx)
Ms.append(np.array([[1, 0   ,  0   ],
                                  [0, cosx, -sinx],
                                  [0, sinx,  cosx]]))
cosy = math.cos(ry)
siny = math.sin(ry)
Ms.append(np.array( [[cosy , 0, siny],
                                    [0    , 1, 0   ],
                                   [-siny, 0, cosy]]))
                                    cosz = math.cos(rz)
sinz = math.sin(rz)
Ms.append(np.array([[cosz, -sinz, 0],
                                   [sinz,  cosz, 0],
                                   [0   ,   0  , 1] ]))
if Ms:
        mt = reduce(np.dot, Ms[::-1])
        # convert to 4x4
        m=   np.zeros((4,4)) ; m[3,3]=1 ;        m[0:3,0:3]=mt
        # add translations 
        m[0:3,3]=[tx,ty,tz]
else:    
        m=  np.eye(3)
print("---------------------------------------------------")
print("   displacement field ")
print("---------------------------------------------------")
# get the displacement vector = len(p) 
d=np.zeros((len(p),4))
#print(p_dis)
for i in range(0,len(p)):
    dt=np.ones(4); dt[0:3] = dt[0:3] * p[i]
    #print(dt)    
    np.matmul(m,dt,d[i])
    print(d[i])
print("---------------------------------------------------")
print("    new transformed points ")
print("---------------------------------------------------")
# get the new points locations 
pn=np.zeros((len(p),3))
for i in range(0,len(p)):
    pn[i]= p[i] + d[i][0:3]
    print(pn[i])
2

Those two classes differ in how they internally represent the rotation and translation. This is important when those transforms are optimized, e.g. during image registration.

1 Like
3

Thanks for your quick response. Do they provide the same result? Do they have the same performance?

The first 9 parameters represents the rotation matrix

Could you please explain how this matrix looks like assuming 3 angles for 3 rotations in each dimension e.g. thetaX , thetaY and theta Z?

4

That class uses the classic 4x4 transformation matrix.

5

Thanks a lot, I will have a look.