如何匹配vtk polydata和itk轉換

Question

我需要使用相同的轉換矩陣轉換（旋轉現在）的itk圖像和vtk polydata，但我遇到了麻煩。

所有的代碼和測試數據是在這裏：https://github.com/jmerkow/vtk_itk_rotate

下面是relavent部分：

import SimpleITK as sitk 
import vtk 
import numpy as np 
def rotate_img(img, rotation_center=None, theta_x=0,theta_y=0, theta_z=0, translation=(0,0,0), interp=sitk.sitkLinear, pixel_type=None, default_value=None): 
    if not rotation_center: 
     rotation_center = np.array(img.GetOrigin())+np.array(img.GetSpacing())*np.array(img.GetSize())/2 
    if default_value is None: 
     default_value = img.GetPixel(0,0,0) 
    pixel_type = img.GetPixelIDValue() 

    rigid_euler = sitk.Euler3DTransform(rotation_center, theta_x, theta_y, theta_z, translation) 
    return sitk.Resample(img, img, rigid_euler, interp, default_value, pixel_type) 

def rotate_polydata(pd, rotation_center, theta_x=0,theta_y=0, theta_z=0, translation=(0,0,0)): 
    rigid_euler = sitk.Euler3DTransform(rotation_center, -theta_x, -theta_y, -theta_z, translation) 
    matrix = np.zeros([4,4]) 
    old_matrix=np.array(rigid_euler.GetMatrix()).reshape(3,3) 
    matrix[:3,:3] = old_matrix 
    matrix[-1,-1] = 1 

    # to rotate about a center we first need to translate 
    transform_t = vtk.vtkTransform() 
    transform_t.Translate(-rotation_center) 
    transformer_t = vtk.vtkTransformPolyDataFilter() 
    transformer_t.SetTransform(transform_t) 
    transformer_t.SetInputData(pd) 
    transformer_t.Update() 

    transform = vtk.vtkTransform() 
    transform.SetMatrix(matrix.ravel()) 

    transformer = vtk.vtkTransformPolyDataFilter() 
    transformer.SetTransform(transform) 
    transformer.SetInputConnection(transformer_t.GetOutputPort()) 
    transformer.Update() 

    # translate back 
    transform_t2 = vtk.vtkTransform() 
    transform_t2.Translate(rotation_center) 
    transformer_t2 = vtk.vtkTransformPolyDataFilter() 
    transformer_t2.SetTransform(transform_t2) 
    transformer_t2.SetInputConnection(transformer.GetOutputPort()) 
    transformer_t2.Update() 

    return transformer_t2.GetOutputDataObject(0) 

datafn = 'test.mha' 
polydata_file = 'test.vtp' 
reader = vtk.vtkXMLPolyDataReader() 
reader.SetFileName(polydata_file) 
reader.Update() 
pd = reader.GetOutput() 

img = sitk.ReadImage(datafn) 
seg = pd_to_itk_image(pd, img) 
rotation_center = np.array(img.GetOrigin())+np.array(img.GetSpacing())*np.array(img.GetSize())/2 
thetas = [0, 50] 
thetas = [0, 50] 
for theta_x in thetas: 
    for theta_y in thetas: 
     for theta_z in thetas: 
      theta_xr = theta_x/180.*np.pi 
      theta_yr = theta_y/180.*np.pi 
      theta_zr = theta_z/180.*np.pi 
      img_rot=rotate_img(img, theta_z=theta_zr, theta_y=theta_yr, theta_x=theta_xr) 
      seg_rot=rotate_img(seg, theta_z=theta_zr, theta_y=theta_yr, theta_x=theta_xr, interp=sitk.sitkNearestNeighbor, default_value=0) 
      pd_rot = rotate_polydata(pd, rotation_center, theta_z=theta_zr, theta_y=theta_yr, theta_x=theta_xr) 
      seg_pd_rot = pd_to_itk_image(pd_rot, img_rot) 
      mse = ((sitk.GetArrayFromImage(seg_pd_rot)-sitk.GetArrayFromImage(seg_rot))**2.).mean() 

      print theta_x, theta_y, theta_z, mse 

#this outputs for this particular volume: 
#0 0 0 mse: 0.0 
#0 0 50 mse: 50.133369863 visually about the same 
#0 50 0 mse: 25.2197787166 visually about the same 
#0 50 50 mse: 863.588476181 visually totally different 
#50 0 0 mse: 20.4021692276 visually about the same 
#50 0 50 mse: 546.699844301 visually totally different 
#50 50 0 mse: 662.337975204 visually totally different 
#50 50 50 mse: 339.220945537 visually totally different 

此代碼旋轉從POLYDATA產生的二進制體積，並在執行相同的旋轉操作polydata然後從那裏生成一個二進制卷。我期望這兩個結果是（大致）相同，但是，如果我圍繞多個軸旋轉，我所得到的是兩個完全不同的旋轉。 這是令我費解的，因爲我正在從一個變換矩陣並直接應用到另一個。

如何設置這些轉換，使兩個操作執行相同的轉換？爲什麼我們會得到不同的結果？

Answer 1

謝謝Dženan指引我在正確的方向。

在這種情況下，答案很簡單。 VTK和ITK爲其矩陣乘法使用不同的行/列主要格式。所以答案只是在將矩陣放入vtkTransform之前轉置矩陣。

這是新功能。

def rotate_polydata(pd, rotation_center, theta_x=0,theta_y=0, theta_z=0): 
    #I don't want to deal with translation 
    translation=(0,0,0) 
    rigid_euler = sitk.Euler3DTransform(rotation_center, theta_x, theta_y, theta_z, translation) 
    matrix = np.zeros([4,4]) 
    old_matrix=np.array(rigid_euler.GetMatrix()).reshape(3,3) 
    matrix[:3,:3] = old_matrix 
    matrix[-1,-1] = 1 
    #ITK and VTK use different orders. 
    matrix= matrix.T 

    # to rotate about a center we first need to translate 
    transform_t = vtk.vtkTransform() 
    transform_t.Translate(-rotation_center) 
    transformer_t = vtk.vtkTransformPolyDataFilter() 
    transformer_t.SetTransform(transform_t) 
    transformer_t.SetInputData(pd) 
    transformer_t.Update() 

    transform = vtk.vtkTransform() 
    transform.SetMatrix(matrix.ravel()) 
    transform.Translate(translation) 
    transform.PostMultiply() 

    transformer = vtk.vtkTransformPolyDataFilter() 
    transformer.SetTransform(transform) 
    transformer.SetInputConnection(transformer_t.GetOutputPort()) 
    transformer.Update() 

    # translate back 
    transform_t2 = vtk.vtkTransform() 
    transform_t2.Translate(rotation_center) 
    transformer_t2 = vtk.vtkTransformPolyDataFilter() 
    transformer_t2.SetTransform(transform_t2) 
    transformer_t2.SetInputConnection(transformer.GetOutputPort()) 
    transformer_t2.Update() 

    return transformer_t2.GetOutputDataObject(0) 

Answer 2

歐拉角的順序與最終結果 [Wikipedia]有關。另外，矩陣預乘也具有相反的順序，以便乘後 [vtkTransform]。嘗試撥打vtkTransform::PostMultiply()或反轉rotate_polydata函數中的轉換順序。這很容易嘗試。

如果不解決這個問題，看看如何ITK在ComputeOffset，TransformPoint和ComputeMatrix應用轉換，並VTK如何它在vtkLinearTransformPoint。這應該解釋行爲差異並提供如何實現相同轉換的線索。