text: # Copy of https://github.com/deepinsight/insightface/tree/master/python-package/insightface/utils/face_align.py
  import cv2
  import numpy as np
  from skimage import transform as trans
  
  src1 = np.array([[51.642, 50.115], [57.617, 49.990], [35.740, 69.007],
                   [51.157, 89.050], [57.025, 89.702]],
                  dtype=np.float32)
  #<--left
  src2 = np.array([[45.031, 50.118], [65.568, 50.872], [39.677, 68.111],
                   [45.177, 86.190], [64.246, 86.758]],
                  dtype=np.float32)
  
  #---frontal
  src3 = np.array([[39.730, 51.138], [72.270, 51.138], [56.000, 68.493],
                   [42.463, 87.010], [69.537, 87.010]],
                  dtype=np.float32)
  
  #-->right
  src4 = np.array([[46.845, 50.872], [67.382, 50.118], [72.737, 68.111],
                   [48.167, 86.758], [67.236, 86.190]],
                  dtype=np.float32)
  
  #-->right profile
  src5 = np.array([[54.796, 49.990], [60.771, 50.115], [76.673, 69.007],
                   [55.388, 89.702], [61.257, 89.050]],
                  dtype=np.float32)
  
  src = np.array([src1, src2, src3, src4, src5])
  src_map = {112: src, 224: src * 2}
  
  arcface_src = np.array(
      [[38.2946, 51.6963], [73.5318, 51.5014], [56.0252, 71.7366],
       [41.5493, 92.3655], [70.7299, 92.2041]],
      dtype=np.float32)
  
  arcface_src = np.expand_dims(arcface_src, axis=0)
  
  # In[66]:
  
  
  # lmk is prediction; src is template
  def estimate_norm(lmk, image_size=112, mode='arcface'):
      assert lmk.shape == (5, 2)
      tform = trans.SimilarityTransform()
      lmk_tran = np.insert(lmk, 2, values=np.ones(5), axis=1)
      min_M = []
      min_index = []
      min_error = float('inf')
      if mode == 'arcface':
          assert image_size == 112
          src = arcface_src
      else:
          src = src_map[image_size]
      for i in np.arange(src.shape[0]):
          tform.estimate(lmk, src[i])
          M = tform.params[0:2, :]
          results = np.dot(M, lmk_tran.T)
          results = results.T
          error = np.sum(np.sqrt(np.sum((results - src[i])**2, axis=1)))
          #         print(error)
          if error < min_error:
              min_error = error
              min_M = M
              min_index = i
      return min_M, min_index
  
  
  def norm_crop(img, landmark, image_size=112, mode='arcface'):
      M, pose_index = estimate_norm(landmark, image_size, mode)
      warped = cv2.warpAffine(img, M, (image_size, image_size), borderValue=0.0)
      return warped
  
  def square_crop(im, S):
      if im.shape[0] > im.shape[1]:
          height = S
          width = int(float(im.shape[1]) / im.shape[0] * S)
          scale = float(S) / im.shape[0]
      else:
          width = S
          height = int(float(im.shape[0]) / im.shape[1] * S)
          scale = float(S) / im.shape[1]
      resized_im = cv2.resize(im, (width, height))
      det_im = np.zeros((S, S, 3), dtype=np.uint8)
      det_im[:resized_im.shape[0], :resized_im.shape[1], :] = resized_im
      return det_im, scale
  
  
  def transform(data, center, output_size, scale, rotation):
      scale_ratio = scale
      rot = float(rotation) * np.pi / 180.0
      #translation = (output_size/2-center[0]*scale_ratio, output_size/2-center[1]*scale_ratio)
      t1 = trans.SimilarityTransform(scale=scale_ratio)
      cx = center[0] * scale_ratio
      cy = center[1] * scale_ratio
      t2 = trans.SimilarityTransform(translation=(-1 * cx, -1 * cy))
      t3 = trans.SimilarityTransform(rotation=rot)
      t4 = trans.SimilarityTransform(translation=(output_size / 2,
                                                  output_size / 2))
      t = t1 + t2 + t3 + t4
      M = t.params[0:2]
      cropped = cv2.warpAffine(data,
                               M, (output_size, output_size),
                               borderValue=0.0)
      return cropped, M
  
  
  def trans_points2d(pts, M):
      new_pts = np.zeros(shape=pts.shape, dtype=np.float32)
      for i in range(pts.shape[0]):
          pt = pts[i]
          new_pt = np.array([pt[0], pt[1], 1.], dtype=np.float32)
          new_pt = np.dot(M, new_pt)
          #print('new_pt', new_pt.shape, new_pt)
          new_pts[i] = new_pt[0:2]
  
      return new_pts
  
  
  def trans_points3d(pts, M):
      scale = np.sqrt(M[0][0] * M[0][0] + M[0][1] * M[0][1])
      #print(scale)
      new_pts = np.zeros(shape=pts.shape, dtype=np.float32)
      for i in range(pts.shape[0]):
          pt = pts[i]
          new_pt = np.array([pt[0], pt[1], 1.], dtype=np.float32)
          new_pt = np.dot(M, new_pt)
          #print('new_pt', new_pt.shape, new_pt)
          new_pts[i][0:2] = new_pt[0:2]
          new_pts[i][2] = pts[i][2] * scale
  
      return new_pts
  
  
  def trans_points(pts, M):
      if pts.shape[1] == 2:
          return trans_points2d(pts, M)
      else:
          return trans_points3d(pts, M)