diff options
Diffstat (limited to 'r_facelib/detection/matlab_cp2tform.py')
| -rw-r--r-- | r_facelib/detection/matlab_cp2tform.py | 317 |
1 files changed, 317 insertions, 0 deletions
diff --git a/r_facelib/detection/matlab_cp2tform.py b/r_facelib/detection/matlab_cp2tform.py new file mode 100644 index 0000000..b1014a8 --- /dev/null +++ b/r_facelib/detection/matlab_cp2tform.py @@ -0,0 +1,317 @@ +import numpy as np
+from numpy.linalg import inv, lstsq
+from numpy.linalg import matrix_rank as rank
+from numpy.linalg import norm
+
+
+class MatlabCp2tormException(Exception):
+
+ def __str__(self):
+ return 'In File {}:{}'.format(__file__, super.__str__(self))
+
+
+def tformfwd(trans, uv):
+ """
+ Function:
+ ----------
+ apply affine transform 'trans' to uv
+
+ Parameters:
+ ----------
+ @trans: 3x3 np.array
+ transform matrix
+ @uv: Kx2 np.array
+ each row is a pair of coordinates (x, y)
+
+ Returns:
+ ----------
+ @xy: Kx2 np.array
+ each row is a pair of transformed coordinates (x, y)
+ """
+ uv = np.hstack((uv, np.ones((uv.shape[0], 1))))
+ xy = np.dot(uv, trans)
+ xy = xy[:, 0:-1]
+ return xy
+
+
+def tforminv(trans, uv):
+ """
+ Function:
+ ----------
+ apply the inverse of affine transform 'trans' to uv
+
+ Parameters:
+ ----------
+ @trans: 3x3 np.array
+ transform matrix
+ @uv: Kx2 np.array
+ each row is a pair of coordinates (x, y)
+
+ Returns:
+ ----------
+ @xy: Kx2 np.array
+ each row is a pair of inverse-transformed coordinates (x, y)
+ """
+ Tinv = inv(trans)
+ xy = tformfwd(Tinv, uv)
+ return xy
+
+
+def findNonreflectiveSimilarity(uv, xy, options=None):
+ options = {'K': 2}
+
+ K = options['K']
+ M = xy.shape[0]
+ x = xy[:, 0].reshape((-1, 1)) # use reshape to keep a column vector
+ y = xy[:, 1].reshape((-1, 1)) # use reshape to keep a column vector
+
+ tmp1 = np.hstack((x, y, np.ones((M, 1)), np.zeros((M, 1))))
+ tmp2 = np.hstack((y, -x, np.zeros((M, 1)), np.ones((M, 1))))
+ X = np.vstack((tmp1, tmp2))
+
+ u = uv[:, 0].reshape((-1, 1)) # use reshape to keep a column vector
+ v = uv[:, 1].reshape((-1, 1)) # use reshape to keep a column vector
+ U = np.vstack((u, v))
+
+ # We know that X * r = U
+ if rank(X) >= 2 * K:
+ r, _, _, _ = lstsq(X, U, rcond=-1)
+ r = np.squeeze(r)
+ else:
+ raise Exception('cp2tform:twoUniquePointsReq')
+ sc = r[0]
+ ss = r[1]
+ tx = r[2]
+ ty = r[3]
+
+ Tinv = np.array([[sc, -ss, 0], [ss, sc, 0], [tx, ty, 1]])
+ T = inv(Tinv)
+ T[:, 2] = np.array([0, 0, 1])
+
+ return T, Tinv
+
+
+def findSimilarity(uv, xy, options=None):
+ options = {'K': 2}
+
+ # uv = np.array(uv)
+ # xy = np.array(xy)
+
+ # Solve for trans1
+ trans1, trans1_inv = findNonreflectiveSimilarity(uv, xy, options)
+
+ # Solve for trans2
+
+ # manually reflect the xy data across the Y-axis
+ xyR = xy
+ xyR[:, 0] = -1 * xyR[:, 0]
+
+ trans2r, trans2r_inv = findNonreflectiveSimilarity(uv, xyR, options)
+
+ # manually reflect the tform to undo the reflection done on xyR
+ TreflectY = np.array([[-1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+ trans2 = np.dot(trans2r, TreflectY)
+
+ # Figure out if trans1 or trans2 is better
+ xy1 = tformfwd(trans1, uv)
+ norm1 = norm(xy1 - xy)
+
+ xy2 = tformfwd(trans2, uv)
+ norm2 = norm(xy2 - xy)
+
+ if norm1 <= norm2:
+ return trans1, trans1_inv
+ else:
+ trans2_inv = inv(trans2)
+ return trans2, trans2_inv
+
+
+def get_similarity_transform(src_pts, dst_pts, reflective=True):
+ """
+ Function:
+ ----------
+ Find Similarity Transform Matrix 'trans':
+ u = src_pts[:, 0]
+ v = src_pts[:, 1]
+ x = dst_pts[:, 0]
+ y = dst_pts[:, 1]
+ [x, y, 1] = [u, v, 1] * trans
+
+ Parameters:
+ ----------
+ @src_pts: Kx2 np.array
+ source points, each row is a pair of coordinates (x, y)
+ @dst_pts: Kx2 np.array
+ destination points, each row is a pair of transformed
+ coordinates (x, y)
+ @reflective: True or False
+ if True:
+ use reflective similarity transform
+ else:
+ use non-reflective similarity transform
+
+ Returns:
+ ----------
+ @trans: 3x3 np.array
+ transform matrix from uv to xy
+ trans_inv: 3x3 np.array
+ inverse of trans, transform matrix from xy to uv
+ """
+
+ if reflective:
+ trans, trans_inv = findSimilarity(src_pts, dst_pts)
+ else:
+ trans, trans_inv = findNonreflectiveSimilarity(src_pts, dst_pts)
+
+ return trans, trans_inv
+
+
+def cvt_tform_mat_for_cv2(trans):
+ """
+ Function:
+ ----------
+ Convert Transform Matrix 'trans' into 'cv2_trans' which could be
+ directly used by cv2.warpAffine():
+ u = src_pts[:, 0]
+ v = src_pts[:, 1]
+ x = dst_pts[:, 0]
+ y = dst_pts[:, 1]
+ [x, y].T = cv_trans * [u, v, 1].T
+
+ Parameters:
+ ----------
+ @trans: 3x3 np.array
+ transform matrix from uv to xy
+
+ Returns:
+ ----------
+ @cv2_trans: 2x3 np.array
+ transform matrix from src_pts to dst_pts, could be directly used
+ for cv2.warpAffine()
+ """
+ cv2_trans = trans[:, 0:2].T
+
+ return cv2_trans
+
+
+def get_similarity_transform_for_cv2(src_pts, dst_pts, reflective=True):
+ """
+ Function:
+ ----------
+ Find Similarity Transform Matrix 'cv2_trans' which could be
+ directly used by cv2.warpAffine():
+ u = src_pts[:, 0]
+ v = src_pts[:, 1]
+ x = dst_pts[:, 0]
+ y = dst_pts[:, 1]
+ [x, y].T = cv_trans * [u, v, 1].T
+
+ Parameters:
+ ----------
+ @src_pts: Kx2 np.array
+ source points, each row is a pair of coordinates (x, y)
+ @dst_pts: Kx2 np.array
+ destination points, each row is a pair of transformed
+ coordinates (x, y)
+ reflective: True or False
+ if True:
+ use reflective similarity transform
+ else:
+ use non-reflective similarity transform
+
+ Returns:
+ ----------
+ @cv2_trans: 2x3 np.array
+ transform matrix from src_pts to dst_pts, could be directly used
+ for cv2.warpAffine()
+ """
+ trans, trans_inv = get_similarity_transform(src_pts, dst_pts, reflective)
+ cv2_trans = cvt_tform_mat_for_cv2(trans)
+
+ return cv2_trans
+
+
+if __name__ == '__main__':
+ """
+ u = [0, 6, -2]
+ v = [0, 3, 5]
+ x = [-1, 0, 4]
+ y = [-1, -10, 4]
+
+ # In Matlab, run:
+ #
+ # uv = [u'; v'];
+ # xy = [x'; y'];
+ # tform_sim=cp2tform(uv,xy,'similarity');
+ #
+ # trans = tform_sim.tdata.T
+ # ans =
+ # -0.0764 -1.6190 0
+ # 1.6190 -0.0764 0
+ # -3.2156 0.0290 1.0000
+ # trans_inv = tform_sim.tdata.Tinv
+ # ans =
+ #
+ # -0.0291 0.6163 0
+ # -0.6163 -0.0291 0
+ # -0.0756 1.9826 1.0000
+ # xy_m=tformfwd(tform_sim, u,v)
+ #
+ # xy_m =
+ #
+ # -3.2156 0.0290
+ # 1.1833 -9.9143
+ # 5.0323 2.8853
+ # uv_m=tforminv(tform_sim, x,y)
+ #
+ # uv_m =
+ #
+ # 0.5698 1.3953
+ # 6.0872 2.2733
+ # -2.6570 4.3314
+ """
+ u = [0, 6, -2]
+ v = [0, 3, 5]
+ x = [-1, 0, 4]
+ y = [-1, -10, 4]
+
+ uv = np.array((u, v)).T
+ xy = np.array((x, y)).T
+
+ print('\n--->uv:')
+ print(uv)
+ print('\n--->xy:')
+ print(xy)
+
+ trans, trans_inv = get_similarity_transform(uv, xy)
+
+ print('\n--->trans matrix:')
+ print(trans)
+
+ print('\n--->trans_inv matrix:')
+ print(trans_inv)
+
+ print('\n---> apply transform to uv')
+ print('\nxy_m = uv_augmented * trans')
+ uv_aug = np.hstack((uv, np.ones((uv.shape[0], 1))))
+ xy_m = np.dot(uv_aug, trans)
+ print(xy_m)
+
+ print('\nxy_m = tformfwd(trans, uv)')
+ xy_m = tformfwd(trans, uv)
+ print(xy_m)
+
+ print('\n---> apply inverse transform to xy')
+ print('\nuv_m = xy_augmented * trans_inv')
+ xy_aug = np.hstack((xy, np.ones((xy.shape[0], 1))))
+ uv_m = np.dot(xy_aug, trans_inv)
+ print(uv_m)
+
+ print('\nuv_m = tformfwd(trans_inv, xy)')
+ uv_m = tformfwd(trans_inv, xy)
+ print(uv_m)
+
+ uv_m = tforminv(trans, xy)
+ print('\nuv_m = tforminv(trans, xy)')
+ print(uv_m)
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