Create function to center and normalize image points

skimage/transform/_geometric.py

@@ -10,6 +10,54 @@ from ..exposure import rescale_intensity
 from ._warps_cy import _warp_fast
 
 
+def _center_and_normalize_points(points):
+    """Center and normalize image points.
+
+    The points are transformed in a two-step procedure that is expressed
+    as a transformation matrix. The matrix of the resulting points is usually
+    better conditioned than the matrix of the original points.
+
+    Center the image points, such that the new coordinate system has its
+    origin at the centroid of the image points.
+
+    Normalize the image points, such that the mean distance from the points
+    to the coordinate system is sqrt(2).
+
+    Parameters
+    ----------
+    points : (N, 2) array
+        The coordinates of the image points.
+
+    Returns
+    -------
+    matrix : (3, 3) array
+        The transformation matrix to obtain the new points.
+    new_points : (N, 2) array
+        The transformed image points.
+
+    """
+
+    centroid = np.mean(points, axis=0)
+
+    rms = math.sqrt(np.sum((points - centroid) ** 2) / points.shape[0])
+
+    norm_factor = math.sqrt(2) / rms
+
+    matrix = np.array([[norm_factor, 0, -norm_factor * centroid[0]],
+                       [0, norm_factor, -norm_factor * centroid[1]],
+                       [0, 0, 1]])
+
+    pointsh = np.row_stack([points.T, np.ones((points.shape[0]),)])
+
+    new_pointsh = np.dot(matrix, pointsh).T
+
+    new_points = new_pointsh[:, :2]
+    new_points[:, 0] /= new_pointsh[:, 2]
+    new_points[:, 1] /= new_pointsh[:, 2]
+
+    return matrix, new_points
+
+
 class GeometricTransform(object):
     """Perform geometric transformations on a set of coordinates.