Propagate update to other docstrings

skimage/transform/_geometric.py

@@ -9,8 +9,9 @@
 
 
 def _affine_matrix_from_vector(v):
-    """Affine matrix from linearized (d, d + 1) matrix entries."""
+    """Affine matrix from linearized (n, n + 1) matrix entries."""
     nparam = v.size
+    # In the code, d denotes n (dimensionality).
     # solve for d in: d * (d + 1) = nparam
     d = (1 + np.sqrt(1 + 4 * nparam)) / 2 - 1
     dimensionality = int(np.round(d))  # round to prevent approx errors
@@ -23,31 +24,31 @@ def _affine_matrix_from_vector(v):
 
 
 def _center_and_normalize_points(points):
-    """Center and normalize image points.
+    """Center and normalize points of an nD image.
 
-    The points are transformed in a two-step procedure that is expressed
+    The N 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 origin of the coordinate system is sqrt(D).
+    to the origin of the coordinate system is sqrt(n).
 
     If the points are all identical, the returned values will contain nan.
 
     Parameters
     ----------
-    points : (N, D) array
+    points : (N, n) array
         The coordinates of the image points.
 
     Returns
     -------
-    matrix : (D+1, D+1) array_like
+    matrix : (n+1, n+1) array_like
         The transformation matrix to obtain the new points.
-    new_points : (N, D) array
-        The transformed image points.
+    new_points : (N, n) array
+        Coordinates of the transformed image points.
 
     References
     ----------
@@ -91,20 +92,20 @@ def _center_and_normalize_points(points):
 
 
 def _umeyama(src, dst, estimate_scale):
-    """Estimate N-D similarity transformation with or without scaling.
+    """Estimate nD similarity transformation with or without scaling.
 
     Parameters
     ----------
-    src : (M, N) array_like
+    src : (N, n) array_like
         Source coordinates.
-    dst : (M, N) array_like
+    dst : (N, n) array_like
         Destination coordinates.
     estimate_scale : bool
         Whether to estimate scaling factor.
 
     Returns
     -------
-    T : (N + 1, N + 1)
+    T : (n + 1, n + 1)
         The homogeneous similarity transformation matrix. The matrix contains
         NaN values only if the problem is not well-conditioned.