From 49967b412ba78e4512950fad5c69bc464b7d9a60 Mon Sep 17 00:00:00 2001
From: Steven Silvester <steven.silvester@ieee.org>
Date: Sun, 14 Jun 2015 17:39:25 -0500
Subject: [PATCH 1/2] Create an optimal step parameter for view_as_windows

---
 skimage/util/shape.py            | 14 +++++++++++++-
 skimage/util/tests/test_shape.py | 16 ++++++++++++++++
 2 files changed, 29 insertions(+), 1 deletion(-)

diff --git a/skimage/util/shape.py b/skimage/util/shape.py
index 78bb7bb9..505ba9cd 100644
--- a/skimage/util/shape.py
+++ b/skimage/util/shape.py
@@ -103,7 +103,7 @@ def view_as_blocks(arr_in, block_shape):
     return arr_out
 
 
-def view_as_windows(arr_in, window_shape, step=1):
+def view_as_windows(arr_in, window_shape, step=1, optimal_step=False):
     """Rolling window view of the input n-dimensional array.
 
     Windows are overlapping views of the input array, with adjacent windows
@@ -121,6 +121,9 @@ def view_as_windows(arr_in, window_shape, step=1):
     step : integer or tuple of length arr_in.ndim
         Indicates step size at which extraction shall be performed.
         If integer is given, then the step is uniform in all dimensions.
+    optimal_step: bool, optional
+        When True, selects a ``step`` that will give full coverage of
+        ``arr_in`` with minimal overlap.
 
     Returns
     -------
@@ -225,6 +228,15 @@ def view_as_windows(arr_in, window_shape, step=1):
     if not (len(window_shape) == ndim):
         raise ValueError("`window_shape` is incompatible with `arr_in.shape`")
 
+    if optimal_step:
+        rem = np.array(arr_in.shape) - np.array(window_shape)
+        step = list(window_shape)
+
+        for (ind, size) in enumerate(window_shape):
+            ns = int(np.ceil(arr_in.shape[ind] / size))
+            while step[ind] * (ns - 1) > rem[ind]:
+                step[ind] -= 1
+
     if isinstance(step, numbers.Number):
         if step < 1:
             raise ValueError("`step` must be >= 1")
diff --git a/skimage/util/tests/test_shape.py b/skimage/util/tests/test_shape.py
index 7a6a785d..5c59edb0 100644
--- a/skimage/util/tests/test_shape.py
+++ b/skimage/util/tests/test_shape.py
@@ -176,5 +176,21 @@ def test_view_as_windows_step_tuple():
                          [22, 23]]]])
 
 
+def test_view_as_windows_optimal_step():
+    A = np.arange(24).reshape((6, 4))
+    B = view_as_windows(A, (3, 2), optimal_step=True)
+    assert B.shape == (2, 2, 3, 2)
+    assert B.size == A.size
+
+    A = np.arange(512 * 512).reshape((512, 512))
+    B = view_as_windows(A, (10, 10), optimal_step=True)
+    assert B.shape == (56, 56, 10, 10)
+    assert B.size >= A.size
+
+    C = view_as_windows(A, (11, 9), optimal_step=True)
+    assert C.shape == (51, 63, 11, 9)
+    assert C.size >= A.size
+
+
 if __name__ == '__main__':
     np.testing.run_module_suite()

From 0ffe44a4f0095b3e6fe0ad4450db44d06c2841a6 Mon Sep 17 00:00:00 2001
From: Steven Silvester <steven.silvester@ieee.org>
Date: Sun, 14 Jun 2015 20:19:13 -0500
Subject: [PATCH 2/2] Ensure consistent handling of division

---
 skimage/util/shape.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/skimage/util/shape.py b/skimage/util/shape.py
index 505ba9cd..48e9a5ef 100644
--- a/skimage/util/shape.py
+++ b/skimage/util/shape.py
@@ -1,3 +1,4 @@
+from __future__ import division
 import numbers
 import numpy as np
 from numpy.lib.stride_tricks import as_strided