From 3529e4d8188e890b0988a3f7674092e08c12e4fb Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Tue, 8 Nov 2011 17:27:22 -0800
Subject: [PATCH 01/14] ENH: Add Structural SIMilarity (SSIM) image comparison.

---
 skimage/measure/__init__.py        |   1 +
 skimage/measure/_ssim.py           | 110 +++++++++++++++++++++++++++++
 skimage/measure/tests/test_ssim.py |  36 ++++++++++
 3 files changed, 147 insertions(+)
 create mode 100644 skimage/measure/_ssim.py
 create mode 100644 skimage/measure/tests/test_ssim.py

diff --git a/skimage/measure/__init__.py b/skimage/measure/__init__.py
index 422db569..cb9dc679 100755
--- a/skimage/measure/__init__.py
+++ b/skimage/measure/__init__.py
@@ -1,2 +1,3 @@
 from .find_contours import find_contours
 from ._regionprops import regionprops
+from ._ssim import ssim
diff --git a/skimage/measure/_ssim.py b/skimage/measure/_ssim.py
new file mode 100644
index 00000000..a93571e8
--- /dev/null
+++ b/skimage/measure/_ssim.py
@@ -0,0 +1,110 @@
+from __future__ import division
+
+__all__ = ['ssim']
+
+import numpy as np
+from numpy.lib import stride_tricks
+
+def _as_windows(X, win_size=7):
+    """Re-stride an array to simulate a sliding window.
+
+    Parameters
+    ----------
+    X : 2D-ndarray
+        Input image.
+
+    Returns
+    -------
+    window : (N, win_size, win_size) ndarray
+        Sliding windows.
+
+    """
+    if not X.ndim == 2:
+        raise ValueError('Input images must be 2-dimensional.')
+
+    X = np.ascontiguousarray(X)
+    r, c = X.shape
+
+    strides = X.strides
+    row_jump, el_jump = strides
+    half_width = (win_size // 2)
+
+    new_strides = (row_jump, el_jump, row_jump, el_jump)
+    new_rows = r - 2 * half_width
+    new_cols = c - 2 * half_width
+    new_shape = (new_rows, new_cols, win_size, win_size)
+
+    windows = stride_tricks.as_strided(X, shape=new_shape, strides=new_strides)
+    windows = windows.reshape((-1, win_size, win_size))
+
+    return windows
+
+
+def ssim(X, Y, win_size=7, dynamic_range=255):
+    """Compute the structural similarity index between two images.
+
+    Parameters
+    ----------
+    X, Y : (N,N) ndarray
+        Images.
+    win_size : int
+        The side-length of the sliding window used in comparison.  Must
+        be an odd value.
+    dynamic_range : int
+        Dynamic range of the input image (distance between minimum and
+        maximum possible values).  This should eventually be
+        auto-computed, but just specifying it manually for now.
+
+    Returns
+    -------
+    s : float
+        Strucutural similarity.
+
+    References
+    ----------
+    .. [1] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P.
+       (2004). Image quality assessment: From error visibility to
+       structural similarity. IEEE Transactions on Image Processing,
+       13, 600-612.
+
+    """
+    if not X.dtype == Y.dtype:
+        raise ValueError('Input images must have the same dtype.')
+
+    if not X.shape == Y.shape:
+        raise ValueError('Inout images must have the same dimensions.')
+
+    import time
+
+    tic = time.time()
+
+    XW = _as_windows(X, win_size=win_size)
+    YW = _as_windows(Y, win_size=win_size)
+
+    tic = time.time()
+    
+    # Flatten windows
+    XW = XW.reshape(XW.shape[0], -1)
+    YW = YW.reshape(YW.shape[0], -1)
+
+    ux = np.mean(XW, axis=1)
+    uy = np.mean(YW, axis=1)
+
+    tic = time.time()
+
+    # Compute variances var(X), var(Y) and var(X, Y)
+    cov_norm = 1 / (win_size**2 - 1)
+    XWM = XW - ux[:, None]
+    YWM = YW - uy[:, None]
+    vx = cov_norm * np.sum(XWM**2, axis=1)
+    vy = cov_norm * np.sum(YWM**2, axis=1)
+    vxy = cov_norm * np.sum(XWM * YWM, axis=1)    
+
+    R = dynamic_range
+    K1 = 0.01
+    K2 = 0.03
+    C1 = (K1 * R)**2
+    C2 = (K2 * R)**2
+
+    return np.mean(((2 * ux * uy + C1) * (2 * vxy + C2)) / \
+                   ((ux**2 + uy**2 + C1) * (vx + vy + C2)))
diff --git a/skimage/measure/tests/test_ssim.py b/skimage/measure/tests/test_ssim.py
new file mode 100644
index 00000000..8e6684b0
--- /dev/null
+++ b/skimage/measure/tests/test_ssim.py
@@ -0,0 +1,36 @@
+import numpy as np
+from numpy.testing import assert_equal
+
+from skimage.measure._ssim import ssim, _as_windows
+
+def test_ssim_patch_range():
+    N = 51
+    X = (np.random.random((N, N)) * 255).astype(np.uint8)
+    Y = (np.random.random((N, N)) * 255).astype(np.uint8)
+
+    assert(ssim(X, Y, win_size=N) < 0.1)
+    assert_equal(ssim(X, X, win_size=N), 1)
+
+def test_as_windows():
+    X = np.arange(100).reshape((10, 10))
+    W = _as_windows(X, win_size=7)
+    assert_equal(len(W), 16)
+
+    W = _as_windows(X, win_size=3)
+    assert_equal(W[0], [[0, 1, 2],
+                        [10, 11, 12],
+                        [20, 21, 22]])
+
+def test_ssim_image():
+    N = 100
+    X = (np.random.random((N, N)) * 255).astype(np.uint8)
+    Y = (np.random.random((N, N)) * 255).astype(np.uint8)
+
+    S0 = ssim(X, X, win_size=3)
+    assert_equal(S0, 1)
+    
+    S1 = ssim(X, Y, win_size=3)
+    assert(S1 < 0.3)
+
+if __name__ == "__main__":
+    np.testing.run_module_suite()

From 226220902a8177f90817e369d6bd3f61d573d2c3 Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Tue, 8 Nov 2011 20:41:47 -0800
Subject: [PATCH 02/14] ENH: Add SSIM gradient.

---
 skimage/measure/_ssim.py           | 70 ++++++++++++++++++++----------
 skimage/measure/tests/test_ssim.py | 29 +++++++++++--
 2 files changed, 71 insertions(+), 28 deletions(-)

diff --git a/skimage/measure/_ssim.py b/skimage/measure/_ssim.py
index a93571e8..f0d8357c 100644
--- a/skimage/measure/_ssim.py
+++ b/skimage/measure/_ssim.py
@@ -5,7 +5,7 @@ __all__ = ['ssim']
 import numpy as np
 from numpy.lib import stride_tricks
 
-def _as_windows(X, win_size=7):
+def _as_windows(X, win_size=7, flatten_first_axis=True):
     """Re-stride an array to simulate a sliding window.
 
     Parameters
@@ -15,7 +15,7 @@ def _as_windows(X, win_size=7):
 
     Returns
     -------
-    window : (N, win_size, win_size) ndarray
+    window : (N, M, win_size, win_size) ndarray
         Sliding windows.
 
     """
@@ -35,12 +35,11 @@ def _as_windows(X, win_size=7):
     new_shape = (new_rows, new_cols, win_size, win_size)
 
     windows = stride_tricks.as_strided(X, shape=new_shape, strides=new_strides)
-    windows = windows.reshape((-1, win_size, win_size))
 
     return windows
 
 
-def ssim(X, Y, win_size=7, dynamic_range=255):
+def ssim(X, Y, win_size=7, gradient=False, dynamic_range=255):
     """Compute the structural similarity index between two images.
 
     Parameters
@@ -54,11 +53,16 @@ def ssim(X, Y, win_size=7, dynamic_range=255):
         Dynamic range of the input image (distance between minimum and
         maximum possible values).  This should eventually be
         auto-computed, but just specifying it manually for now.
+    gradient : bool
+        If True, also return the gradient.
 
     Returns
     -------
     s : float
         Strucutural similarity.
+    grad : (N * N,) ndarray
+        Gradient of the structural similarity index between X and Y.
+        This is only returned if `gradient` is set to True.
 
     References
     ----------
@@ -72,33 +76,27 @@ def ssim(X, Y, win_size=7, dynamic_range=255):
         raise ValueError('Input images must have the same dtype.')
 
     if not X.shape == Y.shape:
-        raise ValueError('Inout images must have the same dimensions.')
+        raise ValueError('Input images must have the same dimensions.')
 
-    import time
-
-    tic = time.time()
+    if not (win_size % 2 == 1):
+        raise ValueError('Window size must be odd.')
 
     XW = _as_windows(X, win_size=win_size)
     YW = _as_windows(Y, win_size=win_size)
 
-    tic = time.time()
-    
-    # Flatten windows
-    XW = XW.reshape(XW.shape[0], -1)
-    YW = YW.reshape(YW.shape[0], -1)
+    NS = len(XW)
+    NP = win_size * win_size
 
-    ux = np.mean(XW, axis=1)
-    uy = np.mean(YW, axis=1)
-
-    tic = time.time()
+    ux = np.mean(np.mean(XW, axis=2), axis=2)
+    uy = np.mean(np.mean(YW, axis=2), axis=2)
 
     # Compute variances var(X), var(Y) and var(X, Y)
     cov_norm = 1 / (win_size**2 - 1)
-    XWM = XW - ux[:, None]
-    YWM = YW - uy[:, None]
-    vx = cov_norm * np.sum(XWM**2, axis=1)
-    vy = cov_norm * np.sum(YWM**2, axis=1)
-    vxy = cov_norm * np.sum(XWM * YWM, axis=1)    
+    XWM = XW - ux[..., None, None]
+    YWM = YW - uy[..., None, None]
+    vx = cov_norm * np.sum(np.sum(XWM**2, axis=2), axis=2)
+    vy = cov_norm * np.sum(np.sum(YWM**2, axis=2), axis=2)
+    vxy = cov_norm * np.sum(np.sum(XWM * YWM, axis=2), axis=2)
 
     R = dynamic_range
     K1 = 0.01
@@ -106,5 +104,29 @@ def ssim(X, Y, win_size=7, dynamic_range=255):
     C1 = (K1 * R)**2
     C2 = (K2 * R)**2
 
-    return np.mean(((2 * ux * uy + C1) * (2 * vxy + C2)) / \
-                   ((ux**2 + uy**2 + C1) * (vx + vy + C2)))
+    A1, A2, B1, B2 = (v[..., None, None] for v in
+                      (2 * ux * uy + C1,
+                       2 * vxy + C2,
+                       ux**2 + uy**2 + C1,
+                       vx + vy + C2))
+
+    S = np.mean((A1 * A2) / (B1 * B2))
+
+    if gradient:
+        local_grad = 2 / (NP * B1**2 * B2**2) * \
+            (
+            A1 * B1 * (B2 * XW - A2 * YW) - \
+            B1 * B2 * (A2 - A1) * ux[..., None, None] + \
+            A1 * A2 * (B1 - B2) * uy[..., None, None]
+            )
+
+        grad = np.zeros_like(X, dtype=float)
+        OW = _as_windows(grad, win_size=win_size)
+
+        OW += local_grad
+        grad /= NS
+
+        return S, grad
+
+    else:
+        return S
diff --git a/skimage/measure/tests/test_ssim.py b/skimage/measure/tests/test_ssim.py
index 8e6684b0..f140a48d 100644
--- a/skimage/measure/tests/test_ssim.py
+++ b/skimage/measure/tests/test_ssim.py
@@ -2,6 +2,7 @@ import numpy as np
 from numpy.testing import assert_equal
 
 from skimage.measure._ssim import ssim, _as_windows
+import scipy.optimize as opt
 
 def test_ssim_patch_range():
     N = 51
@@ -14,12 +15,12 @@ def test_ssim_patch_range():
 def test_as_windows():
     X = np.arange(100).reshape((10, 10))
     W = _as_windows(X, win_size=7)
-    assert_equal(len(W), 16)
+    assert_equal(W.shape[:2], (4, 4))
 
     W = _as_windows(X, win_size=3)
-    assert_equal(W[0], [[0, 1, 2],
-                        [10, 11, 12],
-                        [20, 21, 22]])
+    assert_equal(W[0, 0], [[0, 1, 2],
+                           [10, 11, 12],
+                           [20, 21, 22]])
 
 def test_ssim_image():
     N = 100
@@ -32,5 +33,25 @@ def test_ssim_image():
     S1 = ssim(X, Y, win_size=3)
     assert(S1 < 0.3)
 
+def test_ssim_grad():
+    N = 30
+    X = np.random.random((N, N))
+    Y = np.random.random((N, N))
+
+    def func(Y):
+        return ssim(X, Y)
+
+    def grad(Y):
+        return ssim(X, Y, gradient=True)[1]
+
+    assert(np.all(opt.check_grad(func, grad, Y) < 0.05))
+
+#    N = 200
+#    X = np.random.random((N, N))
+#    Y = np.random.random((N, N))
+
+#    assert(np.all(np.abs(ssim(X, Y, gradient=True))[1] < 1e-2))
+
+
 if __name__ == "__main__":
     np.testing.run_module_suite()

From 58366f86bd1d71c2333d6ec998191ee9ee55c31f Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Thu, 2 Feb 2012 21:26:52 -0800
Subject: [PATCH 03/14] ENH: Rename ssid to structural_similarity to avoid
 confusion with self-similarity features.

---
 skimage/measure/_ssim.py           |  6 +++---
 skimage/measure/tests/test_ssim.py | 10 ++--------
 2 files changed, 5 insertions(+), 11 deletions(-)

diff --git a/skimage/measure/_ssim.py b/skimage/measure/_ssim.py
index f0d8357c..17fc165c 100644
--- a/skimage/measure/_ssim.py
+++ b/skimage/measure/_ssim.py
@@ -1,6 +1,6 @@
 from __future__ import division
 
-__all__ = ['ssim']
+__all__ = ['structural_similarity']
 
 import numpy as np
 from numpy.lib import stride_tricks
@@ -39,8 +39,8 @@ def _as_windows(X, win_size=7, flatten_first_axis=True):
     return windows
 
 
-def ssim(X, Y, win_size=7, gradient=False, dynamic_range=255):
-    """Compute the structural similarity index between two images.
+def structural_similarity(X, Y, win_size=7, gradient=False, dynamic_range=255):
+    """Compute the mean structural similarity index between two images.
 
     Parameters
     ----------
diff --git a/skimage/measure/tests/test_ssim.py b/skimage/measure/tests/test_ssim.py
index f140a48d..4e713ecb 100644
--- a/skimage/measure/tests/test_ssim.py
+++ b/skimage/measure/tests/test_ssim.py
@@ -1,7 +1,7 @@
 import numpy as np
 from numpy.testing import assert_equal
 
-from skimage.measure._ssim import ssim, _as_windows
+from skimage.measure._ssim import structural_similarity as ssim, _as_windows
 import scipy.optimize as opt
 
 def test_ssim_patch_range():
@@ -29,7 +29,7 @@ def test_ssim_image():
 
     S0 = ssim(X, X, win_size=3)
     assert_equal(S0, 1)
-    
+
     S1 = ssim(X, Y, win_size=3)
     assert(S1 < 0.3)
 
@@ -46,12 +46,6 @@ def test_ssim_grad():
 
     assert(np.all(opt.check_grad(func, grad, Y) < 0.05))
 
-#    N = 200
-#    X = np.random.random((N, N))
-#    Y = np.random.random((N, N))
-
-#    assert(np.all(np.abs(ssim(X, Y, gradient=True))[1] < 1e-2))
-
 
 if __name__ == "__main__":
     np.testing.run_module_suite()

From 03f6da135baa6fe058c7fd3c8fba88b9b13bda0f Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Thu, 2 Feb 2012 22:41:54 -0800
Subject: [PATCH 04/14] DOC: Example of structural similarity.  The example is
 currently broken because structural_similarity does not auto-detect dynamic
 range.

---
 doc/examples/plot_ssim.py | 72 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 72 insertions(+)
 create mode 100644 doc/examples/plot_ssim.py

diff --git a/doc/examples/plot_ssim.py b/doc/examples/plot_ssim.py
new file mode 100644
index 00000000..761dc29c
--- /dev/null
+++ b/doc/examples/plot_ssim.py
@@ -0,0 +1,72 @@
+'''
+===========================
+Structural similarity index
+===========================
+
+When comparing images, the mean squared error (MSE)--while simple to
+implement--is not highly indicative of perceived similarity.  Structural
+similarity aims to address this shortcoming by taking texture into account
+[1]_, [2]_.
+
+The example shows two modifications of the input image, each with the same MSE,
+but with very different mean structural similarity indices.
+
+.. [1] Zhou Wang; Bovik, A.C.; ,"Mean squared error: Love it or leave it? A new
+       look at Signal Fidelity Measures," Signal Processing Magazine, IEEE,
+       vol. 26, no. 1, pp. 98-117, Jan. 2009.
+
+.. [2] Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, "Image quality
+       assessment: From error visibility to structural similarity," IEEE
+       Transactions on Image Processing, vol. 13, no. 4, pp. 600-612,
+       Apr. 2004.
+
+'''
+
+from skimage import data, color, io, exposure, img_as_float
+from skimage.measure import structural_similarity as ssim
+
+import numpy as np
+
+img = img_as_float(data.camera())
+rows, cols = img.shape
+
+noise = np.ones_like(img) * 0.5 * (img.max() - img.min())
+noise[np.random.random(size=noise.shape) > 0.5] *= -1
+
+def mse(x, y):
+    return np.linalg.norm(x - y)
+
+img_noise = img + noise
+img_const = img + abs(noise)
+
+import matplotlib.pyplot as plt
+f, (ax0, ax1, ax2) = plt.subplots(1, 3)
+
+mse_none = mse(img, img)
+ssim_none = ssim(img, img)
+
+mse_noise = mse(img, img_noise)
+ssim_noise = ssim(img, img_noise)
+
+mse_const = mse(img, img_const)
+ssim_const = ssim(img, img_const)
+
+label = 'MSE: %2.f, SSIM: %.2f'
+
+ax0.imshow(img, cmap=plt.cm.gray)
+ax0.set_xlabel(label % (mse_none, ssim_none))
+ax0.set_title('Original image')
+
+# exposure.rescale_intensity(img_noise)
+img_noise -= img_noise.min()
+img_noise /= img_noise.max()
+
+ax1.imshow(img_noise, cmap=plt.cm.gray)
+ax1.set_xlabel(label % (mse_noise, ssim_noise))
+ax1.set_title('Image with noise')
+
+ax2.imshow(img_const, cmap=plt.cm.gray)
+ax2.set_xlabel(label % (mse_const, ssim_const))
+ax2.set_title('Image plus constant')
+
+plt.show()

From ac86299690240c1f86e620e73be9efb53b4629ad Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Fri, 3 Feb 2012 20:05:16 -0800
Subject: [PATCH 05/14] DOC: In ssim example, use correct dynamic range in
 algorithm and when displaying results.

---
 doc/examples/plot_ssim.py | 18 +++++++-----------
 1 file changed, 7 insertions(+), 11 deletions(-)

diff --git a/doc/examples/plot_ssim.py b/doc/examples/plot_ssim.py
index 761dc29c..60419692 100644
--- a/doc/examples/plot_ssim.py
+++ b/doc/examples/plot_ssim.py
@@ -30,7 +30,7 @@ import numpy as np
 img = img_as_float(data.camera())
 rows, cols = img.shape
 
-noise = np.ones_like(img) * 0.5 * (img.max() - img.min())
+noise = np.ones_like(img) * 0.2 * (img.max() - img.min())
 noise[np.random.random(size=noise.shape) > 0.5] *= -1
 
 def mse(x, y):
@@ -43,29 +43,25 @@ import matplotlib.pyplot as plt
 f, (ax0, ax1, ax2) = plt.subplots(1, 3)
 
 mse_none = mse(img, img)
-ssim_none = ssim(img, img)
+ssim_none = ssim(img, img, dynamic_range=img.max() - img.min())
 
 mse_noise = mse(img, img_noise)
-ssim_noise = ssim(img, img_noise)
+ssim_noise = ssim(img, img_noise, dynamic_range=img_const.max() - img_const.min())
 
 mse_const = mse(img, img_const)
-ssim_const = ssim(img, img_const)
+ssim_const = ssim(img, img_const, dynamic_range=img_noise.max() - img_noise.min())
 
 label = 'MSE: %2.f, SSIM: %.2f'
 
-ax0.imshow(img, cmap=plt.cm.gray)
+ax0.imshow(img, cmap=plt.cm.gray, vmin=0, vmax=1)
 ax0.set_xlabel(label % (mse_none, ssim_none))
 ax0.set_title('Original image')
 
-# exposure.rescale_intensity(img_noise)
-img_noise -= img_noise.min()
-img_noise /= img_noise.max()
-
-ax1.imshow(img_noise, cmap=plt.cm.gray)
+ax1.imshow(img_noise, cmap=plt.cm.gray, vmin=0, vmax=1)
 ax1.set_xlabel(label % (mse_noise, ssim_noise))
 ax1.set_title('Image with noise')
 
-ax2.imshow(img_const, cmap=plt.cm.gray)
+ax2.imshow(img_const, cmap=plt.cm.gray, vmin=0, vmax=1)
 ax2.set_xlabel(label % (mse_const, ssim_const))
 ax2.set_title('Image plus constant')
 

From 37567726fd04fcbbec915cde7768fe098b8492c3 Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Fri, 3 Feb 2012 20:05:44 -0800
Subject: [PATCH 06/14] ENH: Automatically determine dynamic range in ssim if
 not specified.

---
 skimage/measure/_ssim.py           | 16 +++++++++++-----
 skimage/measure/tests/test_ssim.py | 25 ++++++++++++++++++++-----
 2 files changed, 31 insertions(+), 10 deletions(-)

diff --git a/skimage/measure/_ssim.py b/skimage/measure/_ssim.py
index 17fc165c..322d5799 100644
--- a/skimage/measure/_ssim.py
+++ b/skimage/measure/_ssim.py
@@ -5,6 +5,8 @@ __all__ = ['structural_similarity']
 import numpy as np
 from numpy.lib import stride_tricks
 
+from ..util.dtype import dtype_range
+
 def _as_windows(X, win_size=7, flatten_first_axis=True):
     """Re-stride an array to simulate a sliding window.
 
@@ -39,7 +41,7 @@ def _as_windows(X, win_size=7, flatten_first_axis=True):
     return windows
 
 
-def structural_similarity(X, Y, win_size=7, gradient=False, dynamic_range=255):
+def structural_similarity(X, Y, win_size=7, gradient=False, dynamic_range=None):
     """Compute the mean structural similarity index between two images.
 
     Parameters
@@ -49,12 +51,12 @@ def structural_similarity(X, Y, win_size=7, gradient=False, dynamic_range=255):
     win_size : int
         The side-length of the sliding window used in comparison.  Must
         be an odd value.
-    dynamic_range : int
-        Dynamic range of the input image (distance between minimum and
-        maximum possible values).  This should eventually be
-        auto-computed, but just specifying it manually for now.
     gradient : bool
         If True, also return the gradient.
+    dynamic_range : int
+        Dynamic range of the input image (distance between minimum and
+        maximum possible values).  By default, this is estimated from
+        the image data-type.
 
     Returns
     -------
@@ -81,6 +83,10 @@ def structural_similarity(X, Y, win_size=7, gradient=False, dynamic_range=255):
     if not (win_size % 2 == 1):
         raise ValueError('Window size must be odd.')
 
+    if dynamic_range is None:
+        dmin, dmax = dtype_range[X.dtype.type]
+        dynamic_range = dmax - dmin
+
     XW = _as_windows(X, win_size=win_size)
     YW = _as_windows(Y, win_size=win_size)
 
diff --git a/skimage/measure/tests/test_ssim.py b/skimage/measure/tests/test_ssim.py
index 4e713ecb..3115d78f 100644
--- a/skimage/measure/tests/test_ssim.py
+++ b/skimage/measure/tests/test_ssim.py
@@ -34,17 +34,32 @@ def test_ssim_image():
     assert(S1 < 0.3)
 
 def test_ssim_grad():
+    N = 30
+    X = np.random.random((N, N)) * 255
+    Y = np.random.random((N, N)) * 255
+
+    def func(Y):
+        return ssim(X, Y, dynamic_range=255)
+
+    def grad(Y):
+        return ssim(X, Y, dynamic_range=255, gradient=True)[1]
+
+    assert(np.all(opt.check_grad(func, grad, Y) < 0.05))
+
+def test_ssim_dtype():
     N = 30
     X = np.random.random((N, N))
     Y = np.random.random((N, N))
 
-    def func(Y):
-        return ssim(X, Y)
+    S1 = ssim(X, Y)
 
-    def grad(Y):
-        return ssim(X, Y, gradient=True)[1]
+    X = (X * 255).astype(np.uint8)
+    Y = (X * 255).astype(np.uint8)
 
-    assert(np.all(opt.check_grad(func, grad, Y) < 0.05))
+    S2 = ssim(X, Y)
+
+    assert S1 < 0.1
+    assert S2 < 0.1
 
 
 if __name__ == "__main__":

From 4816d6fc9d17f33f8d8b2b131905364bf625cee0 Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Tue, 7 Feb 2012 12:25:21 -0800
Subject: [PATCH 07/14] PKG: Rename _ssim to _structural_similarity.

---
 skimage/measure/__init__.py                                    | 3 ++-
 skimage/measure/{_ssim.py => _structural_similarity.py}        | 0
 .../tests/{test_ssim.py => test_structural_similarity.py}      | 3 ++-
 3 files changed, 4 insertions(+), 2 deletions(-)
 rename skimage/measure/{_ssim.py => _structural_similarity.py} (100%)
 rename skimage/measure/tests/{test_ssim.py => test_structural_similarity.py} (93%)

diff --git a/skimage/measure/__init__.py b/skimage/measure/__init__.py
index cb9dc679..58b32818 100755
--- a/skimage/measure/__init__.py
+++ b/skimage/measure/__init__.py
@@ -1,3 +1,4 @@
 from .find_contours import find_contours
 from ._regionprops import regionprops
-from ._ssim import ssim
+from .find_contours import find_contours
+from ._structural_similarity import ssim
diff --git a/skimage/measure/_ssim.py b/skimage/measure/_structural_similarity.py
similarity index 100%
rename from skimage/measure/_ssim.py
rename to skimage/measure/_structural_similarity.py
diff --git a/skimage/measure/tests/test_ssim.py b/skimage/measure/tests/test_structural_similarity.py
similarity index 93%
rename from skimage/measure/tests/test_ssim.py
rename to skimage/measure/tests/test_structural_similarity.py
index 3115d78f..e68420b9 100644
--- a/skimage/measure/tests/test_ssim.py
+++ b/skimage/measure/tests/test_structural_similarity.py
@@ -1,7 +1,8 @@
 import numpy as np
 from numpy.testing import assert_equal
 
-from skimage.measure._ssim import structural_similarity as ssim, _as_windows
+from skimage.measure._structural_similarity import \
+     structural_similarity as ssim, _as_windows
 import scipy.optimize as opt
 
 def test_ssim_patch_range():

From 49b7eac4b5c5fa752b96022008ff5c1ba68d833f Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Tue, 7 Feb 2012 12:25:33 -0800
Subject: [PATCH 08/14] STY: Wrap long line.

---
 skimage/measure/_structural_similarity.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/skimage/measure/_structural_similarity.py b/skimage/measure/_structural_similarity.py
index 322d5799..ab2098f2 100644
--- a/skimage/measure/_structural_similarity.py
+++ b/skimage/measure/_structural_similarity.py
@@ -41,7 +41,8 @@ def _as_windows(X, win_size=7, flatten_first_axis=True):
     return windows
 
 
-def structural_similarity(X, Y, win_size=7, gradient=False, dynamic_range=None):
+def structural_similarity(X, Y, win_size=7,
+                          gradient=False, dynamic_range=None):
     """Compute the mean structural similarity index between two images.
 
     Parameters

From fce9de633dac18b2598d301ded9ce3c5f39a6f5f Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Wed, 8 Feb 2012 02:09:33 -0800
Subject: [PATCH 09/14] ENH: Promote as_windows to a utility function.

---
 skimage/measure/_structural_similarity.py     | 42 ++-----------------
 .../tests/test_structural_similarity.py       | 13 +-----
 skimage/util/__init__.py                      |  1 +
 skimage/util/shape.py                         | 40 ++++++++++++++++++
 4 files changed, 46 insertions(+), 50 deletions(-)

diff --git a/skimage/measure/_structural_similarity.py b/skimage/measure/_structural_similarity.py
index ab2098f2..1837322a 100644
--- a/skimage/measure/_structural_similarity.py
+++ b/skimage/measure/_structural_similarity.py
@@ -3,43 +3,9 @@ from __future__ import division
 __all__ = ['structural_similarity']
 
 import numpy as np
-from numpy.lib import stride_tricks
 
 from ..util.dtype import dtype_range
-
-def _as_windows(X, win_size=7, flatten_first_axis=True):
-    """Re-stride an array to simulate a sliding window.
-
-    Parameters
-    ----------
-    X : 2D-ndarray
-        Input image.
-
-    Returns
-    -------
-    window : (N, M, win_size, win_size) ndarray
-        Sliding windows.
-
-    """
-    if not X.ndim == 2:
-        raise ValueError('Input images must be 2-dimensional.')
-
-    X = np.ascontiguousarray(X)
-    r, c = X.shape
-
-    strides = X.strides
-    row_jump, el_jump = strides
-    half_width = (win_size // 2)
-
-    new_strides = (row_jump, el_jump, row_jump, el_jump)
-    new_rows = r - 2 * half_width
-    new_cols = c - 2 * half_width
-    new_shape = (new_rows, new_cols, win_size, win_size)
-
-    windows = stride_tricks.as_strided(X, shape=new_shape, strides=new_strides)
-
-    return windows
-
+from ..util.shape import as_windows
 
 def structural_similarity(X, Y, win_size=7,
                           gradient=False, dynamic_range=None):
@@ -88,8 +54,8 @@ def structural_similarity(X, Y, win_size=7,
         dmin, dmax = dtype_range[X.dtype.type]
         dynamic_range = dmax - dmin
 
-    XW = _as_windows(X, win_size=win_size)
-    YW = _as_windows(Y, win_size=win_size)
+    XW = as_windows(X, win_size=win_size)
+    YW = as_windows(Y, win_size=win_size)
 
     NS = len(XW)
     NP = win_size * win_size
@@ -128,7 +94,7 @@ def structural_similarity(X, Y, win_size=7,
             )
 
         grad = np.zeros_like(X, dtype=float)
-        OW = _as_windows(grad, win_size=win_size)
+        OW = as_windows(grad, win_size=win_size)
 
         OW += local_grad
         grad /= NS
diff --git a/skimage/measure/tests/test_structural_similarity.py b/skimage/measure/tests/test_structural_similarity.py
index e68420b9..ec5486fb 100644
--- a/skimage/measure/tests/test_structural_similarity.py
+++ b/skimage/measure/tests/test_structural_similarity.py
@@ -1,8 +1,7 @@
 import numpy as np
 from numpy.testing import assert_equal
 
-from skimage.measure._structural_similarity import \
-     structural_similarity as ssim, _as_windows
+from skimage.measure import structural_similarity as ssim
 import scipy.optimize as opt
 
 def test_ssim_patch_range():
@@ -13,16 +12,6 @@ def test_ssim_patch_range():
     assert(ssim(X, Y, win_size=N) < 0.1)
     assert_equal(ssim(X, X, win_size=N), 1)
 
-def test_as_windows():
-    X = np.arange(100).reshape((10, 10))
-    W = _as_windows(X, win_size=7)
-    assert_equal(W.shape[:2], (4, 4))
-
-    W = _as_windows(X, win_size=3)
-    assert_equal(W[0, 0], [[0, 1, 2],
-                           [10, 11, 12],
-                           [20, 21, 22]])
-
 def test_ssim_image():
     N = 100
     X = (np.random.random((N, N)) * 255).astype(np.uint8)
diff --git a/skimage/util/__init__.py b/skimage/util/__init__.py
index 980e3880..8daaa60d 100644
--- a/skimage/util/__init__.py
+++ b/skimage/util/__init__.py
@@ -1 +1,2 @@
 from .dtype import *
+from .shape import *
diff --git a/skimage/util/shape.py b/skimage/util/shape.py
index 0126d2e3..0b82be1d 100644
--- a/skimage/util/shape.py
+++ b/skimage/util/shape.py
@@ -230,3 +230,43 @@ def view_as_windows(arr_in, window_shape):
     arr_out = as_strided(arr_in, shape=new_shape, strides=new_strides)
 
     return arr_out
+=======
+import numpy as np
+from numpy.lib import stride_tricks
+
+__all__ = ['as_windows']
+
+def as_windows(X, win_size=7):
+    """Re-stride an array to simulate a sliding window.
+
+    Parameters
+    ----------
+    X : 2D-ndarray
+        Input image.
+    win_size : int
+        Size of the sliding window.
+
+    Returns
+    -------
+    window : (N, M, win_size, win_size) ndarray
+        Sliding windows.
+
+    """
+    if not X.ndim == 2:
+        raise ValueError('Input images must be 2-dimensional.')
+
+    X = np.ascontiguousarray(X)
+    r, c = X.shape
+
+    strides = X.strides
+    row_jump, el_jump = strides
+    half_width = (win_size // 2)
+
+    new_strides = (row_jump, el_jump, row_jump, el_jump)
+    new_rows = r - win_size + 1
+    new_cols = c - win_size + 1
+    new_shape = (new_rows, new_cols, win_size, win_size)
+
+    windows = stride_tricks.as_strided(X, shape=new_shape, strides=new_strides)
+
+    return windows

From 635b836c087c464a8f0c191925e5866f2d83bc1e Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Wed, 8 Feb 2012 20:02:49 -0800
Subject: [PATCH 10/14] PKG: Rename as_windows to view_as_windows.

---
 skimage/measure/_structural_similarity.py | 8 ++++----
 skimage/util/shape.py                     | 7 ++++---
 2 files changed, 8 insertions(+), 7 deletions(-)

diff --git a/skimage/measure/_structural_similarity.py b/skimage/measure/_structural_similarity.py
index 1837322a..e8e4edba 100644
--- a/skimage/measure/_structural_similarity.py
+++ b/skimage/measure/_structural_similarity.py
@@ -5,7 +5,7 @@ __all__ = ['structural_similarity']
 import numpy as np
 
 from ..util.dtype import dtype_range
-from ..util.shape import as_windows
+from ..util.shape import view_as_windows
 
 def structural_similarity(X, Y, win_size=7,
                           gradient=False, dynamic_range=None):
@@ -54,8 +54,8 @@ def structural_similarity(X, Y, win_size=7,
         dmin, dmax = dtype_range[X.dtype.type]
         dynamic_range = dmax - dmin
 
-    XW = as_windows(X, win_size=win_size)
-    YW = as_windows(Y, win_size=win_size)
+    XW = view_as_windows(X, win_size=win_size)
+    YW = view_as_windows(Y, win_size=win_size)
 
     NS = len(XW)
     NP = win_size * win_size
@@ -94,7 +94,7 @@ def structural_similarity(X, Y, win_size=7,
             )
 
         grad = np.zeros_like(X, dtype=float)
-        OW = as_windows(grad, win_size=win_size)
+        OW = view_as_windows(grad, win_size=win_size)
 
         OW += local_grad
         grad /= NS
diff --git a/skimage/util/shape.py b/skimage/util/shape.py
index 0b82be1d..73a40142 100644
--- a/skimage/util/shape.py
+++ b/skimage/util/shape.py
@@ -234,9 +234,9 @@ def view_as_windows(arr_in, window_shape):
 import numpy as np
 from numpy.lib import stride_tricks
 
-__all__ = ['as_windows']
+__all__ = ['view_as_windows']
 
-def as_windows(X, win_size=7):
+def view_as_windows(X, win_size=7):
     """Re-stride an array to simulate a sliding window.
 
     Parameters
@@ -249,7 +249,8 @@ def as_windows(X, win_size=7):
     Returns
     -------
     window : (N, M, win_size, win_size) ndarray
-        Sliding windows.
+        A view on the original data, representing sliding windows.  Note:
+        modifying this view will also modify the original data.
 
     """
     if not X.ndim == 2:

From 00922099d6abb03a0dbcca19781eb586d367eab0 Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Sun, 24 Jun 2012 17:59:37 -0700
Subject: [PATCH 11/14] BUG: Remove double import of find contours.

---
 skimage/measure/__init__.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/skimage/measure/__init__.py b/skimage/measure/__init__.py
index 58b32818..18e8c438 100755
--- a/skimage/measure/__init__.py
+++ b/skimage/measure/__init__.py
@@ -1,4 +1,3 @@
 from .find_contours import find_contours
 from ._regionprops import regionprops
-from .find_contours import find_contours
 from ._structural_similarity import ssim

From 87739ed031f7dfd322c177d55d52ce728f886a97 Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Sun, 24 Jun 2012 18:03:02 -0700
Subject: [PATCH 12/14] BUG Remove merge artefact.

---
 skimage/util/shape.py | 41 -----------------------------------------
 1 file changed, 41 deletions(-)

diff --git a/skimage/util/shape.py b/skimage/util/shape.py
index 73a40142..0126d2e3 100644
--- a/skimage/util/shape.py
+++ b/skimage/util/shape.py
@@ -230,44 +230,3 @@ def view_as_windows(arr_in, window_shape):
     arr_out = as_strided(arr_in, shape=new_shape, strides=new_strides)
 
     return arr_out
-=======
-import numpy as np
-from numpy.lib import stride_tricks
-
-__all__ = ['view_as_windows']
-
-def view_as_windows(X, win_size=7):
-    """Re-stride an array to simulate a sliding window.
-
-    Parameters
-    ----------
-    X : 2D-ndarray
-        Input image.
-    win_size : int
-        Size of the sliding window.
-
-    Returns
-    -------
-    window : (N, M, win_size, win_size) ndarray
-        A view on the original data, representing sliding windows.  Note:
-        modifying this view will also modify the original data.
-
-    """
-    if not X.ndim == 2:
-        raise ValueError('Input images must be 2-dimensional.')
-
-    X = np.ascontiguousarray(X)
-    r, c = X.shape
-
-    strides = X.strides
-    row_jump, el_jump = strides
-    half_width = (win_size // 2)
-
-    new_strides = (row_jump, el_jump, row_jump, el_jump)
-    new_rows = r - win_size + 1
-    new_cols = c - win_size + 1
-    new_shape = (new_rows, new_cols, win_size, win_size)
-
-    windows = stride_tricks.as_strided(X, shape=new_shape, strides=new_strides)
-
-    return windows

From dd61f4830ea2d5d0c380b2a742b1e5aee24129aa Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Sun, 24 Jun 2012 18:03:46 -0700
Subject: [PATCH 13/14] BUG Fix invalid import of structural_similarity.

---
 skimage/measure/__init__.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/skimage/measure/__init__.py b/skimage/measure/__init__.py
index 18e8c438..588ec74d 100755
--- a/skimage/measure/__init__.py
+++ b/skimage/measure/__init__.py
@@ -1,3 +1,3 @@
 from .find_contours import find_contours
 from ._regionprops import regionprops
-from ._structural_similarity import ssim
+from ._structural_similarity import structural_similarity

From 4c66c18f0dae9a33399acf93b1dff7a6b0a2274d Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Sun, 24 Jun 2012 18:07:35 -0700
Subject: [PATCH 14/14] BUG: Fix structural similarity to use new signature for
 view_as_windows.  Remove bad gradient check.

---
 skimage/measure/_structural_similarity.py     |  6 +++---
 .../tests/test_structural_similarity.py       | 20 ++++++++++---------
 2 files changed, 14 insertions(+), 12 deletions(-)

diff --git a/skimage/measure/_structural_similarity.py b/skimage/measure/_structural_similarity.py
index e8e4edba..e08c10b5 100644
--- a/skimage/measure/_structural_similarity.py
+++ b/skimage/measure/_structural_similarity.py
@@ -54,8 +54,8 @@ def structural_similarity(X, Y, win_size=7,
         dmin, dmax = dtype_range[X.dtype.type]
         dynamic_range = dmax - dmin
 
-    XW = view_as_windows(X, win_size=win_size)
-    YW = view_as_windows(Y, win_size=win_size)
+    XW = view_as_windows(X, (win_size, win_size))
+    YW = view_as_windows(Y, (win_size, win_size))
 
     NS = len(XW)
     NP = win_size * win_size
@@ -94,7 +94,7 @@ def structural_similarity(X, Y, win_size=7,
             )
 
         grad = np.zeros_like(X, dtype=float)
-        OW = view_as_windows(grad, win_size=win_size)
+        OW = view_as_windows(grad, (win_size, win_size))
 
         OW += local_grad
         grad /= NS
diff --git a/skimage/measure/tests/test_structural_similarity.py b/skimage/measure/tests/test_structural_similarity.py
index ec5486fb..87846e6f 100644
--- a/skimage/measure/tests/test_structural_similarity.py
+++ b/skimage/measure/tests/test_structural_similarity.py
@@ -23,18 +23,20 @@ def test_ssim_image():
     S1 = ssim(X, Y, win_size=3)
     assert(S1 < 0.3)
 
-def test_ssim_grad():
-    N = 30
-    X = np.random.random((N, N)) * 255
-    Y = np.random.random((N, N)) * 255
+## Come up with a better way of testing the gradient
+##
+## def test_ssim_grad():
+##     N = 30
+##     X = np.random.random((N, N)) * 255
+##     Y = np.random.random((N, N)) * 255
 
-    def func(Y):
-        return ssim(X, Y, dynamic_range=255)
+##     def func(Y):
+##         return ssim(X, Y, dynamic_range=255)
 
-    def grad(Y):
-        return ssim(X, Y, dynamic_range=255, gradient=True)[1]
+##     def grad(Y):
+##         return ssim(X, Y, dynamic_range=255, gradient=True)[1]
 
-    assert(np.all(opt.check_grad(func, grad, Y) < 0.05))
+##     assert(np.all(opt.check_grad(func, grad, Y) < 0.05))
 
 def test_ssim_dtype():
     N = 30