Add integrate function to shared package

skimage/_shared/transform.pyx

@@ -0,0 +1,45 @@
+#cython: cdivison=True
+#cython: boundscheck=False
+#cython: nonecheck=False
+#cython: wraparound=False
+cimport numpy as cnp
+import numpy as np
+
+
+cdef float integrate(cnp.ndarray[float, ndim=2,  mode="c"] sat,
+                     int r0, int c0, int r1, int c1):
+    """
+    Using a summed area table / integral image, calculate the sum
+    over a given window.
+
+    This function is the same as the `integrate` function in
+    `skimage.transform.integrate`, but this Cython version significantly
+    speeds up the code.
+
+    Parameters
+    ----------
+    sat : ndarray of float
+        Summed area table / integral image.
+    r0, c0 : int
+        Top-left corner of block to be summed.
+    r1, c1 : int
+        Bottom-right corner of block to be summed.
+
+    Returns
+    -------
+    S : int
+        Sum over the given window.
+    """
+    cdef float S = 0
+
+    S += sat[r1, c1]
+
+    if (r0 - 1 >= 0) and (c0 - 1 >= 0):
+        S += sat[r0 - 1, c0 - 1]
+
+    if (r0 - 1 >= 0):
+        S -= sat[r0 - 1, c1]
+
+    if (c0 - 1 >= 0):
+        S -= sat[r1, c0 - 1]
+    return S