improc ass4: Fixed function for Gaussian filter.

improc/ass4/canny.py

 #!/usr/bin/env python
 from matplotlib.pyplot import imread, imshow, subplot, show
-from numpy import arctan2, zeros, append, pi#, argmax
+from numpy import arctan2, zeros, append, pi
 from numpy.linalg import norm
 from scipy.ndimage import convolve1d
 from gauss import Gauss1, gD
@@ -9,11 +9,6 @@ def in_image(p, F):
     """Check if given pixel coordinates p are within the bound of image F."""
     return p[0] >= 0 and p[1] >= 0 and p[0] < F.shape[0] and p[1] < F.shape[1]
 
-#def zero_crossing(a, b, F):
-#    """Cech if there is a zero crossing point between F[a] and F[b]."""
-#    return in_image(a, F) and in_image(b, F) \
-#            and ((F[a] < 0 and F[b] > 0) or (F[a] > 0 and F[b] < 0))
-
 def canny(F, s, Tl=None, Th=None):
     """Apply the Canny Edge Detection algorithm with Gauss scale s to an
     image F. Optionally specify a low and high threshold (Tl and Th) for
@@ -36,20 +31,6 @@ def canny(F, s, Tl=None, Th=None):
             G[p] = norm(append(Gx[p], Gy[p]))
             A[p] = int(round(arctan2(Gy[p], Gx[p]) * 4 / pi + 1)) % 4
 
-            #p = (x, y)
-            #compare = [(x, y - 1), (x, y + 1), (x + 1, y - 1), \
-            #           (x - 1, y + 1), (x - 1, y), (x + 1, y), \
-            #           (x - 1, y - 1), (x + 1, y + 1)]
-            #norms = zeros(8)
-
-            #for i, c in enumerate(compare):
-            #    if zero_crossing(p, c, F):
-            #        norms[i] = abs(F[p]) + abs(F[c])
-
-            #m = argmax(norms)
-            #G[p] = norms[m]
-            #A[p] = m >> 1
-
     # Non-maximum suppression
     E = zeros(F.shape)
 

improc/ass4/gauss.py

 #!/usr/bin/env python
-from numpy import zeros, arange, pi, e, ceil, meshgrid, array, dot
+from numpy import zeros, arange, meshgrid, array, dot
+from math import ceil, exp, pi, sqrt
 from matplotlib.pyplot import imread, imshow, plot, xlabel, ylabel, show, \
         subplot, xlim, savefig
 from mpl_toolkits.mplot3d import Axes3D
@@ -30,14 +31,14 @@ def Gauss(s):
     return W / W.sum()
 
 def f_gauss(x, s):
-    return e ** -(x ** 2 / (2 * s ** 2)) / (2 * pi * s ** 2)
+    return exp(-(x ** 2 / (2 * s ** 2))) / (sqrt(2 * pi) * s)
 
 def f_gauss_der_1(x, s):
-    return -x * e ** -(x ** 2 / (2 * s ** 2)) / (2 * pi * s ** 4)
+    return -x * exp(-(x ** 2 / (2 * s ** 2))) / (sqrt(2 * pi) * s ** 3)
 
 def f_gauss_der_2(x, s):
-    return (x ** 2 - s ** 2) * e ** -(x ** 2 / (2 * s ** 2)) \
-            / (2 * pi * s ** 6)
+    return (x ** 2 - s ** 2) * exp(-(x ** 2 / (2 * s ** 2))) \
+            / (sqrt(2 * pi) * s ** 5)
 
 def Gauss1(s, order=0):
     """Sample a one-dimensional Gaussian function of scale s."""