Gaussian Kernel and Derivative of Gaussian Kernel

kernels/kernels.py

@@ -0,0 +1,78 @@
+from skimage import io
+
+import numpy
+from PIL import Image
+from scipy import signal, array
+
+from numpy import mgrid, exp
+
+
+def gauss_kernel(size, size_y=None):
+    """ Returns a normalized 2D gauss kernel array for convolutions """
+    size = int(size)
+    if not size_y:
+        size_y = size
+    else:
+        size_y = int(size_y)
+
+    x, y = mgrid[-size: size + 1, -size_y: size_y + 1]
+
+    g = exp(-(x ** 2 / float(size) + y ** 2 / float(size_y)))
+    return g / g.sum()
+
+
+def gauss_derivative_kernels(size, size_y=None):
+    """ returns x and y derivatives of a 2D
+        gauss kernel array for convolutions """
+    size = int(size)
+    if not size_y:
+        size_y = size
+    else:
+        size_y = int(size_y)
+    y, x = mgrid[-size: size + 1, -size_y: size_y + 1]
+
+    # x and y derivatives of a 2D gaussian with standard dev half of size
+    # (ignore scale factor)
+    gx = - x * exp(-(x ** 2 / float((0.5 * size) ** 2) + y ** 2 / float((0.5 * size_y) ** 2)))
+    gy = - y * exp(-(x ** 2 / float((0.5 * size) ** 2) + y ** 2 / float((0.5 * size_y) ** 2)))
+
+    return gx, gy
+
+
+def gauss_derivatives(im, n, ny=None):
+    """ returns x and y derivatives of an image using gaussian
+        derivative filters of size n. The optional argument
+        ny allows for a different size in the y direction."""
+
+    gx, gy = gauss_derivative_kernels(n, size_y=ny)
+
+    imx = signal.convolve(im, gx, mode='same')
+    imy = signal.convolve(im, gy, mode='same')
+
+    return imx, imy
+
+
+if __name__ == '__main__':
+    im = array(
+        Image.open('path_to_original_image').convert('L')
+    )
+
+    # Calculate the derivatives in x and y axis
+    # using the gauss derivative.
+    # You change the window size.
+    x, y = gauss_derivatives(im, 3)
+
+    x_min = x.min()
+    x_max = x.max()
+
+    x_final = (x - x_min) / (x_max - x_min)
+
+    y_min = y.min()
+    y_max = y.max()
+
+    y_final = (y - y_min) / (y_max - y_min)
+
+    # Concat the x and y derivative images
+    combined = numpy.concatenate((x_final, y_final), axis=1)
+
+    io.imsave('path_to_new_image', combined)

requirements.txt

@@ -1 +1,10 @@
+dask==0.12.0
+decorator==4.0.10
+networkx==1.11
 numpy==1.11.2
+Pillow==3.4.2
+scikit-image==0.12.3
+scikit-learn==0.18
+scipy==0.18.1
+six==1.10.0
+toolz==0.8.0