# convolution.py

# -------------------------------------------------------------------------

# This script creates an eLoG (elongated Laplacian of Gaussian) filter that

# emphasizes long, vertical lines in a figure. The effect of the filter is

# demonstrated on a plus sign.

# -------------------------------------------------------------------------

import numpy as np

import matplotlib.pyplot as plt

import scipy.ndimage as sim

#%% Create a grid of points for the Gaussian filter.

v = np.arange(-25, 26)

X, Y = np.meshgrid(v, v)

#%% Create elongated Gaussian filter, apply Laplacian.

gauss_filter = np.exp(-0.5*(X**2/2 + Y**2/45))

laplace_filter = np.array( [[0, -1, 0], [-1, 4, -1], [0, -1, 0]])

combined_filter = sim.convolve(gauss_filter, laplace_filter)

#%% Create a plus sign '+' to demonstrate effect of filter.

plus = np.zeros((51, 51))

plus[23:28, 25] = 1.0

plus[25, 23:28] = 1.0

plt.figure()

plt.imshow(plus)

plt.gray()

#%% Apply filter to '+' and display resulting image.

# Use vmin/vmax to emphasize features within a restricted range of intensity.

cplus = sim.convolve(plus, combined_filter)

plt.figure()

plt.imshow(cplus, vmin=0, vmax=0.5*cplus.max())

plt.gray()

plt.show()