roberts.py

# Robert's Kernel

import numpy as np
import matplotlib.pyplot as plt
import scipy.misc as misc
from scipy import signal

def show_images(image1, image2, title1, title2):
    f, a = plt.subplots(1, 2)
    a[0].imshow(image1, cmap='gray')
    a[0].set_title(title1)
    a[1].imshow(image2, cmap='gray')
    a[1].set_title(title2)
    plt.show()

def convolve(x, h):
    # We are implementing graphical method.
    # We first need to find the rows and cols of both the matrices
    # as follows
    (row1, col1) = x.shape
    (row2, col2) = h.shape

    # Dimension of output matrix A is given by
    # (number of rows of x + number of rows h - 1) x (number of cols of x + number of cols of h - 1)
    # So we can define an array to store output values with that dimension
    a = np.zeros((row1 + row2 - 1, col1 + col2 - 1))

    # Now, find h(-m, -n)
    h = h[::-1,::-1]

    # Add padding zeros around the x matrix.
    # This step is a bit confusing
    b = np.lib.pad(x, [(row2 - 1, row2 - 1), (col2 - 1, col2 - 1)], mode='constant')

    for i in range(row1 + row2 - 1):
        for j in range(col1 + col2 - 1):
            k = b[i:i+row2, j:j+col2]
            temp = k * h
            a[i, j] = np.sum(temp)

    return a

image = misc.imread('lena.jpg')

# Define the kernels
kernel_x = np.array([[-1, 0], [0, 1]])
kernel_y = np.array([[0, -1], [1, 0]])

# Get the Gx and Gy, the horizontal and vertical derivative components
gx = convolve(image, kernel_x)
gy = convolve(image, kernel_y)

output_image = np.sqrt(gx * gx + gy * gy)
output_image *= 255.0 / np.max(output_image)

show_images(image, output_image, "Image", "Robert's Convolved Image")