Gradient for Color Image in Python

Question

I am trying to determine the gradient image of a color image using skimage in python.

The method I am following is:

1) For each of the RGB bands calculate the gradient for each band. This results in 6 arrays, 2 for each color band. Each color band has a gradient in both x and y directions. (2 directions x 3 colors = 6 arrays).

2) To determine the gradient of the image, calculating the magnitude of each of the color bands as:

Gradient = ((Rx^2 + Ry^2) + (Gx^2 + Gy^2) + (Bx^2 + By^2))^0.5

But the result is very noisy and the gradient is unclear.

import numpy as np
import matplotlib.pyplot as plt
import scipy.ndimage as nd
import skimage.data as dt

img = dt.astronaut()

def gradient(img, x = True, y = True):

      f1 = np.array([[-1,-2,-1], [0,0,0], [1,2,1]])
      f2 = np.array([[-1,-2,-1], [0,0,0], [1,2,1]]).T

      vert_gradient =nd.correlate(img, f1)
      horz_gradient =nd.correlate(img, f2)

      if x:
          return(horz_gradient)
      else:
          return (vert_gradient)

Rx = gradient(img[:,:,0], y = False)
Ry = gradient(img[:,:,0], x = False)
Gx = gradient(img[:,:,1], y = False)
Gy = gradient(img[:,:,1], x = False)
Bx = gradient(img[:,:,2], y = False)
By = gradient(img[:,:,2], x = False)

grad = np.sqrt(np.square(Rx) + np.square(Ry)) + np.sqrt(np.square(Gx) +        np.square(Gy)) + np.sqrt(np.square(Bx) + np.square(By))
grad = ((grad - grad.min()) / (grad.max() - grad.min())) * 255 # rescale for full dynamic range for 8 bit image
grad = grad.astype(np.uint8)

plt.subplot(1,2,1)
plt.imshow(img)
plt.subplot(1,2,2)
plt.imshow(grad)
plt.show()

In the gradient image we can see the color gradients, but they are not so clear and there is a lot of noise.

I have also tried smoothing out the noise on each color band before calculating the gradient.

How to improve this result without using OpenCv?

Answer 1

Find each channel's gradient separately like this

gradR = np.sqrt(np.square(Rx) + np.square(Ry))
gradG = np.sqrt(np.square(Gx) + np.square(Gy))
gradB = np.sqrt(np.square(Bx) + np.square(By))

make a new image

grad = np.dstack((gradR,gradG,gradB))