CODEWITHSUNDEEP
pythongradientmaskconvolution
no_name
no_name

Reputation: 1375

Gradient computation by convolution masks

I need to compute the gradient of a matrix (3,3), say a=array([[1,4,2],[6,2,4],[7,5,1]]).

I simply use:

from numpy import *
dx,dy = gradient(a)
>>> dx
   array([[ 5. , -2. ,  2. ],
   [ 3. ,  0.5, -0.5],
   [ 1. ,  3. , -3. ]])
>>> dy
array([[ 3. ,  0.5, -2. ],
   [-4. , -1. ,  2. ],
   [-2. , -3. , -4. ]])

I know that a way for computing the gradient of a matrix is by convolution with a mask for each direction, but results are different

from scipy import ndimage
mx=array([[-1,0,1],[-1,0,1],[-1,0,1]])
my=array([[-1,-1,-1],[0,0,0],[1,1,1]])
cx=ndimage.convolve(a,mx)
cy=ndimage.convolve(a,my)
>>> cx
array([[-2,  0,  2],
   [ 3,  7,  4],
   [ 8, 14,  6]])
>>> cy
array([[ -8,  -5,  -2],
   [-13,  -6,   1],
   [ -5,  -1,   3]])

Where is the error?

Upvotes: 2

Views: 3207

Answers (1)

Oliver Charlesworth
Oliver Charlesworth

Reputation: 272527

With an image this small (3x3), all but the centre pixel are going to be subject to boundary conditions, making the results pretty meaningless.

But anyway, a quick look at the documentation for numpy.gradient reveals:

The gradient is computed using central differences in the interior and first differences at the boundaries.

In other words, it doesn't use a fixed convolution kernel across the entire image. It sounds like it simply does (array(i+1,j) - array(i-1,j)) / 2 for interior points, and (array(i,j) - array(i-1,j) for boundary points.

Upvotes: 5

Related Questions