Ndtyjky

I'm looking to differentiate my image, first by rows, and then separately, by columns.

A derivative is given as f[i+1]-f[i] where i is the pixel, f is the value/intensity of that pixel.

I was taught that this can be done by convolution - with d/dx convolving with (1,0,-1) as a row vector, and d/dy as the same vector but in column form.

My question is - when convolving in python using scipy.signal.convolve2D, with mode = 'same', convolving with those vectors, I am getting different results than that of numpy.diff.

Say for a 3x3 matrix:

5 4 3



2 1 1 



3 2 5

Convolving with (1,0,-1) gives me

-4 2 4



-1 1 1



-2 -2 2

While numpy's diff gives me:

-3 -3 -2



 1  1  4

The questions I have are as follows:

1.) When convolving a NxN image with a kernel such as (1,0,-1), does the function convolve every row by the vector?

2.) Why are my results different? I understand the shapes are different, with the numpy's result having one more row, but I can understand that since it doesn't include the original row 0

def deriv(image):

    """

    :param im: 2D image

    :return: magnitude of the derivative

    """

    #Horizontal Derivative

    dx = convolve2d(im, DX, mode='same')

    print('dx', dx)

    #Vertical Derivative

    dy = convolve2d(im, DY, mode='same')

    print('dy', dy)

    magnitude = np.sqrt(np.abs(dx)**TWO + np.abs(dy)**TWO)

    return magnitude

The prints are just for me to check their values before the magnitude is calculated.

DX = (1,0,-1)

DY = (1,0,-1) as a column vector