Question

I’m trying to calculate a 3d sobel filter in python. I have a pretty good code for 2d image which is below.

btw. my original image is uint8 type.

    preSobel = preSobel.astype('int32')
    dx = ndimage.sobel(preSobel, 0)  # horizontal derivative
    dy = ndimage.sobel(preSobel, 1)  # vertical derivative
    mag = numpy.hypot(dx, dy)  # magnitude
    mag *= 255.0 / numpy.max(mag)  # normalize (Q&D)
    img[i,:,:]=mag

but from my understanding of the wiki page for calculating 2d, i should have multiplied the 1d sobel results rather than hypot :confused

anyway, to go to 3d, I guess I need to calculate 1d sobel on each axis and then multiply all but I’m not sure… Is there any library out there that calculates 3d sobel faster ?

Answer 1

First, in reference to your wikipedia link: The multiplication there is referring to the way to construct the sobel convolution kernel, not the end result.

For a 2D sobel filter you need a kernel to get the derivate in x direction, and another kernel to get the derivate in Y direction, e.g.

This is essentially what your two commands do, so if you are using numpy you do not need to construct these kernels yourself.

dx = ndimage.sobel(preSobel, 0)  # horizontal derivative
dy = ndimage.sobel(preSobel, 1)  # vertical derivative

Now for the 3D case you need 3 operations with 3 kernels, one for dx, dy, dz.
The linked wiki section is telling you how to construct the kernels by multiplying components. The finished sobel kernel for dZ for example is a 3x3x3 matrix that looks like this:

To get the magnitude you still have to take the square root of the squared derivatives (the hypotenuse) afterwards.

I do not have numpy but as far as I can tell from the documentation the ndimage sobel command can deal with any number of dimensions, so again, the kernels are already provided:

dx = ndimage.sobel(your3Dmatrix, 0)  # x derivative
dy = ndimage.sobel(your3Dmatrix, 1)  # y derivative
dz = ndimage.sobel(your3Dmatrix, 2)  # z derivative

now the hypotenuse command probably only take 2 parameters, so you will have to find another way to efficiently calculate mag = sqrt(dxdx + dydy + dz*dz) .
But NumPy should have everything you need for that.

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Update

Actually, if you are only interested in the magnitude anyway, there is a complete function in numpy for this:

 mag = generic_gradient_magnitude(your3Dmatrix, sobel)