CODEWITHSUNDEEP
numpyscipy
bshanks
bshanks

Reputation: 1248

Inverse of n-dimensional numpy.gradient

Does numpy or scipy contain a function which is an inverse of the n-dimensional "gradient" fn?

E.g. if "image" contains a 2D matrix, then i want a function inv_gradient that behaves as follows:

(gx, gy) = numpy.gradient(image)
constant_vector_0 = image[0,:] - inv_gradient(gx, gy)[0,:]
constant_vector_1 = image[:,0] - inv_gradient(gx, gy)[:,0]
image == inv_gradient(gx, gy) + tile(constant_vector_0,(shape(image)[0],1)) + transpose(tile(constant_vector_1,(shape(image)[1],1)))

Upvotes: 2

Views: 1710

Answers (1)

tom10
tom10

Reputation: 69242

What you are describing is basically an inverse filter. These exist, but are limited.

One way to understand this is via the convolution theorem, and to think of the gradient as a particular kernel for a convolution, in this case something like (-1, 0, 1) in 1D. The issue then, is that the Fourier Transform (FT) of the kernel will have zeroes, and that when the FTs of the kernel and signal are multiplied, the zeroes in the kernel's FT wipes out any data from the original data in this part of the spectrum (and this gets more problematic when noise is added to the image). Specifically for the gradient, there is 0 power in the f=0 band, and this is what people are referring to in the comments, but other information is lost as well.

Still, though, you can get a lot out of an inverse filter, and maybe what you need. It's fairly case specific.

Here's a very basic and quick description of the issue, and an example (though not for gradients).

Upvotes: 3

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