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Questions tagged [separability]

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21
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4answers
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Fast/efficient way to decompose separable integer 2D filter coefficients

I would like to be able to quickly determine whether a given 2D kernel of integer coefficients is separable into two 1D kernels with integer coefficients. E.g. ...
7
votes
1answer
3k views

Why does the separable filter reduce the cost of computing the operator?

A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into 2 onedimensional filters. This reduces ...
1
vote
1answer
2k views

How to find out if a transform matrix is separable?

In image processing, when we have a series of basis images, how could we know if the transformation is separable or not? For example, I know that following bases are separable and transformation can ...
1
vote
2answers
5k views

How to Prove a 2D Filter Is Separable?

I want to prove that 2D Gaussian filter is separable and we can separate it into two dimensions, my problem is about the size of filters. we should prove that $G(x,y)*I$(where $G(x,y)=$$\begin{bmatrix}...
1
vote
1answer
2k views

How does a separable filter work?

I am new to signal processing, and was reading about filters. I came upon the sobel filter which has the following forms, From what I understand to apply this filter to a 2-d signal, place the ...