The main issue of complexity is convolution

Question

I am trying to appreciate the complexity of some basic image filtering algorithms. I was wondering if you can test this theory,

For a basic pixel-pixel filter, such as Inverse, the number of operations grows linearly with the input size (in pixels) and

Let S = image side length; Let M = # pixel input

The converse is of order O (M) or O (S ^ 2).

On the other hand, the convolution filter has a parameter R, which determines the size of the neighborhood for convolution when setting the next pixel value for each filter.

Let R = Convolution Filter Radius

The convolution has the order O (M * ((R + R * 2) ^ 2) = O (M * (4R ^ 2) = O (MR ^ 2)

Or should I allow N = the size of the convolution filter (neighborhood) in pixels?

O (M * (N)) = O (MN)

Ultimately, the convolution filter linearly depends on the product of the number of pixels and the number of pixels in the neighborhood.

If you have links to paper where this has been documented, we will be very grateful.

Yours faithfully,

Gavin

Answer 1

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, , , O (MN) .

P, P, ( , ), .