Re: 2D Convolution
- To: mathgroup at smc.vnet.net
- Subject: [mg76154] Re: 2D Convolution
- From: Joseph Gwinn <joegwinn at comcast.net>
- Date: Thu, 17 May 2007 05:50:27 -0400 (EDT)
- References: <f29389$m7p$1@smc.vnet.net> 29bbo$ppn$11smccvnee.neee <f2emb3$2qn$1@smc.vnet.net>
In article <f2emb3$2qn$1 at smc.vnet.net>, CKWong <CKWong.P at gmail.com>
wrote:
> You need to re-define your Convolve like this:
>
> Convolve[f_, g_, x_?NumberQ, y_?NumberQ] := NIntegrate[f[
> xPrime, yPrime] *g[x - xPrime,
> y - yPrime], {xPrime, -=A1=DB, =A1=DB}, {yPrime, -=A1=DB, =A1=DB}]
>
> When calling Convolve, remember to place the kernel as the first
> function, e.g.,
>
> Convolve[Gaussian2D, SHole, 0, 0]
>
> You can plot the convolution like this:
>
> Plot3D[Convolve[Gaussian2D, SHole, x, y] // Evaluate, {x, -HoleSize,
> HoleSize}, {y, -HoleSize, HoleSize}]
>
> However, this scheme is too slow for the round hole, for which case,
> it's better to switch to polar coordinates so that the angular part
> can be integrated by hand.
An alternative is to implement convolution using 2D Fourier and
InverseFourier. This may be faster, at least for large kernels and/or
strange hole shapes.
Joe Gwinn