Big Bird wrote:
>
> Maybe I'm thinking something completely wrong here somewhere but if my
> array is
>
> 1 0 0
> 0 0 0 ...
> 0 0 0
> .
> .
>
> and my convolution kernel is
>
> a b c
> d e f
> g h i
>
> then I would expect the convolution to be
>
> e f 0
> h i 0 ...
> 0 0 0
> .
> .
>
> At least for a symmetric kernel (I'd have to think about an
> unsymmetric one). I expect that because the fourier transform of a
> delta function is a constant (one) which is thus the multiplicative
> neutral element. And the fourier transform of a convolution of
> functions is the multiplication of the transforms of the functions
> themselves.
>
> The longer I stare at the help, the more confused I get trying to
> figure out whether the [0,0] element of the result should be zero, as
> it seems to have a condition attached that reads (at least on my
> screen with the font the help uses) "if t >= 1-1 and u >= 1-1" . And I
> really don't think either of these "ones" could be 'lower-case ell'
> even though they use an 'ell' in the sum but without apparent
> motivation (or at least they don't seem to say what 'ell' *is*).
>
> /edge_truncate goes in the vague direction
>
> /edge_truncate,center=0 gives me something I don't understand at all
>
> /edge_wrap does what it sounds like (which is not what I would
> consider useful
> for most mathematical applications)
>
> /edge_wrap,center=0 comes closest to what I would have expected
>
> This is all rather mysterious to me - is the term "convolution" used
> differently in engineering than in math? Clearly I have to think about
> this some more ...
Maybe a bound mirror expansion combined with shrinking helps ?
IDL> a = [[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]
IDL> b = [[10,11,12],[13,14,15],[16,17,18]]
IDL> print, boundmirrorshrink(convol(boundmirrorexpand(a),b))
14 13 0 0
11 10 0 0
0 0 0 0
0 0 0 0
not exactly what you want, but closer, isn't it ? :)
FUNCTION BoundMirrorExpand, A
; Expand the matrix using mirror boundary condition
;
; A = [ 1 2 3 11
; 4 5 6 12
; 7 8 9 13 ]
;
; B = BoundMirrorExpand(A) =
; [ 5 4 5 6 12 6
; 2 1 2 3 11 3
; 5 4 5 6 12 6
; 8 7 8 9 13 9
; 5 4 5 6 12 6 ]
m = (size(A))[1]
n = (size(A))[2]
B = [A, A[0,*], A[0,*]]
B = [[B], [B[*,0]], [B[*,0]]] ; B and A have same type
B(1:m,1:n) = A
B(0,0) = B(2,2) ; mirror corners
B(0,n+1) = B(2,n-1)
B(m+1,0) = B(m-1,2)
B(m+1,n+1) = B(m-1,n-1)
B(1:m,0) = B(1:m,2) ; mirror left and right boundary
B(1:m,n+1) = B(1:m,n-1)
B(0,1:n) = B(2,1:n) ; mirror top and bottom boundary
B(m+1,1:n) = B(m-1,1:n)
RETURN, B
END
FUNCTION BoundMirrorShrink, A
; Shrink the matrix to remove the padded mirror boundaries
; for example
;
; A = [ 5 4 5 6 12 6
; 2 1 2 3 11 3
; 5 4 5 6 12 6
; 8 7 8 9 13 9
; 5 4 5 6 12 6 ]
;
; B = BoundMirrorShrink(A) =
; [ 1 2 3 11
; 4 5 6 12
; 7 8 9 13 ]
m = (size(A))[1]
n = (size(A))[2]
B = A(1:m-2,1:n-2)
RETURN, B
END
just my 2 ce^H^Hfunctions,
Tom
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