. - () : z(x,y) = [s(x,y)].
, , , :
z(n,m) = c s(n,m),
z(n,m) = s(n-N,m-M),
z(n,m) = s(n,m)+u(n,m).
, :
s(n,m) = s(i,j) d(n-i,m-j). (18.2.1)
:
z(n,m) = cn,m s(n,m). (18.2.2)
(18.2.2) n,m.
. - :
zn,m = (sn,m)2.
. :
1. .
2. .
, [s(x,y)] z(x,y) = [s(x,y)], q(x,y) = [u(x,y)], [as(x,y)+bu(x,y)] = az(x,y)+bq(x,y). .
(18.2.1) s(i,j) . [.] (18.2.1), :
[s(n,m)] = (n,m) = s(i,j) T[d(n-i,m-j)],
z(n,m) = s(i,j) hij(n,m), (18.2.3)
hij(n,m) - (n,m) (i,j). hij(n,m) (i,j), , , .
. , :
[s(n-N,m-M)] = z(n-N,m-M).
. , , , , .
, - (-).
, (18.2.3), :
hij(n,m) = T[d(n-ni,m-mj)].
i = j = 0 :
ho(n,m) = T[d(n,m)].
, :
hij(n,m) = ho(n-i,m-j) = h(n-i,m-j), (18.2.4)
.e. , .
|
|
. (18.2.4) (18.2.3), :
z(n,m) = Si Sj s(i,j) h(n-i,m-j). (18.2.5)
(18.2.5), . n-i = k, m-j = l, :
z(n,m) = Sk Sl h(k,l) s(n-k,m-l), (18.2.5')
.. , . ( ) ( ). ( ) / .
(**):
z(n,m) = h(k,l) ** s(n-k,m-l).
, :
z()= h() ** s( - ).
. :
h(k,l) = h(k) h(l), (18.2.6)
(18.2.5') :
z(n,m) = Sk h(k) Sl h(l) s(n-k,m-l), (18.2.7)
: z(n,m) = Sk h(k) g(n-k,m), g(n-k,m) = Sl h(l) s(n,m-l).
g(n,m) s(n,m) n = const ( n) h(l), z(n,m) g(n,m) m = const h(k). , , . (18.2.6) . , .
.
. , . : Sk Sl |h(k,l)| < .
. / .
, i- j-, t. i- di(t) , j- hij(t). hij i-, si(t) j- :
zj(t) = Si Sk hij(k) si(t-k). (18.2.8)