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| author | Michael Niedermayer <michaelni@gmx.at> | 2007-08-21 19:22:59 +0000 |
|---|---|---|
| committer | Michael Niedermayer <michaelni@gmx.at> | 2007-08-21 19:22:59 +0000 |
| commit | 09671ce7188e714ca26c06059af28a227f1607a3 (patch) | |
| tree | 65f28b05f0901f71f90be82cb78d083e489faa3e /doc/snow.txt | |
| parent | 5ab657079d0138b7288575c9d4e6fb4d740e8c4e (diff) | |
describe IDWT
Originally committed as revision 10174 to svn://svn.ffmpeg.org/ffmpeg/trunk
Diffstat (limited to 'doc/snow.txt')
| -rw-r--r-- | doc/snow.txt | 62 |
1 files changed, 58 insertions, 4 deletions
diff --git a/doc/snow.txt b/doc/snow.txt index 3f14204cb8..3170c74886 100644 --- a/doc/snow.txt +++ b/doc/snow.txt @@ -246,11 +246,65 @@ Snow supports 2 wavelet transforms, the symmetric biorthogonal 5/3 integer transform and a integer approximation of the symmetric biorthogonal 9/7 daubechies wavelet. -5/3 Integer IDWT: -FIXME +2D IDWT (inverse discrete wavelet transform) +-------------------------------------------- +The 2D IDWT applies a 2D filter recursively, each time combining the +4 lowest frequency subbands into a single subband until only 1 subband +remains. +The 2D filter is done by first applying a 1D filter in the vertical direction +and then applying it in the horizontal one. + --------------- --------------- --------------- --------------- +|LL0|HL0| | | | | | | | | | | | +|---+---| HL1 | | L0|H0 | HL1 | | LL0 | HL1 | | | | +|LH0|HH0| | | | | | | | | | | | +|-------+-------|->|-------+-------|->|-------+-------|->| L1 | H1 |->... +| | | | | | | | | | | | +| LH1 | HH1 | | LH1 | HH1 | | LH1 | HH1 | | | | +| | | | | | | | | | | | + --------------- --------------- --------------- --------------- + + +1D Filter: +---------- +1. interleave the samples of the low and high frequency subbands like +s={L0, H0, L1, H1, L2, H2, L3, H3, ... } +note, this can end with a L or a H, the number of elements shall be w +s[-1] shall be considered equivalent to s[1 ] +s[w ] shall be considered equivalent to s[w-2] + +2. perform the lifting steps in order as described below + +5/3 Integer filter: +1. s[i] -= (s[i-1] + s[i+1] + 2)>>2; for all even i < w +2. s[i] += (s[i-1] + s[i+1] )>>1; for all odd i < w + +\ | /|\ | /|\ | /|\ | /|\ + \|/ | \|/ | \|/ | \|/ | + + | + | + | + | -1/4 + /|\ | /|\ | /|\ | /|\ | +/ | \|/ | \|/ | \|/ | \|/ + | + | + | + | + +1/2 + + +snows 9/7 Integer filter: +1. s[i] -= (3*(s[i-1] + s[i+1]) + 4)>>3; for all even i < w +2. s[i] -= s[i-1] + s[i+1] ; for all odd i < w +3. s[i] += ( s[i-1] + s[i+1] + 4*s[i] + 8)>>4; for all even i < w +4. s[i] += (3*(s[i-1] + s[i+1]) )>>1; for all odd i < w + +\ | /|\ | /|\ | /|\ | /|\ + \|/ | \|/ | \|/ | \|/ | + + | + | + | + | -3/8 + /|\ | /|\ | /|\ | /|\ | +/ | \|/ | \|/ | \|/ | \|/ + (| + (| + (| + (| + -1 +\ + /|\ + /|\ + /|\ + /|\ +1/4 + \|/ | \|/ | \|/ | \|/ | + + | + | + | + | +1/16 + /|\ | /|\ | /|\ | /|\ | +/ | \|/ | \|/ | \|/ | \|/ + | + | + | + | + +3/2 -snows 9/7 Integer IDWT: -FIXME TODO: ===== |