Embedded zerotrees of wavelet transforms: Difference between revisions

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==== (2) Significant pass (or dominant pass) ====
This method will code a bit for each coefficient that is not yet be seen as significant. Once a determination of significance has been made, the significant coefficient is included in a list for further refinement in the refinement pass. And if any coefficient already known to be zero, it will not be coded again.
 
== Example ==
<pre>
DCT data ZeroTree scan order (EZW)
63 -34 49 10 7 13 -12 7 A B BE BF E1 E2 F1 F2
-31 23 14 -13 3 4 6 -1 C D BG BH E3 E4 F3 F4
15 14 3 -12 5 -7 3 9 CI CJ DM DN G1 G2 H1 H2
-9 -7 -14 8 4 -2 3 2 CK CL DO DP G3 G4 H3 H4
-5 9 -1 47 4 6 -2 2 I1 I2 J1 J2 M1 M2 N1 N2
3 0 -3 2 3 -2 0 4 I3 I4 J3 J4 M3 M4 N3 N4
2 -3 6 -4 3 6 3 6 K1 K2 L1 L2 O1 O2 P1 P2
5 11 5 6 0 3 -4 4 K3 K4 L3 L4 O3 O4 P3 P4
 
D1: pnzt p ttt tztt tttttptt (20 codes)
PNZT P(t) TTT TZTT TPTT (D1 by M-EZW, 16 codes)
PNZT P(t) Z(t) TZ(p) TPZ(p) (D1 by NM-EZW, 11 codes)
P N (t), P or N above zerotree scan
P N Z(t p), p=pair T, t=triple T, P/N + TT/TTT in D1 code
S1: 1010
D2: ztnp tttttttt
S2: 1001 10 (Shapiro PDF end here)
D3: zzzz zppnppnttnnp tpttnttttttttptttptttttttttptttttttttttt
S3: 1001 11 01111011011000
D4: zzzzzzztztznzzzzpttptpptpnptntttttptpnpppptttttptptttpnp
S4: 1101 11 11011001000001 110110100010010101100
D5: zzzzztzzzzztpzzzttpttttnptppttptttnppnttttpnnpttpttppttt
S5: 1011 11 00110100010111 110101101100100000000 110110110011000111
D6: zzzttztttztttttnnttt
( http://www.polyvalens.com/wavelets/ezw/ )
 
Detailed: (new S is first, other computed by before cycles)
s-step 1 21 321
val D1 S1 R1 D2 S2 R2 D3 S3. ... R3 ... D4,S4...
A 63 P 1 &gt;=48 56 Z .1 &gt;=56 60 Z ..1 &gt;=60 62
B -34 N 0 &lt;48 -40 T .0 &lt;40 -36 Z ..0 &lt;36 -36
C -31 IZ &lt;32 0 N 1. &gt;=24 -28 Z .1. &gt;=28 -30
D 23 T &lt;32 0 P 0. &lt;24 20 Z .1. &gt;=20 22
 
BE 49 P 1 &gt;=48 56 .0 &lt;56 52 Z ..0 &lt;52 50
BF 10 T &lt;32 0 P 0 &lt;12 10
BG 14 T &lt;32 0 P 1 &gt;=12 14
BH -13 T &lt;32 0 N 1 &gt;=12 -14
CI 15 T &lt;32 0 T &lt;16 0 P 1 &gt;=12 14
CJ 14 IZ &lt;32 0 T &lt;16 0 P 1 &gt;=12 14
CK -9 T &lt;32 0 T &lt;16 0 N 0 &lt;12 -10
CL -7 T &lt;32 0 T &lt;16 0 T &lt;8 0
DM 3 T &lt;16 0 T &lt;8 0
DN -12 T &lt;16 0 N 1 &gt;=12 -14
DO -14 T &lt;16 0 N 1 &gt;=12 -14
DP 8 T &lt;16 0 P &lt;12 10
 
E1 7 T &lt;32 0 .E,F,G,H(1,2,3,4)
E2 13 T &lt;32 0 .I,J,K(1,2,3,4)
E3 3 T &lt;32 0 .N,O,P(1,2,3,4)
E4 4 T &lt;32 0 .
J1 -1 T &lt;32 0 .
J2 47 P 0 &gt;48 40 1 &gt;=40 44 .
J3 -3 T &lt;32 0
J4 2 T &lt;32 0
 
D = dominant pass (P=positive, N=negative, T=ZeroTree, IZ=Izolated zero)
S = subordinate pass;
(R = back reconstructed value)
</pre>
 
==See also==