Æ !" !
#$$$ % % $&'$ !" ! ( )* !+,%, )+,%,
)*-+ . & &
) /+ 0 &
)( 1+ $
2
( 2
Æ
3
4 5,6 / 7
Æ !
Æ
" # Æ $
%& ' " "
* !
8952
)3+ %
: : ; * Æ
,& Æ %& Æ Æ
½ ¾ ¿ ' & <
: )+ !$
!$ )=+ !$
Æ
>6.
)** 7+ ?5>, (--- )*(+ @
25'% )A+ )+ %
>6. Æ
25'% )*(+
Æ & ()!* Æ +"
Æ
!
!
"
#
$
%
& ! ! ' ( Æ
)*(+ %
,
& Æ
3.1 Correlation of wavelet vectors
* $
$
½ ¾ ½ ¿ ¾ ¿ *
Level 1
coefficients
x
y
z
Irregular
mesh
MAPS
3D
DWT
δ
x
y
z
S
C
A
L
A
R
Level N
coefficients
M
O
D
E
L
BIT
ALLO
CATION
{alpha }
{z,q}
E
B
C
O
T
Q
U
A
N
T
I
Z
A
T
I
O
N
Bitstream
Rt
Figure 1. Proposed geometry compression scheme.
!"#
)
&
*
,
$$%&
$$*$
$ *
$ ,)
$)((
'$&&
'$$$&
$$$)
$$&+
'$$ +
$$++
'$),)
µ
C ½ ´¿
´½ µ C ¾ ´½ µ $$(&
'$$$%
$$*,
'$$&%
$$$$*&%
3.3 Rate and distortion models
4 $
!$
;
Table 1. Correlation between coordinates.
B
Æ
$
!
$ %4 . <4 Æ
&
%4 2
3*
!$ ;
¾
¾
¾
¾
4
¾ ;
B
!$ Æ
' Æ
4
( "
:
%4 $
Æ
' %4 " # )*+;
3.2 Wavelet coefficients distribution
C ¾
¾
¾ ¾
D !$ 4 $
,
/ ;
2
)7 =+ ¾
*
(
(d2)
1
(d1)
2
4
(d3)
(d0)
0
3
7
(d5)
(d4)
6
(d6)
(d7)
5
8
Old indices 0 2 1 4 3 5 7 8 6
New indices 0 1 2 3 4 5 6 7 8
Figure 3. Predictive coding of LF coefficients.
Figure 2. Coefficients distributions
' <4
Æ
"
; 1 - A 4.1 Predictive coding for LF coefficients
' <4 Æ
*
½ ( ' &
-
<4 Æ
<4 '
B
(; 8
$
, <
C )- E+ <4 Æ ;
!" " #$ %& #'
#($ ) * Æ
+# # , #"&- . " "
Æ %& &
Æ
3( . & Æ B
4.2 Optimal Bit allocation
$
!$ "
$
¾ )=+
< ;
/ 0
F & "
& !
Æ
C E !
!
B
= " )=+;
¾
1
/
¾
2
C # " A
Æ Æ '$$*
! #
$(+(
Æ Æ $$+
$-%)
! #
! #
$(+-
Æ Æ $)-$
Table 2. Correlation of LF difference vectors.
Figure 4. Geometry coding: PSNR (on semi-regular mesh) vs Rate for venus, rabbit and horse objects.
Æ
Æ
; 8
<4 Æ
<4 ' 5,6 )+
; $ C ½ C ¾ C # 4 ;
$ 3#". ¾ .$ % # "'
#". %
4 2 %5 $ . 5 %& #& . " 3#". .%% .$ %.
. 6 % 4 !$
>6.
"#
78 9 )- 9 :.- ; 9.- , <.% ,#$ $ .$ 5 '
# - )" 22
78 9 <$ =#& #" 22
78 ) >??&- ; @- 4 @5 ;'
$ $#& #" - 7
8 ) - 4 @5- ; @- ; 35 < <%? 9);@A 9.. "
"#( . - 221
78 9 .%&- <+- B 4 9..'
& . %& "$ &"
- 22- 220
78 3 ;- 9 )- 9 :. 9'
% % C"$ "#% 708 3 ;- 9 )- 9 :. D"#
& .# E.( $ 5 '
$ - C.& 718 ) @ 4 ;# ) 5 Æ #$
% "$ - - C. 22
728 = .% B +$ =# #"
.$ "$ .$& )" 221
78 = .% B +$ < $#& #"'
! ""- 222
78 < .%# F$ "# % #$ #'
" 5 G:3D #$% - ).$. 222
78 , B 4= B"$ " &''((()**
. 5,6
)+ ; 0 5
& 2GH;
% C (-#½¼& ' & ' H82> !$
4
3 :
Æ
;
5,6 !
' 3