1. Implementing 3D SPHARM Surfaces
Registration on Cell Processor
Huian Li (huili@indiana.edu) Mi Yan (miyan@us.ibm.com)
Robert Henschel (rhensche@indiana edu)
(rhensche@indiana.edu) Li Shen (shenli@iupui edu)
(shenli@iupui.edu)
July 29, 2009

2. Contents
• SPHARM registration
• Matlab implementation
• Cell implementation
• Performance Analysis
• Conclusion

3. SPHARM Surfaces
• R di l and stellar surfaces
Radial d t ll f
• Simply connected, arbitrarily shaped
• Vision, graphics, imaging, bioinformatics

4. SPHARM Expansion
( )  (x y z)
(,)  (x,y,z)
( )
(,) (x,y,z)
( )
Area-preserving
mapping

5. SHREC
(a) template, (b) object, (c) after ICP, (d) after
registration of p
g parameterization

6. Calculation of coefficients
• After rotating the parameter net on the surface in
Euler angles (α, β, γ), new coefficients will be:
l
c (  ) 
m
l 
nl
D l
mn (  ) c l
n
where
min( l  n ,l  m )
D mn ( )  e (  i m  in ) (
l
 (  1) t d mnt (  ))
t  max( 0 , n  m )
l
and
(l  n)!(l  n)!(l  m)!(l  m)!  
d mnt (  ) 
l
 (cos ) ( 2l nm2t ) (sin ) ( 2t mn )
(l  n  t )!(l  m  t )!(t  m  n)!t! 2 2

7. RMSD
• RMSD (Root Mean Square Distance): distance
between two SPHARM models
L max l
1
RMSD 
4
 
l0 m l
|| c 1ml  c 2 , l || 2
,
m
m m
c and c
1 ,l 2 ,l are coefficients of two
SPHARM models

8. Matlab implementation
• A straightforward implementation in Matlab:
for l = 0 Lmax
0,
for m = -l, l
for n = -l, l
l
for t = max(0, n-m), min(l+m, l-n)
... performing calculations ...
• One rotation for Lmax = 50 took 823 seconds on 2GHz quad
quad-
core Intel Xeon E5335

9. Cell B.E.

10. Cell implementation
• Domain decomposition:
for l = 0, Lmax
for m = -l l
l,
for n = -l, l
for t = max(0 n-m) min(l+m l-n)
max(0, n m), min(l+m, l n)
... calculations ...
• Decomposition along l leads to work load
imbalance among SPUs
• Decomposition along m creates unnecessary data
p g y
communication

11. Cell implementation
• Loop fusion:
for l = 0, Lmax
for m = -l l
l,
for n = -l, l
for t = max(0 n-m) min(l+m l-n)
max(0, n m), min(l+m, l n)
... calculations ...
• Unique index for combined loop:
f(l, m) = l2 + m + l
• W kl d f each SPE :
Workload for h
(Lmax + 1)2/(total # of SPEs)

12. Cell implementation
• Lookup table T for factorial
• Transform exponentials & multiplications into
multiplications & additions respectively
additions, respectively.
(l  n)!(l  n)!(l  m)!(l  m)!  
d l
( )   (cos ) ( 2l nm2t ) (sin ) ( 2t mn )
(l  n  t )!(l  m  t )!(t  m  n)!t!
mnt
2 2
 exp(
1
 (T (l  n )  T (l  n )  T (l  m )  T (l  m ))
2
 T (l  n  t )  T (l  m  t )  T (t  m  n )  T (t )
 
 ( 2l  n  m  2t )  log(cos )  ( 2t  m  n )  log(sin ))
2 2

13. Cell implementation
• Others that specific to Cell:
• Vectorization & data alignment
• DMA data transfer between main memory &
local store
• SPU d decrementert

14. Cell implementation
• Single p
g precision vs. double p
precision: all data in single p
g precision

15. Cell implementation
• Single p
g precision vs. double p
precision: p
partial data in double p
precision

16. Cell implementation
• Single p
g precision vs. double p
precision: all critical data in double p
precision

17. Performance analysis
Performance of one rotation on Cell BE
1.8
18
1.6
1.4
s)
Time (seconds
1.2
1
0.8
0.6
0.4
04
T
0.2
0
1 2 4 8 16
Number of SPEs

18. Performance analysis
Performance of finding the shortest
distance at Level 3 on Cell BE
7000
6000
5000
s)
seconds
4000
Time (s
3000 GNU gcc
IBM xlc
2000
1000
0
4 8 12 16
Number of SPEs

19. Conclusion
• Performance increases dramatically on Cell due to
its unique architecture and algorithm optimization.
• Carefulness must be taken for data placement due
to limited local store.
• Carefulness must also be taken for data transfer
between local store and main memory.

20. The End
Questions?