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MASSACHUSETTS GENERAL HOSPITAL RADIATION ONCOLOGY A CCELERATING MI - B ASED B - S PLINE R EGISTRATION U SING CUDA E NABLED GPU S James Shackleford (1) , Nagarajan Kandasamy (2), Gregory C. Sharp (1) (1) Massachusetts General Hospital, Radiation
MASSACHUSETTS GENERAL HOSPITAL RADIATION ONCOLOGY
James Shackleford(1), Nagarajan Kandasamy(2), Gregory C. Sharp(1)
(1) Massachusetts General Hospital, Radiation Oncology (2) Drexel University, Electrical and Computer Engineering
ACCELERATING MI-BASED B-SPLINE REGISTRATION USING CUDA ENABLED GPUS
SLIDE 2 OF 33
FIXED IMAGE MOVING IMAGE
INTRODUCTION
WHAT IS DEFORMABLE REGISTRATION?
FIXED IMAGE MOVING IMAGE
INTRODUCTION
WHAT IS DEFORMABLE REGISTRATION?
SLIDE 3 OF 33
FIXED IMAGE MOVING IMAGE DEFORMATION VECTOR FIELD
INTRODUCTION
WHAT IS DEFORMABLE REGISTRATION?
SLIDE 4 OF 33
PX PY βX βY PARAMETER COEFF PARAMETER WEIGHT
B-SPLINE GRID
PARAMETERIZATION METHOD REGIONAL INFLUENCE
SLIDE 5 OF 33
PX PY βX βY PARAMETER COEFF PARAMETER WEIGHT PX PY vY vX vY vY vX = (βX βY )PX vY = (βX βY )PY REGIONAL INFLUENCE
SLIDE 6 OF 33
PX PY βX βY PARAMETER COEFF PARAMETER WEIGHT vX = Σ Σ (βX,i βY,j )PX,i,j
i=1 4 j=1 4
vY = Σ Σ (βX,i βY,j )PY,i,j
i=1 4 j=1 4
16 CONTRIBUTIONS REGIONAL INFLUENCE
SLIDE 7 OF 33
M F CORRESPONDANCE AND COST F
? ? ? ? ? ? ? ??? ?? ? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ? ? ?
𝚬 COST w.r.t. VECTORS
F
? ? ? ? ? ? ? ??? ?? ? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ? ? ?
𝚬 COST w.r.t. COEFFICIENTS
F
DECOMPRESS VECTOR FIELD
v ∂C ∂v New P C ∂C ∂P
QUASI-NEWTONIAN OPTIMIZER
SLIDE 8 OF 33
H(F) + H(M) – H(F,M) C = C H(F | M) H(M | F) H(F) H(M) H(F) H(M) H(F,M) M F
FIXED IMAGE VALUE MOVING IMAGE VALUE
Σ Σ
i=1 BM j=1 BF
hj (i, j) ln N ⨉ hj (i, j) hF ( i ) ⨉ hM ( j ) C = 1 N
SLIDE 9 OF 33
M M F F
A B C D 1 2 3 4 1 2 3 4 A B C D
Static Image Moving Image Nearest Neighbors Partial Volumes
# of voxels intensity
ln N ⨉ hj (in, jn ) hF ( in ) ⨉ hM ( jn ) = ∂C ∂h
xn
Σ
n=1 4
∂C ∂v = ∂C ∂h xn
⨉ ∂wn ∂v) ∂C ∂P = ∂C ∂h ∂h ∂v ∂v ∂P ⨉ ⨉
SLIDE 10 OF 33
SERIAL IMPLEMENTATION
FOLLOWING A SINGLE THREAD
SLIDE 11 OF 33
M F
FIXED IMAGE INTENSITY MOVING IMAGE INTENSITY
Generate Histograms
compute vector for each voxel get corresponding voxels in moving image
A B C D
1 2 3 4
Nearest Neighbors Partial Volumes
compute partial volumes use partial volumes for moving & joint SLIDE 12 OF 33
M F
FIXED IMAGE INTENSITY MOVING IMAGE INTENSITY
Σ Σ
i=1 BM j=1 BF
hj (i, j) ln N ⨉ hj (i, j) hF ( i ) ⨉ hM ( j ) C = 1 N
Traditional Serial CPU
is very fast
(time required is negligible)
Generate Histograms
compute vector for each voxel get corresponding voxels in moving image
A B C D
1 2 3 4
Nearest Neighbors Partial Volumes
compute partial volumes use partial volumes for moving & joint
Compute Score
simply cycle thru histograms SLIDE 13 OF 33
M F
FIXED IMAGE INTENSITY MOVING IMAGE INTENSITY
Σ Σ
i=1 BM j=1 BF
hj (i, j) ln N ⨉ hj (i, j) hF ( i ) ⨉ hM ( j ) C = 1 N
Traditional Serial CPU
is very fast
(time required is negligible)
Generate Histograms
compute vector for each voxel get corresponding voxels in moving image
A B C D
1 2 3 4
Nearest Neighbors Partial Volumes
compute partial volumes use partial volumes for moving & joint
Compute Score
simply cycle thru histograms
Compute Gradient
∂C ∂P = ∂C ∂v ∂v ∂P ⨉
M F
get vector for each voxel
A B C D1 2 3 4
Nearest Neighbors Partial Volumescompute partial volume derivatives
get corresponding voxels in moving image
ln N ⨉ hj (in, jn ) hF ( in ) ⨉ hM ( jn ) = ∂C ∂h
xn
Σ
n=1 4
∂C ∂v = ∂C ∂h xn
⨉ ∂wn ∂v)
change in cost as vector changes
NEXT
SLIDE 14 OF 33
M F CORRESPONDANCE AND COST F
? ? ? ? ? ? ? ??? ?? ? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ? ? ?
𝚬 COST w.r.t. VECTORS
F
? ? ? ? ? ? ? ??? ?? ? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ? ? ?
𝚬 COST w.r.t. COEFFICIENTS
F
DECOMPRESS VECTOR FIELD
v ∂C ∂v New P C ∂C ∂P
QUASI-NEWTONIAN OPTIMIZER
SLIDE 15 OF 33
F
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ?
CHANGE IN COST w.r.t. COEFFICIENTS
βX βY 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
vX = Σ Σ (βX,i βY,j )PX,i,j
i=1 4 j=1 4
∂C ∂v ∂C ∂P = ∂v ∂P = βX,i βY,j
Σ Σ
i=1 4 j=1 4
∂C ∂v
Σ
SLIDE 16 OF 33
F
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ?
CHANGE IN COST w.r.t. COEFFICIENTS
βX βY 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
vX = Σ Σ (βX,i βY,j )PX,i,j
i=1 4 j=1 4
∂C ∂v ∂C ∂P = ∂v ∂P = βX,i βY,j
Σ Σ
i=1 4 j=1 4
∂C ∂v
Σ
SLIDE 17 OF 33
PARALLELIZATION
LEVERAGING GPUS, OPENMP, ETC
SLIDE 18 OF 33
M F CORRESPONDANCE AND COST F
? ? ? ? ? ? ? ??? ?? ? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ? ? ?
𝚬 COST w.r.t. VECTORS
F
? ? ? ? ? ? ? ??? ?? ? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ?? ? ? ?
𝚬 COST w.r.t. COEFFICIENTS
F
DECOMPRESS VECTOR FIELD
v ∂C ∂v New P C ∂C ∂P
QUASI-NEWTONIAN OPTIMIZER
What do we parallelize?
SLIDE 19 OF 33
F M F F
? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
COMPUTE VECTOR FROM COEFF COMPUTE HISTOGRAMS COMPUTE CHANGE
IN COST w.r.t
VECTOR CYCLE
HIST
COST
(MI) ∂C ∂v
SLIDE 20 OF 33
SLIDE 21 OF 33
M F
FIXED IMAGE INTENSITY MOVING IMAGE INTENSITY
Σ Σ
i=1 BM j=1 BF
hj (i, j) ln N ⨉ hj (i, j) hF ( i ) ⨉ hM ( j ) C = 1 N
Traditional Serial CPU
is very fast
(time required is negligible)
Generate Histograms
compute vector for each voxel get corresponding voxels in moving image
A B C D
1 2 3 4
Nearest Neighbors Partial Volumes
compute partial volumes use partial volumes for moving & joint
Compute Score
simply cycle thru histograms
Compute Gradient
∂C ∂P = ∂C ∂v ∂v ∂P ⨉
M F
get vector for each voxel
A B C D1 2 3 4
Nearest Neighbors Partial Volumescompute partial volume derivatives
get corresponding voxels in moving image
ln N ⨉ hj (in, jn ) hF ( in ) ⨉ hM ( jn ) = ∂C ∂h
xn
Σ
n=1 4
∂C ∂v = ∂C ∂h xn
⨉ ∂wn ∂v)
change in cost as vector changes
NEXT
SLIDE 22 OF 33
βX βY βX βY 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16
1 2 3 4 5 16
. . .
1 2 3 4 5 16
. . .
1 2 3 4 5 16
. . .
vX = Σ Σ (βX,i βY,j )PX,i,j
i=1 4 j=1 4
∂C ∂v ∂C ∂P = ∂v ∂P = βX,i βY,j
Σ Σ
i=1 4 j=1 4
∂C ∂v F
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ?
CHANGE IN COST w.r.t. COEFFICIENTS
CPU 1
SLIDE 23 OF 33
βX βY βX βY 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16
1 2 3 4 5 16
. . .
1 2 3 4 5 16
. . .
1 2 3 4 5 16
. . .
vX = Σ Σ (βX,i βY,j )PX,i,j
i=1 4 j=1 4
∂C ∂v ∂C ∂P = ∂v ∂P = βX,i βY,j
Σ Σ
i=1 4 j=1 4
∂C ∂v
CPU 2
F
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ?
CHANGE IN COST w.r.t. COEFFICIENTS
CPU 1
CONSTANT CONTROL POINT SPACING
15 x 15 x 15
16x
speedup
30min → 1.8min
multi-core processors,” Physics in Medicine and Biology, vol. 55, p. 6329, 2010.
GPU Computing Gems: Emerald Edition, Morgan Kaufmann Pub, 2011.
SLIDE 24 OF 33
CONSTANT VOLUME SIZE
256 x 256 x 256
multi-core processors,” Physics in Medicine and Biology, vol. 55, p. 6329, 2010.
GPU Computing Gems: Emerald Edition, Morgan Kaufmann Pub, 2011.
SLIDE 25 OF 33
HISTOGRAM COMPUTATION
LEVERAGING GPUS, OPENMP, ETC OpenMP CUDA +
thread-level histograms
(shared memory)
block-level histograms
(global memory)
complete histograms
(global memory)
SLIDE 26 OF 33
HISTOGRAM COMPUTATION
LEVERAGING GPUS, OPENMP, ETC OpenMP CUDA +
thread-level histograms
(shared memory)
block-level histograms
(global memory)
complete histogram
(global memory)
block
SLIDE 27 OF 33
100 x 100 x 100 50 x 50 x 50 25 x 25 x 25 0.5 1 1.5 2 2.5 3 3.5 Quadro 2000 (CC 2.1) Tesla C2075 (CC 2.0) AMD Phenom(tm) 9750 @ 1.2GHz [4-Core] Intel Xeon E5420 @ 2.5GHz [4-Core] Intel Xeon E5620 @ 2.4GHz [4-Core SMT] Intel Xeon X5675 @ 3.0GHz [6-Core SMT]
Control Grid Spacing (mm) Wall Clock Time (s)
32 Fixed Histogram Bins 32 Moving Histogram Bins Fixed Image: 512 x 512 x 115 (0.79 x 0.79 x 2.5) Moving Image: 512 x 384 x 115 (0.74 x 0.74 x 6.0) Compute Resolution: 256 x 256 x 115
Control Grid: 8 x 8 x 6 Regions: 5 x 5 x 3 Vox/Region: 63 x 63 x 40 Control Grid: 11 x 11 x 9 Regions: 8 x 8 x 6 Vox/Region: 32 x 32 x 20 Control Grid: 19 x 19 x 15 Regions: 16 x 16 x 12 Vox/Region: 16 x 16 x 10
100 x 100 x 100 50 x 50 x 50 25 x 25 x 25 0.5 1 1.5 2 2.5 3 3.5 Quadro 2000 (CC 2.1) Tesla C2075 (CC 2.0) AMD Phenom(tm) 9750 @ 1.2GHz [4-Core] Intel Xeon E5420 @ 2.5GHz [4-Core] Intel Xeon E5620 @ 2.4GHz [4-Core SMT] Intel Xeon X5675 @ 3.0GHz [6-Core SMT]
Control Grid Spacing (mm) Wall Clock Time (s)
1.4 1.2 1.4 0.8 1.4 0.8 0.3 0.4 0.3 0.2 0.3 0.2 0.6 1.0 0.8 1.7 0.8 1.7
Histograms Gradient
0.9 1.1 0.9 1.7 0.9 1.6 0.5 0.8 0.5 0.8 0.5 0.8 0.7 1.0 0.7 1.0 0.7 1.0
32 Fixed Histogram Bins 32 Moving Histogram Bins Fixed Image: 512 x 512 x 115 (0.79 x 0.79 x 2.5) Moving Image: 512 x 384 x 115 (0.74 x 0.74 x 6.0) Compute Resolution: 256 x 256 x 115
Control Grid: 8 x 8 x 6 Regions: 5 x 5 x 3 Vox/Region: 63 x 63 x 40 Control Grid: 11 x 11 x 9 Regions: 8 x 8 x 6 Vox/Region: 32 x 32 x 20 Control Grid: 19 x 19 x 15 Regions: 16 x 16 x 12 Vox/Region: 16 x 16 x 10
100 x 100 x 100 50 x 50 x 50 25 x 25 x 25 0.5 1 1.5 2 2.5 3 3.5 Quadro 2000 (CC 2.1) Tesla C2075 (CC 2.0) AMD Phenom(tm) 9750 @ 1.2GHz [4-Core] Intel Xeon E5420 @ 2.5GHz [4-Core] Intel Xeon E5620 @ 2.4GHz [4-Core SMT] Intel Xeon X5675 @ 3.0GHz [6-Core SMT]
Control Grid Spacing (mm) Wall Clock Time (s)
64 Fixed Histogram Bins 64 Moving Histogram Bins Fixed Image: 512 x 512 x 115 (0.79 x 0.79 x 2.5) Moving Image: 512 x 384 x 115 (0.74 x 0.74 x 6.0) Compute Resolution: 256 x 256 x 115
Control Grid: 8 x 8 x 6 Regions: 5 x 5 x 3 Vox/Region: 63 x 63 x 40 Control Grid: 11 x 11 x 9 Regions: 8 x 8 x 6 Vox/Region: 32 x 32 x 20 Control Grid: 19 x 19 x 15 Regions: 16 x 16 x 12 Vox/Region: 16 x 16 x 10
100 x 100 x 100 50 x 50 x 50 25 x 25 x 25 0.5 1 1.5 2 2.5 3 3.5 Quadro 2000 (CC 2.1) Tesla C2075 (CC 2.0) AMD Phenom(tm) 9750 @ 1.2GHz [4-Core] Intel Xeon E5420 @ 2.5GHz [4-Core] Intel Xeon E5620 @ 2.4GHz [4-Core SMT] Intel Xeon X5675 @ 3.0GHz [6-Core SMT]
Control Grid Spacing (mm) Wall Clock Time (s)
0.5 1.2 0.5 0.8 0.5 0.8 0.7 0.4 0.7 0.2 0.6 1.0 0.8 1.7 0.8 1.7 0.9 1.2 0.9 1.7 0.9 1.6 0.5 0.8 0.5 0.8 0.5 0.8 0.7 1.0 0.7 1.0 0.7 1.0 0.7 0.2
Histograms Gradient 64 Fixed Histogram Bins 64 Moving Histogram Bins Fixed Image: 512 x 512 x 115 (0.79 x 0.79 x 2.5) Moving Image: 512 x 384 x 115 (0.74 x 0.74 x 6.0) Compute Resolution: 256 x 256 x 115
Control Grid: 8 x 8 x 6 Regions: 5 x 5 x 3 Vox/Region: 63 x 63 x 40 Control Grid: 11 x 11 x 9 Regions: 8 x 8 x 6 Vox/Region: 32 x 32 x 20 Control Grid: 19 x 19 x 15 Regions: 16 x 16 x 12 Vox/Region: 16 x 16 x 10
*
†
* *
* via OpenMP E5620
† via OpenMP X5675 † †
100 x 100 x 100 50 x 50 x 50 25 x 25 x 25 0.5 1 1.5 2 2.5 3 3.5 Quadro 2000 (CC 2.1) Tesla C2075 (CC 2.0) AMD Phenom(tm) 9750 @ 1.2GHz [4-Core] Intel Xeon E5420 @ 2.5GHz [4-Core] Intel Xeon E5620 @ 2.4GHz [4-Core SMT] Intel Xeon X5675 @ 3.0GHz [6-Core SMT]
Control Point Spacing (mm) Wall Clock Time (s)
512 Fixed Histogram Bins 512 Moving Histogram Bins Fixed Image: 512 x 512 x 115 (0.79 x 0.79 x 2.5) Moving Image: 512 x 384 x 115 (0.74 x 0.74 x 6.0) Compute Resolution: 256 x 256 x 115
Control Grid: 8 x 8 x 6 Regions: 5 x 5 x 3 Vox/Region: 63 x 63 x 40 Control Grid: 11 x 11 x 9 Regions: 8 x 8 x 6 Vox/Region: 32 x 32 x 20 Control Grid: 19 x 19 x 15 Regions: 16 x 16 x 12 Vox/Region: 16 x 16 x 10
100 x 100 x 100 50 x 50 x 50 25 x 25 x 25 0.5 1 1.5 2 2.5 3 3.5 Quadro 2000 (CC 2.1) Tesla C2075 (CC 2.0) AMD Phenom(tm) 9750 @ 1.2GHz [4-Core] Intel Xeon E5420 @ 2.5GHz [4-Core] Intel Xeon E5620 @ 2.4GHz [4-Core SMT] Intel Xeon X5675 @ 3.0GHz [6-Core SMT]
Control Point Spacing (mm) Wall Clock Time (s)
0.5 1.2 0.5 0.8 0.5 0.8 0.7 0.4 0.7 0.2 0.7 1.0 0.9 1.8 0.9 1.8 0.9 1.3 0.9 1.7 0.9 1.6 0.5 0.8 0.5 0.8 0.5 0.8 0.7 1.0 0.7 1.0 0.7 1.0 0.7 0.2
Histograms Gradient
Control Grid: 8 x 8 x 6 Regions: 5 x 5 x 3 Vox/Region: 63 x 63 x 40 Control Grid: 11 x 11 x 9 Regions: 8 x 8 x 6 Vox/Region: 32 x 32 x 20 Control Grid: 19 x 19 x 15 Regions: 16 x 16 x 12 Vox/Region: 16 x 16 x 10
512 Fixed Histogram Bins 512 Moving Histogram Bins Fixed Image: 512 x 512 x 115 (0.79 x 0.79 x 2.5) Moving Image: 512 x 384 x 115 (0.74 x 0.74 x 6.0) Compute Resolution: 256 x 256 x 115 *
†
* *
* via OpenMP E5620
† via OpenMP X5675 † †