new sorting-based lossless motion estimation algorithms and a partial distortion elimination...
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New Sorting-Based Lossless Motion Estimation Algorithms and a Partial Distortion Elimination Performance
Analysis
Bartolomeo Montrucchio and Davide Quaglia
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, 2005
Outline
Introduction Taylor Series of the Distortion Matching Algorithm Experimental Results References
Introduction
Stages in motion estimation
– Searching Choose a candidate mo
tion vector. Lossy vs. lossless
– Matching Calculate SAD between
the candidate block and current block.
Lossy vs. lossess
3575153
70140250
84115255
SAD
4285170
77124223
86191253
SAD =
pixel value
Introduction
Searching stage
– Lossless Raster ordered full search , SpiralPDE, Successive elimi
nation algorithm, …
– Lossy Three-step search, Diamond search, …
…
…
Search range
SpiralPDE for searching
Introduction
successive elimination algorithm
– For an obtained candidate M(a,b) and SAD(a,b), We have to find M(x,y) s.t. SAD(x,y) SAD(a,b)
– SAD(a,b) R – M(x,y), SAD(a,b) M(x,y) – R R – SAD(a,b) M(x,y) SAD(a,b) + R
– Before the calculation of SAD(x,y), check M(x,y) first.
current candidate
current candidate
R M(x,y) SAD(x,y)
|a| - |b| |a – b|
Algorithm DFD PSNR(dB) Check points
Full search 2335 31.647 1089
SEA 2335 31.647 144
TSS 3488 29.113 33
Introduction
Matching stage
Lossless– Raster ordered full matching, PDE, …
Lossy– Down sampling, …
N
N
v
t
),( jif pt
),( jif vp
),(SAD),(),(),(SAD min1 1
vpjifjifvpk
i
N
j
vppt
If then stop
N
i
N
j
vppt jifjifvp
1 1
),(),(),(SAD
pth block pixel (i,j) in a blockcurrent
candidate
Introduction
Matching criterion (lossless)– SAD
– PDE
N
i
N
j
vppt jifjifvp
1 1
),(),(),(SAD
)(SAD),(),(),(SAD min1 1
pjifjifvpk
i
N
j
vpptk
N
N
v
t
),( jif pt
),( jif vp
)(SAD))(())((),(SAD min1
pkSfkSfvpm
k
vpptm
S : Generic matching orderMain purpose of this
paper
m {(1, 1), (1, 2), …, (N, N)}
Taylor Series of the Distortion
Taylor series–
Taylor series of the distortion–
– e.g.
)0(),,0(),,0(
|),(),(|),,(
vjidjid
jifjifjivd
v
vppt
0
00
)(
)(!
)()(
n
nn
xxn
xfxf
)0()',',0()',',0()',',( vjidjidjivd v
)0()",",0()",",0()",",( vjidjidjivd v> > (i’,j’)
(i”,j”)
Matching Algorithm
1. Compute SADmin(p) (every eight pixels).
2. Compute d(v,i,j) for all (i,j) in a block.
3. Sort d(v,i,j) in decreasing order.
4. Check if
5. Goto the next (i,j) and return to 1.
)(SAD))(())((),(SAD min1
pkSfkSfvpm
k
vpptm
m {(1, 1), (1, 2), …, (N, N)}
Searching stage is the same as spiralPDE
Matching Algorithm
Fast full search with sorting by distortion (FFSSD)– Use the first term in the Taylor’s series.
Fast full search with sorting by gradient (FFSSG)– Use the second term in the Taylor’s series. vd(0,i,j) is approximated by
)0(),,0(),,0(|),(),(|),,( vjidjidjifjifjivd vvpp
t
1
1
1
1
),(),(8
1
m n
njmifjif
Experimental Results
Comparisons– SpiralPDE– Sobol partial distortion algorithm (SPD)
Sobol sequence
– Gradient-based adaptive matching scan algorithm (P4)
Candidate MV Real MVPixel position
Distortion at position p in (t+1)th frame
References
SEA– W. Li and E. Salari, “Successive elimination algorithm for m
otion estimation,” IEEE Trans. Image Process.,1999. SPD
– D. Quaglia and B. Montrucchio, “Sobol partial distortion algorithm for fast full search in block motion estimation,” in Proc. 6th Eurographics Workshop Multimedia, 2001.
P4– J. N. Kim and T. S. Choi, “Adaptive matching scan algorith
m based on gradient magnitude for fast full search in motion estimation,” IEEE Trans. Consumer Electron., 1999.