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

Motion estimation in an inter frame

Current frame

Reference frame

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

Experimental Results

Experimental Results

Experimental Results

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.