Fast Lossless Multi-Resolution Motion Estimation for Scalable Wavelet Video Coding

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Fast Lossless Multi-Resolution Motion EstimationFast Lossless Multi-Resolution Motion Estimation for Scalable Wavelet Video Coding for Scalable Wavelet Video Coding

Yu Liu and King Ngi NganYu Liu and King Ngi Ngan

Department of Electronic EngineeringDepartment of Electronic EngineeringThe Chinese University of Hong KongThe Chinese University of Hong Kong

ISCAS2006, May 21-24, Island of Kos, GreeceISCAS2006, May 21-24, Island of Kos, Greece

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OutlineOutline

IntroductionIntroduction BackgroundBackground Proposed AlgorithmProposed Algorithm Experimental ResultsExperimental Results ConclusionConclusion

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IntroductionIntroduction

• Motion Estimation in Critically-Sampled Wavelet Domain• Pro: basically free form the blocking effects• Con: inefficient in high bands

• Motion Estimation in Shift-Invariant Wavelet Domain• Pro: perform ME more precisely and efficiently• Con: computational complexity

e.g. low-band-shift (LBS) and complete-to-overcomplete DWT (CODWT)

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BackgroundBackground

Motion Estimation in Shift-Invariant Wavelet Domain (1)Motion Estimation in Shift-Invariant Wavelet Domain (1)

• Two Level Shift-Invariant Wavelet Decomposition by using Low-Band-Shift (LBS) or Complete-to-Overcomplete DWT (CODWT)

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• Generation of Wavelet BlocksGeneration of Wavelet Blocks

jifjiS pkltpklt ,),( ,,,,,,

• The coefficient of the pth wavelet block of current frame t can be represented by

• The v-pixel-shifted or {dx,dy}-pixel-shifted coefficient of the pth wavelet block of reference frame t’ can be represented by

llllpkltvpklt dyjdxidydxfjiS 2/,2/,2%,2%),( ,,,',,,'

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• The sum of absolute difference (SAD) of the pth wavelet block for the motion vector v is computed as follows:

• The optimum motion vector v ∗ of the pth wavelet block, which has minimum displacement error, is given by:

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Partial Distortion EliminationPartial Distortion Elimination

•Partial Distortion Elimination (PDE) is a fast algorithm which has identical quality as that of FSA.

•The partial SAD (PSAD) is used to eliminate impossible candidates before the complete calculation of the SAD:

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Proposed AlgorithmProposed Algorithm

Wavelet Matching Error CharacteristicWavelet Matching Error Characteristic

• then we assume that this matching order will be generally effective for all of the candidate vectors in the search window.

• Therefore, to fulfill the above objective, we use ep(i, j) to predict the matching error.

• To improve the computational saving of PDE, if the expected values of the matching error dp+v(i, j) in the search window w fulfills the following criterion:

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Wavelet Matching Error CharacteristicWavelet Matching Error Characteristic

To obtain the predicted matching error To obtain the predicted matching error eepp(i, j)(i, j), solve this equation, solve this equation

We finally can obtain an approximate solution of Eq. (6):We finally can obtain an approximate solution of Eq. (6):

Larger wavelet coefficientLarger wavelet coefficient magnitude in the current magnitude in the current wavelet block tends to produce larger matching errorwavelet block tends to produce larger matching error

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MR-WMEC-PDEMR-WMEC-PDE

Three key factors which affect the performance of PDEThree key factors which affect the performance of PDE

• the Searching Orderthe Searching Order in which the wavelet blocks are tested during the searching phase.in which the wavelet blocks are tested during the searching phase.

• the Matching Orderthe Matching Order in which the coefficients within a wavelet block are picked up to in which the coefficients within a wavelet block are picked up to

compute the SAD.compute the SAD.

• the Comparison Intervalthe Comparison Interval in which comparison between PSAD and SADmin is performed.in which comparison between PSAD and SADmin is performed.

Three new strategies for PDE by using wavelet matching Three new strategies for PDE by using wavelet matching error characteristic (WMEC) are proposed.error characteristic (WMEC) are proposed.

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Searching Order Strategy based on Wavelet Multi-Resolution Searching Order Strategy based on Wavelet Multi-Resolution PropertyProperty• Instead of the spiral search order, the proposed searching order Instead of the spiral search order, the proposed searching order

strategy uses the normalized partial SAD in LL subband level as the strategy uses the normalized partial SAD in LL subband level as the estimated SAD (ESAD)estimated SAD (ESAD)

• Then,Then, sort the ESAD using the counting sort algorithm in sort the ESAD using the counting sort algorithm in ascending ascending order to obtain the searching order order to obtain the searching order SO = {vSO = {vnn || n = 0, ...,w−1}n = 0, ...,w−1}..

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MR-WMEC-PDEMR-WMEC-PDE Matching Order Strategy based on Wavelet-tree Grouping Matching Order Strategy based on Wavelet-tree Grouping

SchemeScheme• A A wavelet-tree grouping schemewavelet-tree grouping scheme according to spatial self-similarity according to spatial self-similarity

property and matching error clustering property of wavelet coefficientproperty and matching error clustering property of wavelet coefficient

• SortSort E Epp(B(Bl,bl,bl,ml,m) ) using the quick sort algorithm in descending order to obtain the matching order of leusing the quick sort algorithm in descending order to obtain the matching order of le

velvel l: MO l: MOll = {b = {bl,m l,m | m = 0, ...,M − 1}| m = 0, ...,M − 1}

B2,3

B4,1

B1,0B2,0

B3,0B4,0

B4,2 B4,3

B3,1

B3,2 B3,3

B3,4 B3,5

B3,6 B3,7

B3,8 B3,9

B3,10 B3,11

B2,1

B2,2

B2,7

B2,4 B2,5

B2,6 B2,11

B2,8 B2,9

B2,10

B1,1

B1,2 B1,3

B1,4 B1,5

B1,6 B1,7

B1,8 B1,9

B1,10 B1,11

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Comparison Interval Strategy based on Adaptive Sub-blocks Comparison Interval Strategy based on Adaptive Sub-blocks Checking UnitChecking Unit

• In conventional PDE methods, fixed comparison interval, such as eight-In conventional PDE methods, fixed comparison interval, such as eight-pixels or sixteen-pixels checking unit, is usually adopted.pixels or sixteen-pixels checking unit, is usually adopted.

• Combined with the wavelet-tree grouping scheme, an adaptive Combined with the wavelet-tree grouping scheme, an adaptive comparison interval strategy is proposed. comparison interval strategy is proposed.

• In the proposed strategy, every 2In the proposed strategy, every 2l−l−11 sub-blocks in the decomposition sub-blocks in the decomposition level level l l are used as the checking unit.are used as the checking unit.

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Experimental Results (1)Experimental Results (1)

• Simulation results are reported in the following ways:

• operation number : used to compute the partial distortion

• speed-up ratio : for motion estimation including the required overheads for comparison.

• For performance comparison with other algorithms

• Full Search Algorithm (FSA)

• Spiral-PDE [5]

• CPME-PDS [6]

• proposed MR-WMEC-PDE

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Experimental Results (2)Experimental Results (2)• Average Operation Number per Block for Tested Algorithms

On average speed-up ratio in terms of operation number, MR-WMEC-PDE is better than Spiral-PDE and CPME-PDS by about 92% and 34%, respectively.

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Experimental Results (3)Experimental Results (3)• Average Execution Time per Frame for Tested Algorithms

On average speed-up ratio in terms of execution time, MR-WMEC-PDE is better than Spiral-PDE and CPME-PDS by about 84% and 63%, respectively.

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ConclusionConclusion

Fast Lossless Multi-Resolution Motion Estimation Algorithm• Wavelet Matching Error Characteristic (WMEC)

• Three New Strategies for PDE Searching Order Strategy based on Wavelet Multi-Resolution Propert

y Matching Order Strategy based on Wavelet-tree Grouping Scheme Comparison Interval Strategy based on Adaptive Subblocks Checking

Unit

Fast Lossless Multi-Resolution Motion Estimation for Scalable Wavelet Video Coding

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