Novel CrossDiamondHexagonal Search Algorithms

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Novel Cross-Diamond-Hexagonal Search Algorithms

• Chum-Ho Cheung(???)
• Lai-Man Po (Member IEEE)

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Agenda

• Introduction
• Search Patten Used in CDHS
• Cross-Center-Biased Motion Vector Distribution
• Hexagonal Search Pattens
• Proposed Cross-Diamond-Hexagonal Search
• Flow of the Proposed CDHSs
• Theoretical Analysis
• Experimental Results
• Reference

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Introduction

• Block-matching motion estimation
• Part of todays video coding tech. standard
• Block-matching algorithms (BMA)
• Full Search (FS)
• Fast BMA
• 3-Step Search(3SS),New 3-Step Search
• Orthogonal Search(OSA)
• 2D-LOGarithmic search(2DLOG)
• 4-Step Search (4SS)
• Diamond Search(DS)
• HEXagon-Based Search(HEXBS)
• Cross-Diamond Search(CDS)

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Introduction

• Difference between BMA
• Shape of candidate blocks for matching
• Rectangular vs. Nonrectangular
• Size of searching pattens
• Eg. 3X3 grid in N3SS, BBGDS vs.5X5 in 4SS, DS
• Checking point
• Dynamic size and adaptive feature

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Introduction

• In this paper
• Propose Cross-Diamond-Hexagonal Search (CDHS)
• Faster than DS by about 144, CDS about 73

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Search Patten Used in CDHS

• Cross-Shaped Pattern (CSP)

• Diamond-Shaped Pattern (DSP)

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Search Patten Used in CDHS

• Hexagonal Search Patterns

• Flat version
• Horizontal (HF-HSP)
• Vertical (VF-HSP)

• Thick version
• Horizontal (HT-HSP)
• Vertical (VT-HSP)

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Search Patten Used in CDHS

• Hexagonal Search Patterns
• Small Hexagonal Search Pattern (SHSP)
• Used as the final stepn

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Search Patten Used in CDHS

• Cross-Center-Biased Motion Vector Distribution
• List video sequences used for analysis

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Search Patten Used in CDHS

• in C. H. Cheung and L. M. Po, A novel
  cross-diamond search algorithm for fast block
  motion estimation,
• Simulated Motion Vector Probability (MVP) using
  FS with Mean Absolute Difference (MAD) inside a
  search area ?
• Define P(), P(?), P(?) as prob. that MV is found
  within the cross(), diamond(?), square(?)

Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
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Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
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Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
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Search Patten Used in CDHS

• Table II shows Cross-Center Biased occupy the
  most proportion at different displacement ?,
  especially when 1???2
• For small motion, we can apply CCB to approximate
  Square-Center Biased or Diamond-Center Biased

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Search Patten Used in CDHS

• For large motion sequence type
• Translation, Zooming, pan and tilt are usually
  found, easily fall on the diamond corner in DS
• By switching the LDSP to HSP, we can save fewer
  checking point as search path through diamond
  corner

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Search Patten Used in CDHS

• For the case , we illustrate prob. that pass
  diamond corner in search path

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Search Patten Used in CDHS

• In Table III
• If use smaller SCSP to allow earlier
  halfway-stop, diamond-corner hits will be dropped
• Switching to another search pattern for reducing
  checking points from a diamond corner is a
  improvement issue, especially for rich motion
  clips

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Search Patten Used in CDHS

• By experiment, proposed method use different
  pattern matching in different scale
• In beginning, Small Cross-Shaped Pattern (SCSP)
  prior to Large Cross-Shaped Pattern (LCSP) for
  central 5X5 region (as 0???2 )
• Use Large Diamond-Shaped Pattern (LDSP) and Small
  Diamond-Shaped Pattern (SDSP) on large motion
  vectors
• But apply Large Hexagonal Search Pattern (LHSP)
  when min BDM at diamond corner

Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
Search Patten Used in CDHS
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Search Patten Used in CDHS
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Proposed Cross-Diamond-Hexagonal Search

• Proposed CDHS Algorithm
• Start
• Find min BDM by SCSP in 5 checking points. If min
  BDM occur in center, stop searching
• Large Cross Searching
• Use LCSP to check outermost 4 points, guide
  possible correct direction for next step
• Half-diamond Searching
• Two points of LDSP closest to the current min BDM
  of LCSP are checked i.e., (1, 1)
• If min found is any endpoint of SCSP and still
  min in this step, stop searching

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Proposed Cross-Diamond-Hexagonal Search

• Proposed CDHS Algorithm
• Searching
• LDSP?LDSP If LDSP is used in previous step and
  min BDM found on diamond edge, new LDSP if formed
  which center is the previous min BDM point
• LDSP?LHSP If LDSP is used in previous step and
  min DBM found on horizontal/vertical diamond
  corner, new horizontal/vertical LHSP is formed
  which center is the previous min BDM point
• LHSP?LHSP New LHSP of the same shape is formed
  which center is the previous min BDM point
• For any case above, 3 new checking points are
  evaluated

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Proposed Cross-Diamond-Hexagonal Search

• Proposed CDHS Algorithm
• Ending
• If min BDM point is found as center, new
  SDSP/SHSP is formed if LDSP/SHSP is used in
  previous step
• Has 4 new candidate points in SDSP/SHSP

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Proposed Cross-Diamond-Hexagonal Search

• Some example
• Two halfway-stop

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Proposed Cross-Diamond-Hexagonal Search

• Some example
• Search by CDHS-F

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Proposed Cross-Diamond-Hexagonal Search

• Some example
• Search by CDHS-T

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Proposed Cross-Diamond-Hexagonal Search

• Theoretical analysis
• Max theoretical speedup of CDHSs is about 20.5-45
  time with window size 7 (as halfway-stop)
• The gain Ns

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Proposed Cross-Diamond-Hexagonal Search

• Theoretical analysis
• Average gain over DS with window size of 7 is 3.56

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Proposed Cross-Diamond-Hexagonal Search

• Theoretical analysis
• Average gain using CDHS-F/CDHS-T over 4SS/CS/CDS

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Experimental Results

• For test sequence
• Block size of 16 and sum of SAD as BDM are used
• Window size ifs set to 7 for SIF/CIF/QCIF, and
  15 for CCIR601s

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Experimental Results

• Performance comparisons on SALES(CIF)

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Experimental Results

• Performance of CDHS-F over DS and CDS on all test
  senquences

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Experimental Results

• Plots of average num. of points used

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Experimental Results

• Plots of MAD per pixel frame-by-frame on stefan

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Experimental Results

• Remark
• CDHS-F performs slightly faster than CDHS-T,
• And CDHS-F speedup gain over DS is up to about
  144, CDS up to about 73
• CDHS-F even better prediction quality
• E.g.2.7 lesser MAD error than DSs
• End

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Appendix

• Probability of ? (0???7) in Square

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Appendix

• Gain in checking points using CDHS-F over DS