# Enhanced Hexagonal Search for Fast Block Motion Estimation

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```					 Enhanced Hexagonal
Search for Fast Block
Motion Estimation

Authors：Ce Zhu, Xiao Lin,
Lappui Chau, and Lai-Man Po
IEEE TRANSACTIONS ON CIRCUITS AND
SYSTEMS FOR VIDEO TECHNOLOGY,
OCTOBER 2004
Outline
   Introduction
   HEXBS ( Hexagon-Based Search )
   Predictive HEXBS
   Fast Hexagonal Inner Search
   6-Side-Based Fast Inner Search
   Enhanced HEXBS Algorithm
   Experimental Results And Analysis
   Conclusion
Introduction
   Fast block motion estimation process ：
STEP 1：low-resolution coarse search
→ To identify a small area where the
best motion vector is expected to lie
STEP 2：fine-resolution inner search
→ To select the best motion vector in
the located small region
Introduction
 Most motion estimation algorithms attempt to
speed up the coarse search without considering
accelerating the inner search
 Enhanced hexagonal search algorithm is
proposed to improve the performance：
(1) Reducing number of search points
(2) Decrease the distortion
Introduction
   The two-dimensional logarithmic search
   Three-step search (TSS)
   New three-step search (NTSS)
   Four-step search (4SS)
   Block-based gradient descent search (BBGDS)
   Simple and efficient search (SES)
   Diamond search (DS)
   The hexagonal search
   Hexagon-based search (HEXBS)
   Enhanced hexagon-based search
HEXBS
HEXBS

Inner points in the hexagonal search pattern
The inner search for the HEXBS
 Using the shrunk hexagonal pattern covering the
points 2, 4, 5, and 7
Ex：Points 1 and 3 if point 2 wins in the last step
of the HEXBS algorithm
The flowchart of HEXBS

NHEXBS (mx , my) = 7 + 3n + 4
where n is the number of times of
low-resolution coarse search
Predictive HEXBS
   The error distortion function has monotonic
characteristic in a localized search area
   The motion vector of the current block is
highly correlated to those of its neighboring
blocks.
   The motion information of neighboring blocks
can be utilized for prediction of a good starting
point
Predictive HEXBS
   Consider the upper and the left neighboring
blocks
   Finding a good starting point using the
neighboring motion vectors
   Normally finds better motion vectors than the
original HEXBS scheme
Fast Hexagonal Inner Search

   Not a full inner search , only check a portion of
the inner search points
   Strong correlation exists between the inner
search points
   Based on the monotonic distortion characteristic
in the localized area around the global minimum
6-Side-Based Fast Inner Search
   Group the search points in the six sides of the
hexagon
   Define a group distortion by summing the
distortions of all the points within the group
   We focus the inner search just in the region
near to the group with the smallest group
distortion
   For different groups (sides) in different
locations, we have different number of inner
search points
Enhanced HEXBS Algorithm
 HEXBS incorporate the 6-side-based fast
inner search scheme
 Moreover , incorporate the Predictive HEXBS

 The reduction of number of search points for
the enhanced HEXBS algorithm ：
(1) The prediction for a good starting point
using the predictive HEXBS,
(2) The fast inner search.
Experimental Results And Analysis
TABLE III

N 2 - N1
%SIR  (            ) 100% , where Ni is the number of search points used in the Method i
N1

MSE 2 - MSE 1
%D MSE  (                 ) 100%    ,where MSEi is the distortions for Methods i
MSE 1
Conclusion
   Enhanced HEXBS speeds up the motion
estimation and decreases distortions
   Only part of the inner points will be evaluated
   Enhanced HEXBS algorithm outperforms the
original HEXBS

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