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{{Short description|System used in computer graphics applications}}
A '''Block Matching Algorithm'''
[[File:Block-matching algorithm.png|thumb|405x405px]]
A block matching algorithm involves dividing the current [[Film frame|frame]] of a video into macroblocks and comparing each of the macroblocks with a corresponding block and its adjacent neighbors in a nearby frame of the video (sometimes just the previous one). A [[vector (mathematics and physics)|vector]] is created that models the movement of a macroblock from one ___location to another. This movement, calculated for all the macroblocks comprising a frame, constitutes the motion estimated in a frame.
The search area for a good macroblock match is decided by the ‘search parameter’, p, where p is the number of [[pixels]] on all four sides of the corresponding macro-block in the previous frame. The search parameter is a measure of motion. The larger the value of p, larger is the potential motion and the possibility for finding a good match. A full search of all potential blocks however is a computationally expensive task. Typical inputs are a macroblock of size 16 pixels and a search area of p = 7 pixels.
[[Block-matching and 3D filtering]] makes use of this approach to solve various [[Digital photograph restoration|image restoration]] [[inverse problems]] such as [[noise reduction]]<ref>{{cite journal |last1= Dabov |first1= Kostadin |last2= Foi |first2= Alessandro |first3= Vladimir |last3= Katkovnik |first4= Karen |last4= Egiazarian |date= 16 July 2007 |title= Image denoising by sparse 3D transform-___domain collaborative filtering |journal= IEEE Transactions on Image Processing |volume=16 |issue= 8 |pages= 2080–2095 |doi= 10.1109/TIP.2007.901238 |pmid= 17688213 |bibcode= 2007ITIP...16.2080D |citeseerx= 10.1.1.219.5398 |s2cid= 1475121 }}</ref> and [[deblurring]]<ref>{{Cite journal|last1= Danielyan|first1= Aram|last2= Katkovnik|first2= Vladimir|last3= Egiazarian|first3= Karen|arxiv=1106.6180 |title= BM3D Frames and Variational Image Deblurring |journal= IEEE Transactions on Image Processing|volume= 21|issue= 4|pages= 1715–28|date=30 June 2011 |doi= 10.1109/TIP.2011.2176954|pmid= 22128008|bibcode= 2012ITIP...21.1715D|s2cid= 11204616}}</ref> in both still images and [[digital video]].
== Motivation ==
Applying the motion vectors to an image to predict the transformation to another image, on account of moving camera or object in the image is called [[motion compensation]]. The combination of motion estimation and motion compensation is a key part of [[video compression]] as used by [[MPEG]] 1, 2 and 4 as well as many other [[video codecs]].
Motion estimation based video compression helps in saving bits by sending encoded difference images which have inherently less
== Evaluation Metrics ==
[[Mean absolute difference|Mean difference]] or Mean Absolute Difference (MAD) = <math>\frac{1}{N^2}\sum_{i=0}^{n-1}\sum_{j=0}^{n-1} |C_{ij}-R_{ij}|</math>
[[Mean Squared Error]] (MSE) = <math>\frac{1}{N^2}\sum_{i=0}^{n-1}\sum_{j=0}^{n-1} (C_{ij}-R_{ij})^2</math>
where N is the size of the macro-block, and <math>C_{ij}</math> and <math>R_{ij}</math> are the pixels being compared in current
The motion compensated image that is created using the
<math>\text{PSNR} =
== Algorithms ==
{{More citations needed|date=January 2024}}
Block Matching algorithms have been researched since mid-1980s. Many algorithms have been developed, but only some of the most basic or commonly used have been described below.
This algorithm calculates the [[Loss function|cost function]] at each possible ___location in the search window. This leads to the best possible match of the macro-block in the reference frame with a block in another frame. The resulting motion compensated image has highest peak signal-to-noise ratio as compared to any other block matching algorithm.
However this is the most computationally extensive block matching algorithm among all. A larger search window requires greater number of computations.
===
The optimized hierarchical block matching (OHBM) algorithm speeds up the exhaustive search based on the optimized image pyramids.<ref name="Je_spic13_ohbm">{{Cite journal |doi = 10.1016/j.image.2013.04.002|title = Optimized hierarchical block matching for fast and accurate image registration|journal = Signal Processing: Image Communication|volume = 28|issue = 7|pages = 779–791|year = 2013|last1 = Je|first1 = Changsoo|last2 = Park|first2 = Hyung-Min}}</ref>
=== Three Step Search ===
It is one of the earliest fast block matching algorithms. It runs as follows:
# Start with search ___location at center
# Set step size S = 4 and search parameter p = 7
# Search 8 locations +/- S pixels around ___location (0,0) and the ___location (0,0)
# Pick among the 9 locations searched, the one with minimum cost function
# Set the new step size as S = S/2
The resulting ___location for S=1 is the one with minimum cost function and the macro block at this ___location is the best match.
There is a reduction in computation by a factor of 9 in this algorithm. For p=7, while ES evaluates cost for
=== Two Dimensional Logarithmic Search
TDLS is closely related to TSS however it is more accurate for estimating
# Select an initial step size say, S = 8
# Search for 4 locations at a distance of S from center on the X and Y axes
# Find the ___location of point with least cost function
# If a point other than center is the best matching point,
## Select this point as the new center
# If the best matching point is at the center, set S = S/2
# Repeat steps 2 to 3
# If S = 1, all 8 locations around the center at a [[distance]] S are searched
# Set the motion vector as the point with least cost function
=== New Three Step Search ===
TSS uses a uniformly allocated checking pattern and is prone to miss small motions. NTSS <ref name=tss>{{cite journal|last1=Li|first1=Renxiang|last2=Zeng|first2=Bing|last3=Liou|first3=Ming|title=A New Three-Step Search Algorithm for Block Motion Estimation|journal= IEEE Transactions on Circuits and Systems for Video Technology|date=August 1994|volume=4|issue=4|pages=438–442|doi=10.1109/76.313138}}</ref> is an improvement over TSS as it provides a center biased search scheme and has provisions to stop halfway to reduce the computational cost. It was one of the first widely accepted fast algorithms and frequently used for implementing earlier standards like [[MPEG]] 1 and H.261.
The algorithm runs as follows:
# Search 8 locations +/- S pixels with S = 4 and 8 locations +/- S pixels with S = 1 around ___location (0,0)
# Pick among the 16 locations searched, the one with minimum cost function
# If the minimum cost function occurs at origin, stop the search and set motion vector to (0,0)
## Check adjacent weights for this ___location, depending on ___location it may check either 3 or 5 points
# If the lowest weight after the first step was one of the 8 locations at S = 4, the normal TSS procedure follows
## Set the new search origin to the above picked ___location
## Set the new step size as S = S/2
## Repeat the search procedure until S = 1
Thus this algorithm checks 17 points for each macro-block and the worst-case scenario involves checking 33 locations, which is still much faster than TSS
=== Simple and Efficient Search
The idea behind TSS is that the error surface due to motion in every macro block is [[unimodal]]. A
SES algorithm improves upon TSS algorithm as each search step in SES is divided into two phases:
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• First Phase :
• Divide the area of search in four [[quadrant (plane geometry)|quadrant]]s
• Start search with three locations, one at center (A) and others (B and C), S=4 locations away from A in orthogonal directions
• Find points in search quadrant for second phase using the weight distribution for A, B, C:
• If (MAD(A)>=MAD(B) and MAD(A)>=MAD(C)), select points in second phase quadrant IV
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• Repeat the SES search procedure until S=1
• Select the ___location with lowest weight as
SES is computationally very efficient as compared to TSS. However the peak signal-to-noise ratio achieved is poor as compared to TSS as the error surfaces are not strictly unimodal in reality.
=== Four Step Search ===
Four Step Search is an improvement over TSS in terms of lower computational cost and better peak signal-to-noise ratio. Similar to NTSS, FSS <ref>{{cite journal|last1=Po|first1=Lai-Man|last2=Ma|first2=Wing-Chung|title=A Novel Four-Step Search Algorithm for Fast Block Motion Estimation|journal= IEEE Transactions on Circuits and Systems for Video Technology|date=June 1996|volume=6|issue=3|pages=313–317|doi=10.1109/76.499840}}</ref> also employs center [[bias (statistics)|bias]]ed searching and has a halfway stop provision.
The algorithm runs as follows:
# Set step size S = 2, (irrespective of search parameter p)
# Search 8 locations +/- S pixels around ___location (0,0)
# Pick among the 9 locations searched, the one with minimum cost function
# If the minimum weight is found at center for search window:
## Set the new step size as S = S/2 (that is S = 1)
## Repeat the search procedure from steps 3 to 4
## Select ___location with the least weight as motion vector
# If the minimum weight is found at one of the 8 locations other than the center:
## Set the new origin to this ___location
## Fix the step size as S = 2
## Repeat the search procedure from steps 3 to 4. Depending on ___location of new origin, search through 5 locations or 3 locations
## Select the ___location with the least weight
## If the least weight ___location is at the center of new window go to step 5, else go to step 6
=== Diamond Search ===
Diamond Search (DS)<ref>{{cite journal|last1=Zhu|first1=Shan|last2=Ma|first2=Kai-Kuang|title=A New Diamond Search Algorithm for Fast Block-Matching Motion Estimation|journal= IEEE Transactions on Image Processing|date=February 2000|volume=9|issue=12|pages=287–290|doi=10.1109/83.821744|pmid=18255398|bibcode=2000ITIP....9..287Z}}</ref> algorithm uses a diamond search point pattern and the algorithm runs exactly the same as 4SS. However, there is no limit on the number of steps that the algorithm can take.
Two different types of fixed patterns are used for search,
* Small Diamond Search Pattern (SDSP)
The algorithm runs as follows:
## Pick among the 9 locations searched, the one with minimum cost function
## If the minimum weight is found at center for search window, go to SDSP step
## Repeat LDSP
* SDSP:
## Set the new search origin
## Set the new step size as S = S/2 (that is S = 1)
## Repeat the search procedure to find ___location with least weight
## Select ___location
This algorithm finds the global minimum very accurately as the search pattern is neither too big nor too small. Diamond Search algorithm has a peak signal-to-noise ratio close to that of Exhaustive Search with significantly less computational expense.
=== Adaptive Rood Pattern Search
Adaptive rood pattern search (ARPS) <ref>{{cite journal|last1=Nie|first1=Yao|last2=Ma|first2=Kai-Kuang|title=Adaptive Rood Pattern Search for Fast Block-Matching Motion Estimation|journal= IEEE
# Find the predicted motion vector for the block
# Set step size S = max (|X|,|Y|), where (X,Y) is the [[coordinate]] of predicted motion vector
# Search for rood pattern distributed points around the origin at step size S
# Set the point with least weight as origin
# Search using small diamond search pattern (SDSP) around the new origin
# Repeat SDSP search until least weighted point is at the center of SDSP
Rood pattern search directly puts the search in an area where there is a high probability of finding a good matching block. The main advantage of ARPS over DS is if the predicted motion vector is (0, 0), it does not waste computational time in doing LDSP, but it directly starts using SDSP. Furthermore, if the predicted motion vector is far away from the center, then again ARPS saves on computations by directly jumping to that vicinity and using SDSP, whereas DS takes its time doing LDSP.
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==References==
{{reflist}}
== External links ==
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