# Motion The research report Block matching algorithm Motion

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```					The research report
Block matching algorithm
Motion compensation
Spatial transformation

Xiaomei Yu

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Motion compensation:
   Motion compensation methods can be defined as
techniques that divide images into local regions (block or
patches) and estimate a set of motion paramaters for
each region.
   The procedure is to synthesizes the predicted image of
the nth frame        from the decoded image of the
previous frame          can be regarded as an image
warping or texture mapping process. It can be written
as
where the geometic relationship between         and
is defined by the transformation funcations       and
.

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Motion compensation:
   Block matching algorithm (BMA) estimates the
motion of blockes and transmits the estimated
motion vectors. BMA can be regarded as a
method that applies spaial transformations on
the blocks of the image.
   Pel-recursive algorithm (PRA) estimates the
motion of each pixel and does not transmit the
motion information.

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Block matching algorithm
   BMA adopts a motionmodel that describes the motion
of the image objects by the translational motion of
blocks. The problems of BMA (e.g. blocking artifacts)
are caused by the insufficiency of the motion model to
represent the real world. To overcome this defect,
many coding methods have been proposed.
   BMA can be regarded as a method that applies spatial
transformations on the blocks of the image. By
generalizing this transformation, new motion
compensation methods that adopt different motion
models can be developed.

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   For example in BMA, the transformation
functions for the pixels in the i th block of
the image are

   Various motion compensation methods can
be composed by adopting different
transformation functions.
Transformation function:
----- Approximate the original motion vector field woth a
smaller number of parameters.
----- A smaller amount of computation.

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   The total amount of computation in texture mapping is a
sum of the following three processes: (a) computation
of the motion parameters (b) computation of the
transformation function ( c) interpolation of intensity
values. The later two are important since they are
performed each pixel. The computational cost of (b)
depend on the existence of an effective scan line
algorithm, which scans the image computing f(x, y) and
g(x, y) for each pixel.

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Spatial transformation
   Affine transformation (AFMC)

   Bilinear transformation (BLMC)

   Perspective transformation

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The advantages/disadvantages
   The parameters can be determined from motion vectors of
three vertices. Then, the patches of this transformation are
triangles. The cost in computing the motion parameters
remains cheap regardless of the shape of the patch. An
effective scan line algorithm exists.
   Only rectangular patches are allowable since otherwise the
computation of the motion parameters become
complicated. An effective scan line algorithm with two
additions per pixel exists for this transformation.
   The scan line algorithm requires two divisions for each
pixel.

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