A video sequence consists of a number of pictures  usually called frames. Subsequent frames are very similar, thus, containing a lot of redundancy. The goal is to remove the redundancy to gain better compression ratios.
A first approach would be to simply subtract a reference frame from a given frame. The difference is then called residual and usually contains less energy (or information) than the original frame. The residual can be encoded at a lower bitrate with the same quality. The decoder can reconstruct the original frame by adding the reference frame again.
A more sophisticated approach is to approximate the motion of the whole scene and the objects of a video sequence. The motion is described by some parameters that have to be encoded in the bitstream. The pixels of the predicted frame are approximated by appropriately translated pixels of the reference frame. This gives much better residuals than a simple subtraction. However, the bitrate occupied by the parameters of the motion model must not become too big.
Usually, the frames are processed in groups. One frame (usually the first) is encoded without motion compensation just as a normal image. This frame is called Iframe (intracoded frame, MPEG terminology) or Ipicture. The other frames are called Pframes or Ppictures and are predicted from the Iframe or Pframe that comes (temporally) immediately before it. The prediction schemes are, for instance, described as IPPPP, meaning that a group consists of one Iframe followed by four Pframes.
Frames can also be predicted from future frames. The future frames have to be encoded before the predicted frames, of course. Thus, the encoding order does not necesserily match the real frame order. Such frames are usually predicted from two direction, i.e. from the I or Pframes that immediately precede or follow the predicted frame. These bidirectionally predicted frames are called Bframes. A coding scheme could, for instance, be IBBPBBPBBPBB.

In global motion compensation, the motion model basically reflects camera motions such as dolly (forward, backwards), track (left, right), boom (up, down), pan (left, right), tilt (up, down) and roll (along the view axis). It works best for still scenes without moving objects. There are several advantages of global motion compensation:
However, moving objects are not sufficiently represented by global motion compensation. Thus, other methods are preferable.
In block motion compensation (BMC), the frames are partitioned in blocks of pixels (e.g. macroblocks of 16×16 pixels in MPEG). Each block is predicted from a block of equal size in the reference frame. The blocks are not transformed in any way apart from being shifted to the position of the predicted block. This shift is represented by a motion vector.
The motion vectors are the parameters of this motion model and have to be encoded into the bitstream. As the motion vectors are not independent (e.g. if two neighbouring blocks belong to the same moving object), they are usually encoded differentially to save bitrate. This means that the difference of the motion vector and the neighbouring motion vector(s) encoded before is encoded. An entropy codec can exploit the resulting statistical distribution of the motion vectors (around the zero vector).
It is possible to shift blocks by noninteger vectors, which is called subpixel precision. This is done by interpolating the pixel's values. Usually, the precision of the motion vectors is increased by one bit: halfpixel precision. Of course, the computational expense for subpixel precision is much higher since the interpolation functions can be quite consuming.
The big disadvantage of block motion compensation are the discontinuities introduced at block borders (blocking artifacts). They have the form of sharp horizontal and vertical edges which, firstly, are highly visual for the human eye and, secondly, produce ringing effects (big coefficients in high frequency subbands) in the frequency transform used for transform coding of the residual frames.
Overlapped Block Motion Compensation
Overlapped block motion compensation (OBMC) is a good solution to these problems because it not only increases prediction accuracy but also avoids blocking artifacts. Blocks are usually twice as big in each dimension and overlap quadrantwise with all 8 neighbouring blocks. Thus, each pixel belongs to 4 blocks. There are 4 predictions for each pixel which are summed up to a weighted mean. For this purpose, blocks are associated with a window function that owns the property that the sum of 4 overlapped windows is equal to 1 everywhere.
Motion estimation (BME, OBME) is the process of finding optimal or nearoptimal motion vectors which minimise the overall prediction error. The prediction error of a block is defined as the mean squared error (MSE) between predicted and actual pixel values over all pixels of the block.
To find optimal motion vectors, one basically has to calculate the block prediction error for each motion vector within a certain search range and pick the one with the smallest error (full search). A faster and suboptimal method is to use a coarse search grid for a first approximation and to refine the grid in the surrounding of this approximation in further steps. The most common representative of this method is the 3step search which uses search grids of 3×3 motion vectors and 3 refinement steps to get an overall search range of 15×15 pixel.
For OBME, the pixelwise prediction errors of a block and its overlapping neighbouring blocks have to be weighted and summed according to the window function before being squared. As in the process of successively finding/refining motion vectors some neighbouring MVs are not known yet, the corresponding prediction errors can be ignored (not added) as a suboptimal solution.
The major disadvantages of OBMC are increased computational complexity of OBME, and the fact that prediction errors and, thus, also the optimal motion vectors depend on neighbouring blocks/motion vectors. Therefore, there is no algorithm with polynomial computational complexity that guarantees optimal motion vectors. However, there are nearoptimal iterative and noniterative methods with acceptable computational complexity.
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