Motion estimation is the process of determining ''motion vectors'' that describe the transformation from one 2D image to another; usually from adjacent frames in a video sequence. It is an ill-posed problem as the motion is in three dimensions but the images are a projection of the 3D scene onto a 2D plane. The motion vectors may relate to the whole image (global motion estimation) or specific parts, such as rectangular blocks, arbitrary shaped patches or even per

pixel In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device. In most digital display devices, pixels are the sm ...

. The motion vectors may be represented by a translational model or many other models that can approximate the motion of a real video camera, such as rotation and translation in all three dimensions and zoom.

Related terms

More often than not, the term motion estimation and the term ''

optical flow Optical flow or optic flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and a scene. Optical flow can also be defined as the distribution of apparent veloci ...

'' are used interchangeably. It is also related in concept to '' image registration'' and ''

stereo correspondence The correspondence problem refers to the problem of ascertaining which parts of one image correspond to which parts of another image, where differences are due to movement of the camera, the elapse of time, and/or movement of objects in the photo ...

''. In fact all of these terms refer to the process of finding corresponding points between two images or video frames. The points that correspond to each other in two views (images or frames) of a real scene or object are "usually" the same point in that scene or on that object. Before we do motion estimation, we must define our measurement of correspondence, i.e., the matching metric, which is a measurement of how similar two image points are. There is no right or wrong here; the choice of matching metric is usually related to what the final estimated motion is used for as well as the optimisation strategy in the estimation process. Each ''motion vector'' is used to represent a ''

macroblock The macroblock is a processing unit in image and video compression formats based on linear block transforms, typically the discrete cosine transform (DCT). A macroblock typically consists of 16×16 samples, and is further subdivided into transform ...

'' in a picture based on the position of this macroblock (or a similar one) in another picture, called the reference picture. The H.264/MPEG-4 AVC standard defines ''motion vector'' as:

motion vector: a two-dimensional vector used for inter prediction that provides an offset from the coordinates in the decoded picture to the coordinates in a reference picture.

Algorithms

The methods for finding motion vectors can be categorised into pixel based methods ("direct") and feature based methods ("indirect"). A famous debate resulted in two papers from the opposing factions being produced to try to establish a conclusion.

Direct methods

* Block-matching algorithm *

Phase correlation Phase correlation is an approach to estimate the relative translative offset between two similar images ( digital image correlation) or other data sets. It is commonly used in image registration and relies on a frequency-domain representation of th ...

and frequency domain methods * Pixel recursive algorithms *

Optical flow Optical flow or optic flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and a scene. Optical flow can also be defined as the distribution of apparent veloci ...

Indirect methods

''Indirect methods'' use features, such as

corner detection Corner detection is an approach used within computer vision systems to extract certain kinds of features and infer the contents of an image. Corner detection is frequently used in motion detection, image registration, video tracking, image mos ...

, and match corresponding features between frames, usually with a statistical function applied over a local or global area. The purpose of the statistical function is to remove matches that do not correspond to the actual motion. Statistical functions that have been successfully used include RANSAC.

Additional note on the categorization

It can be argued that almost all methods require some kind of definition of the matching criteria. The difference is only whether you summarise over a local image region first and then compare the summarisation (such as feature based methods), or you compare each pixel first (such as squaring the difference) and then summarise over a local image region (block base motion and filter based motion). An emerging type of matching criteria summarises a local image region first for every pixel location (through some feature transform such as Laplacian transform), compares each summarised pixel and summarises over a local image region again. Some matching criteria have the ability to exclude points that do not actually correspond to each other albeit producing a good matching score, others do not have this ability, but they are still matching criteria.

Applications

Video coding

Applying the motion vectors to an image to synthesize the transformation to the next image is called

motion compensation Motion compensation in computing, is an algorithmic technique used to predict a frame in a video, given the previous and/or future frames by accounting for motion of the camera and/or objects in the video. It is employed in the encoding of video d ...

. It is most easily applied to discrete cosine transform (DCT) based video coding standards, because the coding is performed in blocks. As a way of exploiting temporal redundancy, motion estimation and compensation are key parts of

video compression In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression ...

. Almost all video coding standards use block-based motion estimation and compensation such as the

MPEG The Moving Picture Experts Group (MPEG) is an alliance of working groups established jointly by ISO and IEC that sets standards for media coding, including compression coding of audio, video, graphics, and genomic data; and transmission and ...

series including the most recent

HEVC High Efficiency Video Coding (HEVC), also known as H.265 and MPEG-H Part 2, is a video compression standard designed as part of the MPEG-H project as a successor to the widely used Advanced Video Coding (AVC, H.264, or MPEG-4 Part 10). In compar ...

3D reconstruction

simultaneous localization and mapping Simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. While this initially appears to be a chi ...

, a 3D model of a scene is reconstructed using images from a moving camera.Kerl, Christian, Jürgen Sturm, and

Daniel Cremers Daniel Cremers (born 1971) is a German computer scientist, Professor of Informatics and Mathematics and Chair of Computer Vision & Artificial Intelligence at the Technische Universität München. His research foci are computer vision, mathematica ...

.
Dense visual SLAM for RGB-D cameras
" 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2013.

References

Video processing Motion (physics) Motion in computer vision