Page 120 - Video Coding for Mobile Communications Efficiency, Complexity, and Resilience

Section 4.2. Motion Estimation 97

• Continuity of solution: The motion estimate is highly sensitive to the
presence of noise.

Because of this ill-posed nature of the problem, motion estimation algo-
rithms use additional assumptions about the structure of the motion eld. Such
assumptions are referred to as motion models. They can be deterministic or
probabilistic, parametric or nonparametric, as will be discussed in the follow-
ing subsections.

4.2.4 Deterministic and Probabilistic Models
In a deterministic model, motion is seen as an unknown deterministic quantity.
By maximizing the probability of the observed video sequence with respect
to the unknown motion, this deterministic quantity can be estimated. The cor-
responding estimator is usually referred to as a maximum likelihood (ML)
estimator. All motion estimation methods discussed in this chapter follow this
deterministic approach.
In a probabilistic (or Bayesian) model, motion is seen as a random variable.
Thus, the ensemble of motion vectors forms a random eld. This eld is
usually modeled using a Markovrandom eld (MRF). Given this model,
motion estimation can be formulated as a maximum a posteriori probability
(MAP) estimation problem. This problem can be solved using optimization
techniques like simulated annealing, iterated conditional modes, mean eld
annealing, and highest con dence rst. For a detailed description of Bayesian
motion estimation methods, the reader is referred to Ref. 10.

4.2.5 Parametric and Nonparametric Models

In a parametric model, motion is represented by a set of motion parameters.
Thus, the problem of motion estimation becomes a problem of estimating
the motion parameters rather than the motion eld itself. Since 2-D motion
results from the projection of 3-D motion onto the image plane, a parametric
2-D motion model is usually derived from models describing 3-D motion,
3-D surfaces, and the projection geometry. For example, the assumptions of
a planar 3-D surface moving in space according to a 3-D a!ne model and
projected onto the image plane using an orthographic projection results in
2
a 2-D 6-parameter a!ne model. Di erent assumptions lead to di erent 2-D
models. The 2-D models can be as complex as a quadratic 12-parameter model

2 In an orthographic projection, it is assumed that all rays from a projected 3-D object to the
image plane travel parallel to each other [10].