**2. Definition of global motion**

*Global motions in a video sequence are caused by camera motion, which can be modeled by parametric transforms [4]. The process of estimating the transform parameters is called global motion estimation.* 

From the definition, it is clear that global motion is closely related to camera motion. The camera is operated by camera man. Thus the global motion pattern can reveal video

Global Motion Estimation and Its Applications 85

*x*

*y*

Eq.(2) can be simplified as follows

a translation model as follows

be improved significantly.

**4.1 Pixel domain based GME** 

**4. Global Motion Estimation (GME) approaches** 

which is obtained after transforming all the pixels in *Ik*.

intensive; 2) it is often sensitive to noises (local object motions).

domain based global motion estimation approaches are also very popular.

012 6 7 345 6 7

*mx m y m*

*mx my mx m y m*

*mx my*

where (,) *x y* and (,) *x y* are the coordinates in the current and the reference image respectively, with the set of parameters 0 7 **m** [ ,, ] *m m* denoting the global motion parameters to be estimated. If *m*6=*m*7=0, then it is an affine model with 6 parameters. Then

> *x mx my m y mx my m*

When *m*0= *m*4=1 and ,*m*1=*m*3=*m*6=*m*7=0, then the perspective model is actually simplified into

*x xm y y m* 

Intuitively, global motion estimation can be carried out in pixel domain. In the pixel domain based approaches, all the pixels are involved in the estimation of global motion parameters. There are two shortcomings in pixel domain based approach: 1) it is very computational

In order to improve the convergence and speed up the calculation, coarse to fine searching approach is often adopted. Moreover, the subset of pixels having the largest gradient magnitude is adopted to estimate the global motion parameters [6]. Sub-point based global motion estimation approaches are very effective in reducing computational costs. To guarantee the accuracy of global motion estimation, how to determine the optimal sub-sets are the key steps. Except the pixel domain based global motion estimation, compressed

Robust global motion estimation usually carries out by identifying the pixels (blocks or regions) that undergo local motions. Fig.2 shows the global motion and local motions. If the local motion blocks can be determined as outliers, then the global motion performance can

In GME involving two image frames *Ik* and *Iv* (with *k*<*v*), one seeks to minimize the following sum of squared differences between *Iv* and its predicted image *Ik*(*x*(*i*, *j*), *y*(*i*, *j*))

*i j*

<sup>2</sup> (, )

*E ei j* (5)

012 345

> 2 5

1

(2)

(3)

(4)

1

shooting style which has some relationship with video contents [18]. The global motion information is especially useful in sport video content analysis [13]-[18].

From the definition, we find that the global motions have certain consistence for the whole frame as shown in Fig.1. The global motion in Fig.1 (a) is a zoom out and that in Fig.1 (b) is a translation respectively. From Fig.1 (a), we find that the motion direction is from outer to inner regions, which means that the coordinates of a current frame *t* can be generated in the inner regions of the reference frame *v* (*t* > *v*). In Fig.l, the motion vectors in the motion field correspond to the global motion vectors at the coordinates.

*Global motion vector is the motion vector calculated from the estimated global motion parameters.* Global motion vector (,) *GMVx GMVy t t* for the current pixel with its coordinates (,) *t t x y* is determined as

$$\begin{cases} \mathbf{G}MV\mathbf{x}\_t = \mathbf{x}'\_t - \mathbf{x}\_t\\ \mathbf{G}MVy\_t = y'\_t - y\_t \end{cases} \tag{1}$$

where (,) *t t x y* are the warped coordinates in the reference frame by the global motion parameters from the coordinate (,) *t t x y* .

(a)Zoom-out (b) Translation

Fig. 1. Global motion fields. (a) Zoom-out and (b) Translation.
