**3. Differential-type method**

the analogy of the human eyeball, the center of camera rotation is set behind the lens center by *Z*<sup>0</sup> along the optical axis, and there is no explicit translational motion of the

on the coordinate origin, which is the lens center, using the same component. On the other hand, this difference between the coordinate origin and the center of rotation

� �<sup>T</sup>

2 6 4

0 0 *Z*0

In general, the translational motion of a camera lens is essential to recover depth,

From Eq. (1), it can be known that *rz* causes no translations. Therefore, we can set *rz* <sup>¼</sup> 0 and redefine *<sup>r</sup>* <sup>¼</sup> *rx*,*ry*, 0 � �<sup>T</sup> as a rotational vector like an eyeball. Using Eq. (1) and the inverse depth *d x*ð Þ¼ , *y* 1*=Z x*ð Þ , *y* , image motion called "optical flow"

In the above equations, *d* is an unknown variable at each pixel, and *u* and *r* are

In this study, we treat *r* ð Þ*t* as a white stochastic process to simplify the motion model, and *t* indicates time. *r* ð Þ*t* is defined as the rotation speed with respect to the camera orientation of *t* ¼ 0, not the derivative between consecutive frames. In the actual fixational eye movement, the temporal correlation of tremor that forms the drift component is ignored. We assume that each fluctuation of *r* ð Þ*t*

and our camera motion model can implicitly achieve that translation simply by rotating the camera. This facilitates camera control. In addition, the system can recover absolute depth by pre-calibrating *Z*0. We show the coordinate system and

3 7 <sup>5</sup> <sup>¼</sup> *<sup>Z</sup>*<sup>0</sup>

� �<sup>T</sup> also expresses a rotation vector centered

*ry* �*rx* 0

3 7

2 6 4

*vx* <sup>¼</sup> *xyrx* � <sup>1</sup> <sup>þ</sup> *<sup>x</sup>*<sup>2</sup> � �*ry* � *<sup>Z</sup>*0*ryd*, (2) *vy* <sup>¼</sup> <sup>1</sup> <sup>þ</sup> *<sup>y</sup>*<sup>2</sup> � �*rx* � *xyry* <sup>þ</sup> *<sup>Z</sup>*0*rxd:* (3)

, which is formulated as follows:

<sup>5</sup>*:* (1)

camera. This rotation vector *r* ¼ *rx*,*ry*,*rz*

*Applications of Pattern Recognition*

results in the translation vector *u* ¼ *ux*, *uy*, *uz*

2 6 4

*ux uy uz*

camera motion model used in this study in **Figure 1**.

unknown common parameters for the whole image.

*Coordinate system and camera motion model used in this study.*

� �<sup>T</sup> is given as follows:

**v** ¼ *vx*, *vy*

**Figure 1.**

**6**

*rx ry rz*

2 6 4
