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Use of Stereoscopic Photography to Distinguish Object Depth in Outdoor Scene

Chapter 3 The Geometry of Multiple Views

3.1 Depth Perception Methodology

Figure 2. A demonstration of binocular parallax. (a) Left image frame. (b) Right image frame.

In Figure 2(a) we can see that the signs appearing in the rear of the scene is

tended to left just like human’s left eye which has observed it or otherwise vice versa

as shown in Figure 2(b). The phenomenon of binocular parallax is the principal

theory of stereoscopic photography. We put the camera in two different places and

took the picture in turn. In other words, we can take a pair of pictures to simulate

binocular parallax effect. Binocular parallax effect depends on the distance between

two shots which we call it as stereo base line. We can get that the longer the stereo

base line the better the stereo effect for the view of a far way mountain. Figure 3 is a

demonstration of stereoscopic photograph taken by a camera.

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Figure 3. A demonstration of stereoscopic photograph.

Some new and advantageous photographic technologies are being introduced

such as image base virtual reality, panama, and stereo photo. Many of them are

being implemented in the commercial digital camera, with the only exception of

stereo photo efficacy, which is being implemented only in some types of Pentax

cameras. We proposed a simplified method of taking stereo photo by introducing

the use of only one commercial digital camera. We propose two stages of works in

our experiment.

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Use of Stereoscopic Photography to Distinguish Object Depth in Outdoor Scene

First stage, we can take serial photos with regular displacement along the slide

bar and make preprocesses if necessary. The steps of taking stereo photo are showed

as follows.

1. Estimate the distance of the main objects which you want to take the photo.

2. Determine the horizontal distance of the camera between two shots.

3. Carry out post processing to combine left and right image and take a look with

accessories.

Second stage, according to the different purposes, we can divide the works into

two parts. First part, for entertainment we can select photo-pairs and use

stereoscopic glasses to present with 3D scene. Second part, for application we

propose the model of lineal regression after training and validation. We can use the

results in real world for depth estimation.

The flowchart of stereoscopic photograph is shown in Figure 4.

The X-Z plane coordination of our proposed stereoscopic photograph camera

system is shown in Figure 5. Many important parameters are also shown in this

Figure.

x

l

z

= fx (2.1)

x

r

z b x f ( − )

= (2.2)

From Eq. 2.1 and Eq. 2.2, we obtain Eq. 2.3, as follows.

(4)

Figure 4. The flowchart of stereoscopic photograph.

x - x

l r

z b x f

fx − ( − )

=

z

r

l

x

x

b x f fx

= − ( )

z d

= fb (2-3)

where d = x

l

- x

r

, is the disparity of two corresponding point.

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Use of Stereoscopic Photography to Distinguish Object Depth in Outdoor Scene

Figure 5. Coordinate system in X-Z plane.

⎥ ⎥

⎥ ⎥

⎥ ⎥

⎢ ⎢

⎢ ⎢

⎢ ⎢

=

⎥ ⎥

⎥ ⎥

⎥ ⎥

⎢ ⎢

⎢ ⎢

⎢ ⎢

=

⎥ ⎥

⎢ ⎢

d fb

f z y

f z x

x x

fb f

z y

f z x

z y x

l l

r l

l l

(2.4)

Depth (z) goes to infinite as disparity (d) approaches to zero. As shown in Eq.

2.5 we can see that depth(z) is increased while disparity(d) is down if base line(b)

keeps a constant. We can use this property to estimate the focus of the camera by

Least Square Method.

z

0

lim

d

fb d

=

= ∞ (2.5) An example of the simple stereo system is introduced as follows. We can

measure the projections of a stereoscopic point on the left and right cameras as (x

l

, y

l

)

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cameras is 40cm and the focal lengths of the two cameras are f=1000 pixels. We can

calculate with Eq. 2.4. The stereoscopic coordinate of the stereoscopic point with

respect to the left camera is [64, 160, 800].

3.2 Calculation Methodology

From Eq. 2.3, we obtain

f

b = zd (2.6)

b zm

f = zd = (2.7)

In Eq. 2.7, we assume m = d/b. If we want to derive optimum baseline, some

steps must be taken. First, we must calculate the focus of the camera. Second, we

need to know how far is the main object which we want to take, and the proper

disparity. As to how to figure it out, we try to combine z and d together, assume k =

zd. We obtain as follows.

f

b = k (2.8)

Let us summarize the procedure as follows. Firstly, we try to do camera

calibration to find the focal length. Secondly, we solve the value of zd with

statistical method. And then we can obtain b easily in Eq. 2.8.

數據

Figure 2. A demonstration of binocular parallax. (a) Left image frame. (b) Right  image frame
Figure 3. A demonstration of stereoscopic photograph.
Figure 4. The flowchart of stereoscopic photograph.  x - xl  r z bxffx−(− )= z rl xx bxffx−−=−( ) z d= fb                                                                                                                      (2-3)
Figure 5. Coordinate system in X-Z plane.

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