Report itu-r bt. 2160-2 (10/2011)



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2.2 Size distortion


The size of the reproduced image of an object shot by a camera at a certain distance (i.e. the size of recognized objects) varies with the image shooting conditions and display conditions, but is generally subject to size distortion. When size distortion causes objects to appear unnaturally small, it is often referred to as the “puppet theatre” effect7.

2.2.1 Theoretical analysis


The puppet theatre effect has various interpretations. Here, we will not concern ourselves with the perceived absolute size of the reproduced image. Instead, we will concentrate on cases where the size of objects appears to be unnaturally deformed in comparison with the foreground and background.

If Wb is an object’s size in the real space and Wr is its apparent size in the stereoscopic image space (i.e., its perceived size based on its depth position), then the relationship between these values is expressed by the formula below, where a2 has the value shown in Table 2.


(2)

Now let us introduce the magnification Ms of the reproduced image. As shown in equation (3), Ms expresses the apparent size change of objects, taking their depth position into consideration. It corresponds to the ratio of the size Wr of the reproduced image to the size Wb of the object in real space.

(3)
Table 3 shows the results of applying Ms to the parameters of the parallel and toed-in camera configurations shown in Table 2. In the parallel configuration, Ms is constant regardless of the camera-to-object distance Lb, but in the toed-in configuration, Ms varies with Lb. In the toed-in configuration, the sizes of two objects at different depth distances (i.e. background and foreground objects) can be perceived very differently depending on the combination of parameters, and this is liable to cause puppet theatre effects in some cases.

TABLE 3


Analysis of magnitude distortion



2.2.2 Subjective evaluation tests


In the discussion of the previous section, we showed that an object’s reproduced magnification Ms changes with various different parameters. Thus, when two objects (e.g. foreground and background objects) are reproduced at different magnifications, it is expected that unnatural phenomena such as the puppet theatre effect will occur.

We tried to apply the geometrical discussion of the previous section to the results of subjective evaluation tests.

In the subjective evaluation tests, stereoscopic images were reproduced under a number of different imaging and display conditions, and the test subjects evaluated their subjective impressions of the object size8.

For the evaluation images, we used images of a roughly life-sized mannequin (shown in Fig. 6) using three different configurations of shooting distances and camera lenses, each with three different distances separating the left and right cameras. This resulted in a total of nine different evaluation images. Table 4 lists the details of these imaging and display conditions. In these images, the foreground consists of the mannequin, and the background consists of a corridor doorway 4.5 m behind it. In each case, the depth position of the mannequin in the stereoscopic image was at the position of the screen, and the image was displayed life-size on a 120-inch screen.

The test subjects were asked to evaluate the subjective size of the reproduced stereoscopic image of the mannequin on the following five-grade scale:

5: Large


4: Somewhat large

3: Normal

2: Somewhat small

1: Small


FigURE 6

Object used for subjective evaluation tests of puppet theatre effect


TABLE 4

Shooting and display conditions used in subjective
evaluation tests of puppet theatre effect


Figure 7


Correspondence with subjective evaluation scores

We used the ratio Ep of the foreground and background magnifications (Ms(F) and Ms(B)) as a predicted value of the puppet theatre effect. Here, the depth position of the foreground and background are assumed to be given.


(4)
Figure 7 shows the correspondence between the predicted value Ep and the subjective evaluation scores. The evaluation scores and the reproduced image magnification ratio Ep show a strong correlation.

In practice, subjective size distortion phenomena such as the puppet theatre effect are thought to depend on the foreground and background and on the type of object depicted in the image, and it would be worth verifying these results with many more images. In this report, we have at least shown the geometrical criteria that cause this effect.


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