Geometrical analysis of puppet-theater and cardboard effects in stereoscopic HDTV images

A fundamental element of stereoscopic image production is to geometrically analyze the conversion from real space to stereoscopic images by binocular parallax under various shooting and viewing conditions. This paper reports on this analysis, particularly on the setting of the optical axes of three-dimensional (3-D) cameras, which has received little attention in the past. First, we identified the conditions for setting the optical axes that maintain linearity during the conversion from real space to stereoscopic images. We then clarified, in geometrical terms, the shooting and viewing conditions and also conditions under which the puppet-theater effect and cardboard effect occur. The results showed that the parallel camera configuration, by which optical axes are kept parallel to each other, does not produce the puppet-theater effect as the apparent magnification (lateral magnification) of a shooting target is not dependent on the shooting distance. However, the toed-in camera configuration, where the apparent magnification of a shooting target is dependent on the shooting distance, may produce this effect. The cardboard effect is shown to be likely to occur for both camera configurations by defining this phenomenon by the ratio of depthwise reproduction magnification (depth magnification) and apparent reproduction magnification (lateral magnification). Lastly, the paper reports on the relationship between the results of this analysis and those of subjective evaluation experiments. The results need a closer examination by using many more images.