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Virtual image in
front of the screen
Figure 3.18 Horizontal parallax is defined by the DPG angle
Yei-Yu Yeh and Silverstein (1990) included the criterion of the duration of viewing
the images to examine the limit of merging and the estimation of depth. The limit of
merging is analysed on the basis of different parameters of stimuli displayed on a
cathode screen with active eyeglasses: colour, display time and horizontal parallax.
The results imply that the limit of merging (given in angle of parallax) is very low for
a brief stimulus of 0.2 second, i.e. 27 to 24 minutes of arc compared to a stimulus
of 2 seconds, i.e. 1.5 degrees. It is therefore more difficult to observe rapidly moving
3D images. Red is easier to merge than white (for the 2 seconds stimuli: 6.2 degrees
for red and 3.7 degrees for white). Errors in estimating the depth are determined by
experiments: Error in parallax angle is 2.2 minutes for images with parallax angles
between 0 and 30 minutes.
The studies show that it is difficult to merge images creating vertical parallaxes
(and thus vertical disparities). Eyes, generally placed on the same horizontal plane,
are not capable of perceiving vertical disparities, except if they are very low. For 3D
images, vertical parallaxes must be less than an angle of 20' arc (Julesz, 1971). We will
see that this constraint needs to be considered when we talk about creating 3D images.
The results of the studies conducted at the Cerma (Centre d'Etudes et de Recherche
de Médecine Aérospatiale [Centre for studies and research in aerospace medicine]) of
the Defence Ministry, being more accurate, corroborate the previous results. The limit
of merging also depends on the spatial frequency of images , which is not studied
in the previously mentioned works. On the basis of their studies, we can conclude
that greater horizontal disparities can be merged when the visual simulations have
low spatial frequencies. From a practical point of view, we can say that the objects
represented by their outlines (high spatial frequencies) are more difficult to merge.
Their studies have highlighted two mechanisms involved in merging, differentiated by
the duration of stimulus: immediate merging for smaller disparities and non-immediate
merging for greater disparities, putting the reflex vergence of eyes into play. The results
also show that at a spatial frequency of 4.8 cycles/degree, there is immediate merging
up to 20' of arc and maximum merging at about 52' of arc. At a spatial frequency of
0.22 cycles/degree, there is immediate merging up to 80' of arc and maximum merging
at about 176' of arc (Plantier et al., 1990; Perrin, 1998).
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