We propose a novel three-dimensional (3-D) display using only two 2-D images displayed at different depths. It is based on a new perceptual phenomenon induced by the human binocular visual system and enables an observer using no extra equipment to perceive an apparent 3-D image of continuous depth when the luminance is divided between the 2-D images according to the 3-D image depth. Our prototype direct-vision 3-D display using this mechanism can easily produce moving 3-D color images by using conventional 2-D color displays.

We clarify the effective range of distance between the front and rear images of the depth-fused 3-D (DFD) visual illusion. The DFD visual illusion is perceived when two images with many edges in the front and rear frontal-parallel planes at different depths are overlapped from the viewpoint of an observer. We evaluated how the fusion of the DFD visual illusion depended on the difference in distance between the front and rear images when the distance between the two images was changed. Subjective tests clarified the cases where DFD can be applied.

We estimated the dependence of the perceived depth on luminance ratio by increasing the distance between the front and rear planes of a depth-fused 3-D (DFD) display. When the distance is great, the perceived depth has the tendency of nonlinear dependence on luminance ratio, which is very different from the almost linear dependence in a short-distance conventional DFD display. In a long-distance DFD display, the perceived depth is split to near the front plane at 0-40% of the rear luminance, near the rear plane at 70-100%, and the midpoint of the front and rear planes at 40-60%. Thus, the luminance-ratio dependence of perceived depth changes widely with the distance.

Three methods of presenting a three-dimensional (3-D) image – a real object, a protruding stereoscopic display, and the depth-fused 3-D (DFD) display – have different tendencies for the change in perceived depth produced when the visual acuity of the dominant eye is decreased by an occlusion foil. These different tendencies are estimated from the slope and correlation coefficient of the plot of perceived depth difference versus stimuli depth difference. This estimation was derived using the same experimental system setup composed of two displays and a half mirror for all three 3-D display methods. The perceived depth difference was measured for four subjects by calipers using two fingers. The slope and correlation coefficient had almost the same tendencies as follows. The real object had the smallest decrease among the three 3-D display methods when the dominant eye's visual acuity was decreased and the protruding stereoscopic display had the largest decrease. The DFD display method had an intermediate decrease between those of the real object and protruding stereoscopic display. When the dominant eye's visual acuity was high enough, the differences among the three 3-D display methods were small. When its visual acuity was decreased, the differences increased among the three 3-D display methods and became statistically significant.

We are developing a simple three-dimensional (3-D) display method that uses only two transparent images using luminance division displays without any extra equipment. This method can be applied to not only electronic displays but also the printed sheets. The method utilizes a 3-D visual illusion in which two ordinary images with many edges can be perceived as an apparent 3-D image with continuous depth between the two image planes, when two identical images are overlapped from the midpoint of the observer's eyes and their optical-density ratio is changed according to the desired image depths. We can use transparent printed sheets or transparent liquid crystal displays to display two overlapping transparent images using this 3-D display method. Subjective test results show that the perceived depths changed continuously as the optical-density ratio changed. Deviations of the perceived depths from the average for each observer were sufficiently small. The depths perceived by all six observers coincided well.