诱导立体，跟随聚焦，自由視觉的分析

【摘要】  本文简要地回顾立体（3D）成像中的几个重要事件。对产生立体感觉的所有诱因进行了重新分类。对诱导立体、跟随聚焦、自由视觉进行了较仔细的分析，并说明了它们的应用。最后介绍了一种新型的立体成像器的设计。使每个具有数码相机的人均可自行拍摄立体像对，并用此装置观看放大的立体像，其彩色、保真度与彩色照片相当。

【关键词】  诱导立体; 跟随聚焦; 自由视觉; 立体成像器

    In 280 BC, Euclid realized that the sense of spacial object was caused by the dissimilar image between visions in our two eyes. Now it is called binocular parallax. According to this principle, in 1838, C. Wheatstone invented the first stereoscope. During the time of renaissance (1400~1600 AD), L. Da. Vinci and other artists gradually understood the scenography, and they learned to use shadows, luster to stress the stereo perception. In 1948 D. Gabor invented the Hologram. It has recorded not only the wave intensity but also the phase of it. His new idea was realized by Leith E. N and Upatnieks J. using coherent laser beam in 1962.  The holographic stereo image can be seen from different direction so we can get the lateral information of the object. This was the optimal approach for 3D image and people have placed a great hope on it. In 1960, Bela Julesz invented that the depth feeling is priori by means of random dots figure. In 1976  a  Japanese scholar Takanori Okoshi published a book［1］ where he synthesized the early studies and concluded that ten cues are available for perceiving the depth of an image. These cues are classified further into two major groups: physiological and psychological cues. The former 4 cues can be believed to be more important than the latter 6. However this classification is not so complete since several new discovered cues have not yet been included and the similar perspective can be combined into one. So they are reclassified as following:

    1  12 cues of depth perception〖*2〗(A) Physiological cues    1. Accommodation

    It is the muscular tension of the ciliary?s body that adjusts the focal length of the crystalline lens. It is a monocular depth cue. The cue is effective for a distance less than 2 meter.

    2. Convergence

    When we turn our two eyeballs and look at a certain point on an object, the angle made by the two viewing axes is called the convergence angle. It gives us a cue of depth perception. But it will be invalid beyond 10 meters. It will also unify the retinal images of the two eyes. We call this kind of action pattern matching. Experiments showed that an interaction exists between convergence and accommodation.

    3. Binocular parallax

    The distance between two eyes is approximately 6.5 cm horizontally, so the image on retinas in both eyes are slightly different. It is called binocular parallax. This difference will be more significant when getting closer. So we could judge how far the object is. It is the most significant factor to the depth perception, when objects are within 250 meters.

    4. Monocular movement parallax

    When we close one of our eyes, and have a relative movement to objects, just like when we are in a train, near object fleet away, distant object move slowly. This forms the sense of far and near. And it is only valid for several hundred meters.

    5. Color Difference

    Because of the refraction ratio of our eye?s crystalline lens between different colors is different, it may cause the image position on the retina different, too. The blue objects will stay top on red ones, and green ones stay in the middle.

    (B) Psychological cues

    1. Retinal image size

    Generally speaking, the smaller the image on the retina, the further the object will be. But common sense has already told us the size of some objects, so we can distinguish some objects in similar size. Therefore, if we see a man and a similar sized elephant, we will understand that the elephant must be somewhere further than the man.

    2. Linear perspective

    The scenery will diminish linearly as the distance grows. For example, it seems to be narrower in the further end of two parallel rails. Painters always use this cue.

    3. Areal perspective

    Distant landscapes often look hazy due to the scattering by small particles in the air (like smoke, dust, vapor). So the Chinese painters use less ink to draw mountains and trees far away.

    4. Shades and shadows

    A three dimensional object exposed to the light will present different shades and shadows in different parts. Western painters use this characteristics to stress the sense of stereo.

    5. Overlapping

    Front objects always overlap the things behind them. Generally, an object whose outline pattern looks relatively continuous is felt to be closer, and vice versa.

    6. Induced Stereovision［2］

    If monocular vision is near the real stereo vision, it would be induced to be “Induced Stereovision”. Its stereo feeling is almost close to the real stereovision. (More details later)

    7. Large Screen Stereovision

    We have a wide range of visual field, horizontal: 220°and vertical: 130°. It is like a wider angle camera. Generally we can easily see any thing in those ranges: horizontal: 90° and vertical: 70°. When we watch movies on a large or ultra large screen, even a dome screen, we will get stereo perception as well as immerse feelings although the pictures are planar.

    In general, there are totally 12 cues of depth perception, 5 of which are physiological, another 7 are psychological. We may classify this from another angle, except A2, A3, A5, B6, the rest are all determined by one eye alone. So we usually call this as monocular vision. The modern painting, photography, movie and TV are now paying more attention to the stereo information concerning monocular vision, and they have tried their best to make it optimal, but it is still far from enough. In the prospective display technology, we should rely more on the double eyes stereo vision, and use all the factors that may cause the sense of stereo described above.

    Now let us discuss the new “induced stereo” cues and the related following focus, free view more detail.

    2  Following Focus and Free View

    When we insert the “image pair” into the new stereoscope［3］, we will get a so real 3D vision if you stare at the image for a while. That means your eyes have adjusted to a good condition. Then you could insert slowly the “image pair” a little deeper, the depth perception will get even better. Somebody can even push the image pair to the end of this 3D device where the 3D vision will be the best. But if you put the “image pair” at the end of the device to begin with, you will see double images instead of a 3D image. This is the so-called “following focus”, it comes from the auto focus and auto convergence of human eyes. People?s eyes will adjust curvature of crystalline lens upon environment to attain desirable focus so that we can get a clear view of both back and forth. Meanwhile, people need to roll their eyeballs to make adjustment to get a matched image from the right and left eye. This capability to adjust your eyeballs varies from different people, and it could be enhanced after practice, especially the juveniles.

    Now let us discuss how to get a 3D image from our naked eyes directly through “free view”. Let us start with a simple example. Suppose a ball locating in a far position. Like the ball labeled 1 in the Fig. 1a. Close your right eye to observe with your left eye only. There will be no surrounding references to help you locate the ball. Maybe it is a bigger B from a further position or a smaller B? from nearer.  It is possible to place the B ball in any position of that triangle area. Only if you open the right eye can you make sure where the B ball truly is according to the two eyes convergences angle. Now let us change the condition a little bit. Place a planar left image at the position 1(see Fig.1b), and another right eye image of the same object in position 2. Let these two images suitably away from your eyes. At first, we can still see two apart images from each other, but after we relax our eyes for a while, with the free view, the left eye and right eye image will converge into one in the position B and become a three dimensional ball, it has even enlarged a little. B is the real 3D image of the original object.

    Fig. 1

    3  Induced 3D image

    Let the six images of a dancer arranged in a line. The label numbers of those circles are from 1 to 6. 1, 2, 3 are left eye images and the 4, 5, 6 are right eye image of the same dancer, as shown in fig. 2 (a). At the first glance, they are all the same plane image.

    If you use the free view method to stare at the two middle dark dots, when they become three dots, the free view is accomplished. And move your eyesight slowly to the dancer and you may see 7 dancers at one time. The middle one is a real 3D image, her hand and long nails are extending out of the screen and the Christmas tree and the upper clock are extending to the back. Other 6 images on its two sides remain planar. If you use an opaque slip to cover the second image on the left, Fig. 2(b), you can still see 3 images on the left, but they all become 3D images, and the 3D effect is as good as the middle one. If you cover the second image on the right, same things will happen. If we cover those 2 images at the same time, we can still get 7 images, and they all become stereo. The middle 3D image is called real 3D image, the rest six 3D images are called “induced 3D image”. This phenomenon can be explained by Fig. 3, and we can discover an implicit rationale called “induced stereo” classified as psychological cues.

    Fig. 2

    Fig. 3

    Suppose we use 6 circles to replace the 6 images of the dancer. Draw a left parenthesis in the left three circles to denote left eye images of the dancer, and right parenthesis in the right three to denote right eye image, through free view, extend the eyesight along their own directions to make it 7 circles. Use bigger circles to represent them, and label them as A, B, C, D, E, F, G.

    We can see that, through free view method, the image in the D position is the combination of No. 3 from the left and No. 4 from the right, so within the D circle, we have a left and a right parenthesis, which means the right and the left image overlap right in that place. That is a real stereo image. But why are the lateral images still planar?

    Examine B first, it is the combination of No.1 and No.2 through free view method, there are two left parenthesis in it, these two are both left eye images, no binocular parallax exists, so it is a planar image. So are C, E, F. About A and G, if you observe closer, they are more or less stereo. Because A can be seen only by right eye, and G by left eye, so these are monocular vision, and it is called monocular stereo or single eye stereo.

    When no. 2 is covered, the situation will be changed. B is formed only by No.1 and can only be seen by the left eye, C is formed by no. 3, can only be seen by the right eye, they both belong to monocular vision. But D, which is on the right side of B, is a real stereo image, the adjacent C will be induced by D, the adjacent B will then be induced by its neighbor C, and A is induced by B, they will all become stereo images. Same things will happen if we cover the no. 5. Through this trial, we can compare “ binocular parallax”, “induced stereo” and  “monocular stereo” under the same condition. The effect of induced stereo is far better than monocular stereo, so it can be concluded into neither monocular stereo, nor any traditional cues, it belongs to a new category in psychological cues. We call it “induced sereo”.

    The trial above described can only demonstrate that induced stereo exists in the horizontal direction, but it does exist in the vertical direction too. So we can get the following conclusion:

    If planar images of single eye vision exist around a real stereo image, they will be induced to become stereo as well, and have a strong sense of stereo.

    Induced stereo can be not only applied to extend the vision field［3］, but also applied to other respects. For example, when you are shooting the second right eye image to make the image pair, a bird or a person rush in, it is not necessary to delete them from the right eye image. They will be induced to 3D image too and will not influence the whole 3D system. When shooting only with one camera, some people will not be easy to stay stationary, we only need delete the moved person in one eye image (left or right eye image) by Photoshop to keep the 3D image good enough. In sum, induced stereo can be used in many respects.

    4  A design of new stereoscope

    We have produced a kind of stereoscope. Its appearance is shown in Fig 4a and its configuration in Fig. 4b. Its image-pair plate is shown in Fig. 5a.  It is made from the left eye image and the right eye image. Folded it and became a 3D photo plate shown in Fig 5b. The left eye image and right eye image on its two sides. Due to the high quality of the prevalent color photo and no aberrations of the image can be observed in this device, therefore, the color, definition, and the fidelity of such 3D image are almost the same from the original ones, even complementary. What is more, those “image pairs” can be self-made by any DC (digital camera) owners. Only printing a standard 5 inches photo will be good enough to get a 20—25 inches enlarged 3D image. So the performance/value ratio is higher.

    However this device can be improved much better by modern technical progress. A new star OLED, its thickness can be made below 1 mm, its definition is very high above UXGA and it is also a self-luminescence display device. So if the image pair is replaced by two OLED plates, the digital image pair in digital camera can be input to those two OLED screens directly, then we can watch 3D image in such device and do not need to print photos now. Even more, if those pictures we synchronized are motion ones, a mini 3D movie can be shown.Fig. 4

    Fig. 5

    5  Conclusion

    Through the study of depth perception and the analysis of induced stereo, following focus and free view, it is quite helpful to design a modern stereoscope. Lastly a new stereoscope design has been introduced which don?t need to print photo and can watch static 3D image even watch 3D movies.

【】
  ［1］ Okoshi T, Three-dimensional imaging Techniques. Academic Press, New York, San Francisco, London, 1976.

［2］ Ding SQ, Chen JY, Li JL. The Discovery of Induced Stereovision and its Application. ASID?00, Proceedings, Oct., 2000. pp.87-90.

［3］ Ding SQ, An Introduction of a new Stereoscope. Proceedings of Asia Display Mar. 2007 Shanghai, Vol. 1, pp.456-459.