The Stereo Image

The Stereo Image

Introduction

How does the projection of a three-dimensional world onto a two-dimensional retina create a stereo image? The majority of related theories share the view that there is a correspondence between the left and right images. It is generally accepted that the matching of the two retinal images allows the visual system to reconstruct a three-dimensional image from two flat two-dimensional images.

The three-dimensional image is thought to be derived geometrically, by comparing the small difference between the two retinal images that result from the slightly different vantage points of the two eyes, as caused by their 6.5cm separation. Most analysts believe that the matching and correspondence problems are insurmountable. These theories would most likely result in double vision rather than any type of stereo image.

There are many cues to depth in every image, for example, shading, size, correlation, or texture. All of these cues are significant, especially for people who possess only monocular vision. Many of these cues can also be used to obtain information on depth, even from a two-dimensional surface such as a painting or a photograph. How we perceive a stereo image has never been defined in a logical on understandable way, not even in theory. SSSRD explains how a stereo image is created, even before the function of the cortex eye occurs. There are six retinal-section divisions, three in each eye and all opposite to each other. All three retinal-section images of one eye are viewed at a different vantage angle to the corresponding three retinal-section images of the other eye. The outcome of this angular differential is that every sectional area in the single image is viewed at a different vantage angle to the sectional area that joins it. Thus, there are no matching or correspondence problems.

The three opposite, retinal-sections of each eye assembled in the cortex eye, create one single eye, which in turn creates a unique stereo single image in every fixation. Perhaps another way of visualising how this occurs, would be the comparison of looking at each eye comprising of three separate cameras, with each camera simultaneously taking a snapshot of a specific section of the scene. All these sections are opposite to the other sectional snapshots of the other eye, but all fit together like a jigsaw, to create a single image and all the opposite sectional snapshots are taken at two different vantage angles. If we could imagine a scene photographed in this way, we can appreciate the three-dimensional stereo quality of this image. That is even ignoring the fact that each image comprises of a mathematical computation, which informs the brain of depth and distance calculations for every object in that entire scene. All of this occurs during each fixation. Observing the change in vantage angle is another way of identifying the retinal-section boundaries.

In chapter 2, we observed how a target changes from the view of one eye to the other when it crosses a retinal-section boundary. In the stereo image, not only does the target change from the view of one eye to the other, but the vantage angle that the target is viewed at also changes. To illustrate this, an ordinary office ruler may be used because the side of the ruler is wide and the edge of the ruler is narrow.

Figure 5.1: The vantage angle view of the targets changes as it crosses retinal-section boundary VL and VR.

In figure 5.1A, ruler 1A is positioned with only the view of the left eye with the focus on ‘F’. It is aligned left of VL in section B, so that the edge of the ruler is only visible to the left eye. When ‘F’ is then binocularly focused on, and the ruler is moved from left to right, over the retinal sectional boundary VL to position 1B in section A, the side of the ruler 1B is now visible as it is viewed in section A at the vantage angle of the right eye.

In figure 5.1B, ruler 2A is positioned with only the view of the left eye with the focus on ‘F’. It is aligned right of VR in section B, so that the edge of the ruler is only visible to the left eye. When ‘F’ is then binocularly focused on, and the ruler is moved from right to left, over the retinal sectional boundary VL to position 2B in section A1, the side of the ruler is now visible because it is viewed in section A1at the vantage angle of the right eye. This observation proves that when a target crosses either retinal-section boundary VL or VR, the vantage angle that the target is viewed at also changes. Not only does the target change from the view of the left eye to the view of the right eye, but the vantage angle that the target is viewed at also changes, and they are all viewed by each eye separately, in opposite retinal-section divisions.

Figure 5.2: The vantage angle view of targets crossing VR1 and VL1 does not change, as VR1 and VL1 are not retinal-section boundaries.

In figure 5.2A, ruler 1 in section A is viewed only with the right eye with the focus on ‘F’. It is positioned left of VR1 so that the edge of the ruler is only visible. The fixation point ‘F’ is then binocularly focused upon and ruler 1 is moved slowly across the retinal-section boundary VR. When the ruler crosses the VR boundary in section A, it is still viewed by the right eye. As a result, the edge of the ruler is still viewed as the vantage angle of the ruler has not changed and is still viewed in section A only by the right eye. The reason why there is no change in the vantage angle of the ruler is that VR1, unlike VR, is not a retinal-section boundary and the ruler has not changed from one retinal-section to an opposite retinal-section, but remains in section A.

In figure 5.2B, ruler 2 in section B1 is viewed only with the left eye with the focus on ‘F’. It is positioned left of VL1 so that the edge of the ruler is only visible to the left eye. The fixation point ‘F’ is then binocularly focused upon and ruler 2 is moved slowly across the retinal-section boundary VL1. When the ruler crosses the boundary VL1 in section B1, it is still viewed by the left eye. Consequently, the edge of the ruler is still viewed. The vantage angle of the ruler has not changed and is still viewed only by the left eye in section B1. The reason why no change occurs in the vantage angle of the ruler is that VL1, unlike VL, is not a retinal-section boundary, and the ruler has not changed from one retinal-section to an opposite retinal-section, it remains in section B1.

Figure 5.3: The vantage angle view of the targets changes as they cross the monocular retinal-section boundaries OBL and OBR. As previously illustrated, these boundaries farther than the fixation point are between opposite retinal-sections. As a result, targets crossing these boundaries change from the monocular view of one eye to the other.

In figure 5.3A, rulers are positioned on all sides of all the retinal-section boundaries viewed only with the left eye with the focus on ‘F’. Ruler 3 is positioned left of OBL (the occluded boundary on the left) so that the edge of the ruler is only visible to the left eye. The fixation point ‘F’ is then binocularly focused upon in figure 5.3B and ruler 3 is moved slowly across the retinal-section boundary OBL When the ruler crosses the boundary from the left monocular area into section A1, it is no longer viewed by the left eye but is viewed by the right eye. As a result, the edge of the ruler is no longer viewed but the side of the ruler is visible. Not only has the ruler changed from the view of the left eye to the view of the right but also the vantage angle the ruler is viewed at also changes.

Ruler 4 is positioned in section B1 left of OBR (the occluded boundary on the right) so that the edge of the ruler is only visible to the left eye. The fixation point ‘F’ is then binocularly focused upon in figure 5.3B and ruler 4 is moved slowly across the retinal-section boundary OBR When the ruler crosses the boundary OBR from section B1 into the monocular area, the ruler is no longer viewed by the left eye but by the right eye. Consequently, the edge of the ruler is no longer viewed but the side of the ruler is visible. Not only has the ruler changed from the view of the left eye to the view of the right but the vantage angle that the ruler is viewed at also changes.

Figure 5.3B illustrates all the retinal-section boundaries in the visual field where targets on opposite sides of these boundaries are viewed at a different vantage angle, individually by each eye. The only two boundaries where this does not occur are the two monocular boundaries, OBL and OBR, nearer than the focal plane. These two natural boundaries are created by the occlusion of the nose but the retinal-sections on opposite sides of these boundaries are always in the view of the same eye. Thus, the vantage angle of targets crossing these boundaries does not change. Therefore, the vantage angles of target 5 and target 6 do not change as they cross these boundaries from locations A to B, B to A, etc.

In figure 5.4A, ruler 1 and ruler 2 are positioned in the retinal-sections of B and A, so that the edges of the rulers are only visible with the monocular view of the left eye focused on F. In figure 5.4B, once ‘F’ is binocularly focused on in the cortex eye, only the edge of ruler 1 is visible in section B. This is because the ruler in section B is in the retinal-section of the left eye. However, with ruler 2 in section A, the right eye views the retinal-sections of the right eye at a different vantage angle and the side of the ruler is visible.

Figure 5.4: The vantage angle of the rulers are retained after the rotation of the axis in the cortex eye positioned in the visual direction of the left eye with the focus on ‘F’ in sections B and A.

Either of two targets in the same visual direction of one eye, located in these two opposite retinal-sections nearer than the fixation point, are viewed separately at a different vantage angle by each eye. These different vantage angle views are retained after the rotation of the visual axes in the cortex eye.

In figure 5.5A, ruler 3 and ruler 4 are positioned in the retinal-sections of A1 and B1, so that the edges of the rulers are only visible with the monocular view of the left eye with the focus on ‘F’. In figure 5.5B, ‘F’ is binocularly focused upon in the cortex eye, and only the edge of ruler 4 is visible in section B1. The reason for this is that the ruler in section B1 is in the retinal-section of the left eye. However, ruler 3 is in section A1, the retinal-section of the right eye, and it is viewed at a different vantage angle by the right eye and the side of the ruler is thus visible.

Any one of two targets in the same visual direction of one eye, located in these two opposite retinal-sections farther than the fixation point, are viewed separately at a different vantage angle by each eye. These different vantage angle views are retained after the rotation of the axes in the cortex eye.

Figure 5.5: The vantage angles of the rulers are retained after the rotation of the axes in the cortex eye, positioned in the visual direction of the left eye with the focus on ‘F’ in sections A1 and B1.

Figure 5.6: The vantage angles of the rulers are retained after the rotation of the axes in the cortex eye, positioned in the visual direction of the left eye with the focus on ‘F’ in each retinal-section area.

In figure 5.6A, rulers are positioned in every retinal-section so that the edges of the rulers are visible only with the monocular view of the left eye with the focus on ‘F’. In figure 5.6B, ‘F’ is binocularly focused upon in the cortex eye, and only the edges of the rulers are visible in section B and section B1, but the sides of the rulers are visible in section A and section A1. The reason for this is that rulers in these sections (A and A1) are in the retinal-sections of the right eye. However, the rulers in section A and section A1 are viewed at a different vantage angle by the right eye. This proves that all targets, surfaces, and textures are viewed from different angles in all the opposite retinal-sections.

Figure 5.7: The vantage angle of the rulers are retained after the rotation of the axes in the cortex eye, positioned in the visual direction of the right eye with the focus on ‘F’ in all the retinal-section divisions.

In figure 5.7A, the rulers are positioned in all the retinal-sections so that the edges of the rulers are only visible with the monocular view of the right eye with the focus on ‘F’. In figure 5.7B, ‘F’ is binocularly focused upon in the cortex eye and only the edges of the rulers are visible in section A and section A1. This is because the rulers in these sections are in the retinal-section of the right eye. However, the rulers in section B and section B1, the retinal-sections of the left eye, are viewed at a different vantage angle by the left eye and the sides of the rulers are visible. This is in contrast to figure 5.6, when the rulers were positioned with the monocular view of the left eye, and it proves that all targets, surfaces, and textures are viewed from different angles in all the opposite retinal-sections.

In these illustrations, rulers are positioned in the visual direction of the left eye with the focus on ‘F’, in retinal-sections in the binocular fields B and A1. In figure 5.8A, ruler 1 and ruler 2 are positioned in the retinal-sections of B and A1, so that the edges of the rulers are only visible with the monocular view of the left eye with the focus on ‘F’. When ‘F’ is binocularly focused upon, in the cortex eye in figure 5.8B, only the edge of the ruler 1 is still visible in section B. The reason for this is that the ruler in section B is in the retinal-section of the left eye. However, the right eye views ruler 2 at a different vantage angle in section A1, the retinal-section of the right eye, and the side of the ruler is therefore visible.

Figure 5.8: The vantage angle views of the same targets change nearer and farther than the fixation point, when the fixation point changes.

When the fixation point changes to ‘F1’, the opposite occurs; ruler 1 is now in section A and ruler 2 is now in section B1 (two opposite retinal-section divisions). Therefore, the edge of ruler 2 is now visible in section B1 while the side of ruler 1 is visible in section A, in figure 5.8C. The rulers are rulers are viewed with the left eye in section B and section B1, the retinal-sections of the left eye. The rulers are viewed with the right eye in section A and section A1, the retinal-sections of the right eye. In the binocular field, all of the retinal-sections are constantly interchanging with motion or change in the fixation point. Thus, targets are continuously viewed from different angles whenever the slightest eye movements occur, even when the head is in a static position.

Rulers are now positioned with the view of the right eye with the focus on ‘F’ in retinal-sections in the binocular field, B and A1. These are the same targets, in the same locations, but this time they are positioned using the view of the right eye. In figure 5.9A, ruler 1 and ruler 2 are positioned in section B and section A1, so that the edges of the rulers are only visible with the monocular view of the right eye with the focus on ‘F’.

Figure 5.9: The vantage angle views of the same targets change nearer and farther than the fixation point, when the fixation point changes.

In figure 5.9B, ‘F’ is binocularly focused upon in the cortex eye, and the side of the ruler 1 is visible in section B1, but the edge of the ruler 2 is visible in section A1. When the fixation point changes to F1, the opposite occurs; ruler 1 is now in section A1 and ruler 2 is now in section B1 (two opposite retinal-section divisions). Consequently, the edge of ruler 1 is now visible in section A1 while the side of ruler 2 is visible in section B1, as shown in figure 5.9C.

Targets in the retinal-sections of the left eye, including the monocular area, are viewed at the vantage angle the left eye. For targets in the retinal-sections of the right eye, including the monocular area, the rulers are viewed at the vantage angle of the right eye. When the eye or head moves, targets in the entire visual field in all the retinal-sections are constantly interchanging, as targets are continuously crossing back and forth across these boundaries. Targets are not only changing from the view of one eye to the other, they are also changing from the vantage angle view of the left eye to the vantage view of the right eye in all these opposite retinal-sections.

Figure 5.10: A target in section B, a retinal-section of the left eye, is viewed at the vantage angle view of the right eye, due to occlusion.

In figure 5.10A, rulers are positioned in all the retinal-sections so that the edges of the rulers are only visible with the monocular view of the left eye with the focus on ‘F’. However, target 3 is occluded to the left eye in section B. When ‘F’ is binocularly focused upon in the cortex eye, in figure 5.10B, the edges of the rulers, except that of ruler 3, are still visible in section B and section B1. This is because the rulers are in section B and section B1, retinal-sections of the left eye. The right eye now views target 3, as a result from being occluded to the left eye and the side, rather than the edge, of the ruler is now visible.

The rulers in section A and section A1, the retinal-sections of the right eye, are viewed at a different angle. This results in the sides of the rulers being viewed in these two retinal-sections. The occluded target 3 is also viewed here as a sub-sectional area in section B, a retinal-section of the left eye. Not only is target 3 viewed at a different angle, it is also viewed to have moved ½ ‘D’ distance in the opposite direction to all other targets in this section. This results from target 3 not just being viewed by the right eye, but also moving ½ ‘D’ distance with the rotation of the visual axis of the right eye, instead of the visual axis of the left eye, in the cortex eye. This proves that all targets, surfaces, and textures are viewed from different angles in all the opposite retinal-sections. It also proves that any of these retinal-sections can be subdivided because of occlusion and the single image can consist of multiple, retinal-section sub areas, viewed at different vantage angles.

Below, four rulers are positioned the same ‘D1’ distance left of visual axes of both eyes, nearer and farther than the fixation point ‘F’. In the cortex eye, in figure 5.11B, they are all viewed in a straight line, ‘D1’ distance left of ‘F’. All these rulers are at different depth locations along the visual axes, which means they all move a different ½ ‘D’ distance, to be viewed in a straight line when ‘F’ is focused on in the cortex eye.

Figure 5.11: Targets separately viewed at a different angle view by each eye in the overlap area in the cortex eye.

In figure 5.11A, rulers are positioned in all the retinal-sections so that their edges are only visible with the monocular view of the left eye, when the focus is on ‘F’. Ruler 1 and ruler 4 are positioned the same ‘D1’ distance left of ‘F’ with the left eye in section B and section B1. Target 1 and target 3 are positioned ‘D1’ distance left of ‘F’ with the right eye, in section A and section A1.

In figure 5.11B, ruler 1, ruler 2, ruler 3, and ruler 4 are viewed in a straight line with ‘F’ in the overlap area of the cortex eye, when ‘F’ is binocularly focused on. The edges of ruler 1 and ruler 4, located in sections B and B1, are still viewed by the left eye. However, in section A and section A1, the right eye also views the sides of ruler 3 and ruler 4, due to these areas being retinal-sections of the right eye. This observation not only proves that targets are separately viewed by each eye in the overlap in the cortex eye, but also that the exact vantage view of all targets viewed by each eye is retained in the overlap area in the cortex eye. This also proves that the cortex eye is the final function in each fixation and could not occur if all the retinal-sections in SSSRD were not precisely assembled before the rotation of the visual axes.

In section B and section B1, the retinal-sections of the left eye, the rulers are viewed at the vantage angle of the left eye. In section A and section A1, the retinal-sections of the right eye, the rulers are viewed at the vantage angle of the right eye. This occurs throughout the entire visual field as all of the retinal-sections are constantly interchanging with motion or change in the fixation point. Every fixated image consists of six separate, retinal-section snapshots, taken from two different vantage angle points.

Observers:

All stereo image tests consisted of simulated models of each individual illustration and the same five right-eye dominant observers participated in each test. Great care was taken to ensure that all tests were performed in optimal light conditions, in three-dimensional space.

Results:

All five observers confirmed that each target in its own sectional area was viewed at the vantage angle of the viewing eye, and that when the fixation point changed, the vantage angle view of targets also changed. This change was directly linked with the retinal-section change that occurred with change in the location of the fixation point while the targets remained constant. The significance of these observations is immense because they explain how our stereo image is created.