Perceived Stereo Roundness -- the Mythical Value

One of the keys to thinking about Perceived Stereo Roundness is to always remember that it is a subjective perception rather than a purely calculable value.  Even in the real world, it is often difficult to tell the size, speed and direction of objects in the absence of clear external clues, and the constraints of our current 3D display methods force the viewer's brain to deal with contradictory stereo information in an extremely artificial manner. 

Even in the best of situations, this contradictory information includes the unnatural separation between focus and convergence, the lack of occlusion changes as the viewer moves their head and during their eye saccades, in addition to any window or edge violations that may be present.

Perceived Stereo Roundness relies as much on Non-Stereoscopic Depth Cues to tell the brain about the "roundness" of an object as it does on any actual measurable parallax and volume.  These Non-Stereoscopic Depth Cues include composition, lighting and shadows, backgrounds, texture gradation, parallel lines that guide the eye, camera movement, object occlusion etc. and even with a "perfect" stereo rig setup and viewing conditions, a shot can appear completely cardboarded if the non-stereoscopic depth cues do not support the stereo.

Conversely, of course, you can have a shooting situation where there is only a small amount of stereo volume recorded but with such a wealth of depth cues that most viewers would describe the objects in the shot as looking fully natural and round.

Perceived Stereo Roundness -- Calculating it Regardless

If it's a fundamentally incalculable value, then what is the RealD^® Professional S3D Stereo Calculator calculating?

Since Perceived Stereo Roundness is combined from a huge number of variables as discussed above; what the calculator is giving you is one of those variables, the "optical roundness" as calculated geometrically based on the combination of the shooting and viewing conditions.  This value should be considered as only one of several data points that will contribute to the ultimate perception of the shot, and it is your job as a stereographer to make use of this information in whatever way the shot demands.

How then, is this Optical Stereo Roundness Calculated?

There are two algorithms that the Stereo Calculator can use, and they are selected using the segmented controller under the label Roundness Algorithm as shown below.  This functions the same way for the iPhone/iTouch and the iPad, though it's in a slightly different layout on the iPad due to the greater screen space.

Kuhn's Algorithm

stands for the formula published in Gerhardt Kuhn's book Stereofotografie und Raumbildprojektion. Theorie und Praxis, Geräte und Materialien also released in English as Stereoscopy and 3D-Projection. A modern Guide to Theory and Practice although the latter seems to be out of print.

While this is a published formula and it is well-accepted in some circles, in our tests we felt that it did not always accurately predict the viewing experience in our test subjects.  However, as mentioned above, since perceived stereo roundness is such a subjective experience and is heavily influenced by so many different factors, we decided to leave this algorithm in place as an option for those who would prefer to use it.

S-W Algorithm

stands for Schafer-Walker, co-designers of a new algorithm which we believe is a better predictor of perceived stereo roundness, given good shot composition and strong non-stereoscopic depth cues. Ken Schafer is the lead program architect for both the Stereo Calculator and FrameForge Previz Studio 3 and Dr. James Walker, PhD is the mathematician / programmer who designed the actual mathematical algorithm and has programmed the core 3D code in FrameForge Previz Studio 3's engine.

The fundamental difference between the S-W algorithm and the one Kuhn described, is that the S-W Algorithm breaks down the problem of calculating perceived stereo roundness into three steps: (1) calculate the recorded volumetric differences between the left and right images as recorded by the cameras on set; (2) calculate the distortion in the viewing environment based on the differences between the recording and viewing conditions (screen size, viewer distance, IA vs. IO etc.); (3) apply a weighted combination of the two, weighted so that objects with low volumetric differences will not be reported as been distorted into roundness, despite whatever distortion the viewing situation creates.

We leave it to you to decide which of the two formulas best matches your perception of stereo roundness, though we feel confident that S-W is the better choice.

The Stereo Roundness Parameters

Despite their differences, both roundness algorithms use the same input parameters:

• Screen Size in the viewing situation, taken from the value entered as the Target Screen Width on the Screen Setup page
• Cameras' Optics & the Shot's Rig Settings -- taken from the Rig Solver™ view (vertical calculator)
• Distance of Subject (or subjects in the case of the iPad) from the Rig -- initially taken from the Rig Solver™ view (vertical calculator) though you can modify them here by entering a new value numerically in the field labeled Subject Distance, or by dynamically dragging the Subject Distance slider found below it.
  • On the iPad the Subject Distance Sliders and their corresponding numeric entry fields are to the left of the central Framing View and in addition to using them, you can also directly drag the subjects forwards and backwards within the framing view, thus increasing or decreasing their distance from the camera rigs.
• Distance of the Viewer from Screen--since distortion caused by viewing conditions can greatly increase or decrease the perceived stereo roundness, the calculator allows you to define a Theater (or Viewing) Space where you can specify the closest and farthest possible viewers and see how their perceptions of a shot will differ.

Setting the Theater (or Viewing) Space

You can define the Viewing Space either dynamically by dragging the sliders to either side of the image of the theater up or down until the desired distance is achieved or...

On the iPhone -- tap the graphic of the Theater and numeric entry fields will appear on top of it along with an OK button.  Enter the exact distances desired and tap the OK button.

 On the iPad -- due to the much larger screen area, these numeric entry fields are always available to the left of the theater image, as shown in the bottom half of the image below.

 

Perceived Stereo Roundness "Graphs" -- Subject vs. Distance Map

As you can see at the top of the image to the above (labeled "Viewing Space on iPhone"), there is another segmented control, this one labeled "Subject" and "Distance Map."  While the contents of the data is the same for both the Subject & Distance Map displays, the way it is shown is rather different.

When you select "Subject" it will display roundness for a single subject at the distance specified in the lower left controls on this screen.  It displays the roundness in the form of a distorted half-circle where “perfect roundness” is shown as a full half-circle that extends to the mid-point of the graph, with flattened and stretched being shown in the corresponding manner.

As spatial distortion is a function of viewer distance and screen size, this display graph uses your defined target screen size (set in the Screen Settings window) and the observer distances of your viewing space (shown under the graphic of the theater).

We show results for the closest viewer, a mid-point viewer and the farthest viewer.  Thus in the graph below, for an object that was recorded at a distance of  3.2 meters from the camera with the current IA, focal length, etc. the viewer at 25m from the screen will see it as distorted (e.g. stretched in the z axis), while the viewer at 13.8m will see it somewhat distorted, while the one at 2.5m will see it as nearly perfectly round.

In this view the colors of the half-circles represent the viewer distances, thus red is 25.0m, violet is 13.8m and purple 2.5m.

The “Distance Map” view, on the other hand, displays roundness across the entire range of the distances within your shooting area as a false color map, ranging from yellow (highly distorted or stretched), green (round) to blue (flat) as shown in the color key to the lower right in the image.

Thus this graph (using the Kuhn's algorithm) shows that if a subject is 0.1m from the camera rig at shoot time, in the current viewing conditions it will be highly distorted for all viewers. 

A subject at 15m (roughly half the working area) will have good roundness for all seating positions, while a subject approaching the 30m will be fairly round for all but the the closest viewers. 

This situation, however, is an example of where the Kuhn’s formula seems to be inaccurate as any objects at 30m from the camera rig will have very little stereo volume.  So despite the fact that they are not stretched or flattened by the spatial distortions of the viewing conditions, the S-W formula will show them as flatter than the Kuhn's algorithm to take into accoun tthat initial lack of recorded stereo volume.

In Conclusion

Perceived Stereo Roundness is a complicated phenomenon that does not lend itself to real calculations. The values that the Stereo 3D Calculator displays are predicated on a well composed shot with strong non-stereoscopic depth cues and should be taken as only one data point in designing your shot.

And finally, flatter is not necessarily worse.  We EXPECT objects farther away from us to be less "round" than closer ones, so it does not necessarily mean there is anything wrong with a shot as should farther objects appear significantly flatter than the closer ones.  Remember the "roundness" values have no judgement associated with one color versus another, it is merely a mathematical representation of part of the factors that will contribute to the viewer’s ultimate experience.