Deviation (stereography)

In stereography, the deviation denotes the different horizontal spacing of the same image elements on both partial images and is thus the image of the parallax . In adopting the English term disparity , deviation is now increasingly referred to as transverse disparity or disparity . The deviation is referred to as relative deviation depending on the width of the image.

Visible deviation in two cross-faded fields

Factors that determine the spatial impression of the stereo photo

The object closest to the camera defines the near plane

The projection plane (window) is included ${\displaystyle dev_{\mathrm {0} }}$

3D image for red / green glasses

Effect of the deviation

Image elements that do not shift when the two individual images are superimposed are, for the viewer in the three-dimensional view, directly on the image plane - that is, the screen or the printed paper . Accordingly, no spatial impression can be obtained from recordings that do not show any deviation.

The greater the deviation in areas of the image, the greater the depth deviation from the image plane (also: projection or window plane). This can mean that the object stands out from the picture or sinks into it. In the case of extreme deviations, however, it is no longer possible for the viewer to merge both 2D partial images in a stable manner into one three-dimensional one.

Calculation of the base width

The deviation depends on five factors:

• ${\displaystyle a_{\mathrm {N} }}$ - Distance of the near plane to the lens
• ${\displaystyle a_{\mathrm {P} }}$ - Distance between the projection plane and the lens ${\displaystyle a_{\mathrm {N} }\leqq a_{\mathrm {P} }<a_{\mathrm {F} }}$
• ${\displaystyle a_{\mathrm {F} }}$ - Distance from the far plane to the lens
• ${\displaystyle \partial }$- horizontal angle of the field of view of the camera (English field of view, FOV.)
• ${\displaystyle b}$ - Base width (horizontal distance between the cameras / views)

A common problem in stereo photography is the question of which base width to use. To answer them, you have to measure and . The accuracy of in the meter range is always more important than that of the kilometer range (an estimate is sufficient). The projection plane (dummy window plane) should and be. The FoV can be calculated from the focal length and the horizontal size of the image sensor or the negative. Guidelines for the desired deviation can be found under guidelines for deviation . ${\displaystyle a_{\mathrm {N} }}$ ${\displaystyle a_{\mathrm {F} }}$ ${\displaystyle a_{\mathrm {N} }}$ ${\displaystyle a_{\mathrm {F} }}$ ${\displaystyle a_{\mathrm {P} }}$ ${\displaystyle \geqq a_{\mathrm {N} }}$ ${\displaystyle <a_{\mathrm {F} }}$ ${\displaystyle \partial }$

${\displaystyle b={\frac {dev_{\mathrm {rel} }\cdot \tan {\frac {\partial }{2}}\cdot 2a_{\mathrm {P} }\cdot a_{\mathrm {F} }\cdot a_{\mathrm {N} }}{a_{\mathrm {P} }\cdot (a_{\mathrm {F} }-a_{\mathrm {N} })}}={\frac {dev_{\mathrm {rel} }\cdot \tan {\frac {\partial }{2}}\cdot 2\cdot a_{\mathrm {F} }\cdot a_{\mathrm {N} }}{(a_{\mathrm {F} }-a_{\mathrm {N} })}}}$

The visual axes of an ideal 3D camera run parallel to each other. This has the consequence that the projection plane ( ) is inevitably close to the far plane. To move the projection plane, the image must be cropped. This reduces its width and thus slightly changes the relative deviation specified in the calculation. The formula must be expanded accordingly. This effect does not occur in the image examples. The scenes were calculated by the computer and displayed with an off-axis projection. There are optical systems that imitate this projection. ${\displaystyle dev_{\mathrm {0} }}$

Guidelines on deviation

The optimal relative deviation always depends on the output medium. The reference is the reproduction on canvas with polarizing filter technology ( spatial projection ). The deviation should not exceed. In general, the smaller the reproduced image is due to (a) its size or (b) acts due to the distance of the viewer, the greater the relative deviation may be. For spatial images with a cross view , between and may lie. Since cross-eyed image pairs are mostly taken in a narrow portrait format, they are no longer suitable for spatial image projection . For this reason and the small reproduction size (squint technique), an increase in the deviation and thus the spatial effect is absolutely desirable. ${\displaystyle {\frac {1}{30}}}$ ${\displaystyle dev_{\mathrm {rel} }}$ ${\displaystyle {\frac {1}{30}}}$ ${\displaystyle {\frac {1}{10}}}$

The anaglyph image on a monitor or paper image can tolerate a relative deviation of up to . Since the half images could also be presented at any time with the spatial projection or projected as an anaglyph on the screen, a deviation of is also recommended here . This also reduces the perception of so-called ghosts, which are more clearly visible in the event of large disparities. Autostereoscopic monitors with two views ask for . MultiView monitors (5,8,9 views) only tolerate a much smaller deviation. This depends on the barrier used and the number of views. The relative deviation between two neighboring views of a 5-view display is approx . ${\displaystyle {\frac {1}{15}}}$ ${\displaystyle {\frac {1}{30}}}$ ${\displaystyle dev_{\mathrm {rel} }={\frac {1}{30}}}$ ${\displaystyle {\frac {1}{120}}}$

Literature and web links

• Franz Ackerl : Geodesy and Photogrammetry (Volume I), chapter stereoscopic vision and measurement . Publisher G. Fromme, Vienna 1950
• Zentra (Medicine, 2011): Stereoscopy
• OpenGL example of a stereoscopic off-axis projection