Photogrammetry: Stereoscopy and Parallax

Faculty of engineering - Shoubra
Benha University
Article Review
in fulfillment of the requirements of
Department Surveying Engineering Department
Division
Academic Year 2nd
Year Surveying
Course name Photogrammetry 1B
Course code SUR 222
Topic (1): “Stereoscopy and Parallax”
By:
Name Edu mail B. N
Ahmed Yasser Ahmed Mohamed Nassar ahmed170165@feng.bu.edu.eg 210018
Approved by:
Examiners committee Signature
‫الحلي‬ ‫عبد‬ .‫د‬.‫أ‬
‫م‬
‫بحيري‬
‫السمري‬ ‫حسام‬ .‫د‬.‫م‬.‫أ‬
‫أشرف‬ .‫د‬.‫م‬.‫أ‬
‫غني‬
‫م‬
‫الستار‬ ‫عبد‬ ‫أحمد‬ .‫د‬.‫أ‬

Benha University
Faculty of Engineering - Shoubra
Academic year 2019-2020
1 | P a g e
Research Objectives
• Discuss the principles of stereoscopic vision and how it works.
• Discuss the stereoscopic parallax and how to measure it.

Benha University
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Abstract
This literature review talks about the principles of stereoscopy and the stereoscopic
instruments used, in addition to the steps for correcting the rotation of photos under the
stereoscope, then talks about the Y-Parallax which result of Principal points line not
parallel with Flight line. also, the stereoscopic parallax principles and it's measurement.

Benha University
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Table of contents
Research Objectives.............................................................................................................................1
Abstract.................................................................................................................................................2
Table of contents ..................................................................................................................................3
Introduction..........................................................................................................................................5
Literature Review ................................................................................................................................6
1. Binocular Vision........................................................................................................................6
2. Stereoscopic Vision Conditions................................................................................................6
3. Types of Stereoscopes ...............................................................................................................7
3.1. Pocket Stereoscopes...........................................................................................................7
3.2. Mirror Stereoscopes ..........................................................................................................7
4. Orienting Photographs.............................................................................................................8
5. Y-Parallax..................................................................................................................................8
6. Vertical Exaggeration.............................................................................................................10
7. Stereoscopic Parallax..............................................................................................................12
8. Stereoscopic Parallax Difference...........................................................................................12
9. Floating Mark..........................................................................................................................13
10. Measuring Parallax.............................................................................................................13

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Table of Figures
Fig I. D Description Page
Figure 1 Stereoscopic viewing of overlapping photos 5
Figure 2 Binocular Vision 5
Figure 3 Pocket stereoscope 6
Figure 4 Mirror stereoscope 7
Figure 5 Correct-Oriented stereoscopic photo 8
Figure 6 Y-parallax due to incorrect orientation of photos 8
Figure 7 Y-Parallax due to different flight height of two photos 9
Figure 8 Y-Parallax due to tilt of the photo 9
Figure 9 Aerial Photography 10
Figure 10 Stereoscopic vision of photography 10
Figure 11 Base-height ratio 11
Figure 12 Eye base to model height ratio 11
Figure 13 Stereoscopic Parallax 12
Figure 14 Left and right photos congruence 12
Figure 15 Parallax Difference 12
Figure 16 Principal of floating mark 13
Figure 17 Stereometer 13

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Introduction
Stereoscopic vision is a phenomenon through which a people can see the three
dimensions of an object with their normal eyes and without any instruments, But from
different positions according to the length of the eye base. Stereoscopic vision can also
be defined as the science and art of stereoscopic effect by using optical devices to
measure the relative heights of the visible objects and to determine the shape and
location of such objects. there are two types of Stereoscopic instruments, first is mirror
reflecting stereoscope, and second is prism stereoscope, also may be a combination of
the two types. In 1838, Robert Wheatstone developed the first stereoscopic optical
instrument, the instrument consisting of two mirrors that reflected photos from a pair of
stereoscopic photos directly to the eyes.
Figure 1:Stereoscopic viewing of overlapping photos

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Literature Review
1. Binocular Vision
in (Figure 2), Point P and its surroundings are
observed, the axis of the two eyes converges
at point P by an angle (𝛾) called parallactic
angle. The focal length and aperture of the
eye lenses change to generate a sharp imag1e
on the retina, this phenomenon is called
accommodation. There will be two different
photos of the one object, one on each retina
in the plane of Eye base (BA) (varies around
65 mm) and the fixed object point (P). (PA) is the difference in parallax which relates to
the difference in distance between the object point Ρ and its neighboring point (Q).
Depth precipitation (D) is the difference between (DP) and (DQ).
2. Stereoscopic Vision Conditions
• The scale of both photos should be very close.
• The axes of the camera must be in a very close plane during successive shots.
• The overlap between the two photos is usually 60% (between 55% and 90%).
• Along the flight line, the ratio between the exposure station and the plane height
should not be less than 0.25 and not more than 2.
Figure 2: Binocular Vision
DP
DQ
D

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3. Types of Stereoscopes
There are several types of stereoscopes, which includes:
3.1.Pocket Stereoscopes
Also known as “ lens stereoscope”, pocket stereoscope is
characterized as the simplest and cheapest type and can be
easily used in the field, suitable for small photos, the two
photos are placed in the focal plane of the magnifiers, the eye
base should not be more than 75 mm or less than 56 mm. In
addition, the magnification power of the lenses is about 2.5
times. The stereoscopic effect resulting from pocket
stereoscope is weak and the stereoscopic model is at a small
scale. In advanced multi-dimensional aerial imagery, pocket
stereoscope is not recommended due to its small size and
inaccuracy. In addition to the limited vision of these
stereoscopes.
3.2.Mirror Stereoscopes
In this type of stereoscope, all problems of pocket
stereoscope have been fixed by adding reflective mirrors.
The distance between the two photos can be increased, as
well as the use of large-size photos. The stereoscopic effect
occurs by reflecting the two photos through the mirrors. The
magnification power of this stereoscope is 4.5 to 8 times.
There are other types of stereoscopes, such as the zoom
stereoscope, where the magnification power reaches 20
times
Figure 3: Pocket stereoscope
Figure 4: Mirror stereoscope

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4. Orienting Photographs
Before starting the stereoscopic model, you must ensure that the correct orientation of
the photos under the stereoscope is as follows:
1. The principal point of each photo is determined by connecting the fiducial marks
and setting the intersection point.
2. Select the conjugate principal point on the first photo, and then place it on the
second photo, and vice versa
3. Place the two photos so that the overlap area between them is on top of each other
and keep the shadows in the direction of the observer.
4. Place the stereoscope over the two photos and place the base point of the left
photo in the center of the field of vision for the left eye and move the right photo
until the circle drawn over this area appears. Then, move the two photos to obtain
a clear stereoscopic.
5. Then connect the two principal points and the
conjugate principal points so that the 4 points (P1,
P`
2, P`
1, P2) make a straight-line opposite to the line
connecting the identical points (a1, a2) as shown in
figure 5.
5. Y-Parallax
In figure 5, To obtain a clear stereoscopic view, the line connecting the principal
points (a1, a2) must be parallel to the flight line (P1, P`
2, P`
1, P2). If these two lines are
not parallel, then there is Y-Parallax
Figure 5: Correct-Oriented stereoscopic photo
Flight
line
Distance between
conjugate principal
points.

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in figure 6, non-correct oriented stereoscopic model, because the principal points and
the conjugate principal points on the two photos are not directed on one line so the result
is a y-parallax at (a1, a2).
In Figure 7, the two photos are completely vertical, and the orientation direction is
correct, but the right photo was taken from a higher-flying height than the left photo, so
the scale of the right photo will differ from the left. For a corrected stereoscopic view,
the y-parallax can be removed by moving the right photo up vertically along the flight
direction.
In Figure 8, the left photo appears completely vertical with the (a1 b1 c1 d1) square
representing a square plot of land. The right-hand photo is taken oblique and the same
piece of land appears as a trapezoid.
Figure 6: Y-parallax due to incorrect orientation of photos.
Figure 7: Y-Parallax due to the different flight height of the two photos
Figure 8: Y-Parallax due to tilt of the photo

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6. Vertical Exaggeration
in Vertical Exaggeration, the scale of the stereoscopic model is larger than the horizontal
scale, so the heights appear to be higher than normal.
Calculating Vertical Exaggeration
• From figure 9
𝑥𝑎
𝑓
=
𝐵
𝐻`−𝑍
∴ 𝑥𝑎 =
𝐵𝑓
𝐻`−𝑍
𝑥𝑐
𝑓
=
𝐵
𝐻`
∴ 𝑥𝑐 =
𝐵𝑓
𝐻`
∴ 𝑥𝑎 − 𝑥𝑐 =
𝐵𝑓𝑍
𝐻`2 − 𝐻`𝑍
• From figure 10
𝑥𝑎
𝑖
=
𝑏𝑒
ℎ−𝑧
∴ 𝑥𝑎 =
𝑏𝑒𝑖
ℎ−𝑧
𝑥𝑐
𝑏𝑒
=
𝑖
ℎ
∴ 𝑥𝑐 =
𝑏𝑒𝑖
ℎ
∴ 𝑥𝑎 − 𝑥𝑐 =
𝑏𝑒𝑖𝑧
ℎ2 − ℎ𝑧
XK
XC
Figure 9: Aerial Photography Figure 10: Stereoscopic vision of photography

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• 𝑍 and 𝑧 Values are smaller than 𝐻′ and ℎ
𝐵𝑓𝑍
𝐻`2
=
𝑏𝑒𝑖𝑧
ℎ2
∴
𝑧
𝑍
=
𝑓𝐵(ℎ)2
𝑖𝑏𝑒(𝐻`)2
• From similar triangles at figure 9 and figure 10
𝐷
𝐻`
=
𝑥𝑐−𝑥𝑘
𝑓
∴ 𝐷 =
𝐻`(𝑥𝑐−𝑥𝑘)
𝑓
𝑑
ℎ
=
𝑥𝑐−𝑥𝑘
𝑖
∴ 𝑑 =
ℎ(𝑥𝑐−𝑥𝑘)
𝑖
∴
𝑑
𝐷
=
𝑓ℎ
𝑖𝐻`
and
𝑧
𝑍
=
𝑑𝐵ℎ
𝐷𝐻`𝑏𝑒
𝑽 =
𝑩𝒉
𝒃𝒆𝑯`
𝑩 = 𝑮 [𝟏 −
𝑷𝑬
𝟏𝟎𝟎
]
𝐻`
𝐺
=
𝑓
𝑑
∴ 𝑯` =
𝑮𝒇
𝒅
• Dividing B and H`
𝑩
𝑯`
=
𝒅
𝒇
[𝟏 −
𝑷𝑬
𝟏𝟎𝟎
]
𝒃𝒆
𝒉
=
𝒃𝒆 − 𝒃𝒔
𝒊
Figure 11: Base-height ratio
Figure 12: Eye base to model height ratio

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7. Stereoscopic Parallax
in figure 13, When taking two photos of an area from two sequent exposure stations, the
baseline (B) is the distance between the (O1) and (O2) exposure stations. Point (i) on the
terrain appears on the left photo at position (i1) and on the right photo at position (i2).
Likewise, for terrain point (j).
In Figure 14, Due to the difference in exposure station location, when the two photos
are placed on each other, the right photo conjugate point congruent with left photo
conjugate point, and a flight-line in the right photo congruent with flight-line in the left
photo. Point (i1) will not congruent to point (i2), and the distance between them is called
stereoscopic parallax (Pi). This distance enables stereoscopic vision, but the line
connecting the two points (i1) and (i2) must be parallel to the flight line.
8. Stereoscopic Parallax Difference
Stereoscopic difference is caused by the difference of the
level of the two visible points in a pair of overlapped aerial
photos and equal the difference between the two conjugate
points and distance between the two nadir points for both
photos. Stereoscopic parallax is directly proportional with
the point level.
Figure 13: Stereoscopic Parallax Figure 14: Left and right photos congruence
Photo
Negative
Figure 15: Parallax Difference

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𝑃𝐴 = 𝑎1 × 𝑎2– 𝑛1 × 𝑛2 𝑃𝑇 = 𝑡1 × 𝑡2– 𝑛1 × 𝑛2
𝑷𝑨𝑻 = 𝑷𝑨 − 𝑷𝑻 = 𝒂𝟏 × 𝒂𝟐 – 𝒕𝟏 × 𝒕𝟐
Where 𝑷𝑨𝑻: Parallax difference between stereoscopic parallax between point A and
point T
9. Floating Mark
floating mark is used to move the principal point or other
points from a photo to the next stereoscopic photo. And
through which the accurate position of a pair of points
corresponding to the two photos is determined, even if it is
difficult to determine the two points on the photos.
10.Measuring Parallax
The parallax of point is measured by the X-coordinate (𝑋𝑎1
) of the point on the left
photo, and the X-coordinate (𝑋𝑎2
) of the corresponding point on the right photo. The X-
coordinate represents the flight line, so it can be determined by transferring the principal
points from each photo to another.
𝑷𝑨 = 𝑿𝒂𝟏
− 𝑿𝒂𝟐
Where 𝑷𝑨: parallax of point A
Figure 17: Stereometer
Flight
line
Figure 16: Principal of floating mark
full millimeters ruler 0.01 of millimeters ruler
Glass installed
in the beginning of work
Glass moved left and
right by micrometer
micrometer

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The x-coordinate measurements are measured by a Stereometer (or Parallax Bar)
(Figure 17), a device to measure the difference in distance between points. The stereo
meter has two advantages:
• Stereoscopic glasses are used to take readings instead of using one eye, giving more
accurate readings
• It allows the mark to be moved left and right with a micrometer, which gives more
accurate results for the distance difference and the accuracy is ±0.03mm.

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References
Aber, James S et al. Small-Format Aerial Photography and UAS Imagery. 1st ed.,
Elsevier Science, 2016.
Kraus, Karl et al. Photogrammetry. De Gruyter, 2007.
Trorey, Lyle G. Handbook of Aerial Mapping and Photogrammetry. CAMBRIDGE
UNIVERSITY PRESS, 2013.
Wolf, Paul R, and Bon a Dewitt. Elements of Photogrammetry. McGraw-Hill, 2000.
Slama, Chester C et al. Manual of Photogrammetry. American Society of
Photogrammetry, 1980.
‫الم‬
‫سح‬
‫التصوي‬
‫ري‬
‫الجوي‬
.
‫ق‬
‫تقنيات‬ ‫سم‬
‫المساحة‬
‫المعه‬ ،
‫د‬
‫الموصل‬ ‫في‬ ‫التقني‬
.
‫المساحة‬
،‫التصويرية‬
‫الثاني‬ ‫الصف‬
.
‫المؤسسة‬
‫العامة‬
‫للتعليم‬
‫الفني‬
‫والتدريب‬
‫المهني‬
.
‫السعودية‬

Photogrammetry: Stereoscopy and Parallax

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