Measurement of Relief Displacement from Vertical Photographijsetr.org/wp-content/uploads/2014/10/IJSETR-VOL-3-ISSUE-10-2800... · International Journal of Science, ... consequence,

International Journal of Science, Engineering and Technology Research (IJSETR), Volume 3, Issue 10, October 2014

2800

ISSN: 2278 – 7798 All Rights Reserved © 2014 IJSETR

Abstract —The surface of the earth is not smooth and flat. As a

consequence, there is a natural phenomenon that disrupts true

orthogonality of photo image feature. On an aerial photograph

the displacement of image due to variation in relief of the terrain

is known as relief displacement or height distortion. Relief

displacement can also be used to determine the height of an

object from a single vertical photograph if the amount of

displacement (d) can be accurately measured on the photograph.

Height determination is more accurate for tall features imaged

near the edge of the photograph. This is because relief

displacement at this location is more exaggerated and separation

between the top and the base of features is clearly visible on the

photograph, thus, the distance between the top and the base is

more precisely measured.

Index Terms—Aerial Photograph, Flying Height, Focal

Length, Relief Displacement, Remote Sensing

I. INTRODUCTION

Relief displacement is the radial distance between where an

object appears in an image to where it actually should be

according to a Planimetric coordinate system. The images of

ground positions are shifted or displaced due to terrain relief,

in the central projection of an aerial photograph. If a

photograph is truly vertical, the displacement of images is in

a direction radial from the photograph center. This

displacement is called the radial displacement due to relief.

Radial displacement due to relief is also responsible for scale

differences within any one photograph, and for this reason a

photograph is not an accurate map.

Relief displacement is caused by differences in relative

elevation of objects photographed. All objects that extend

above or below a datum plane have their photographic

images displaced to a greater or lesser extent. This

displacement occurs always along the line which connects

the photo point and the nadir and is, therefore termed “radial

line displacement”. Or this displacement is always radial

with respect to principal point. It increases with increasing

height of the feature and the distance from nadir.

II. RELIEF DISPLACEMENT

Fig. 1 illustrates the geometric distortion, called relief

displacement that is present on all vertical aerial

photographs that are acquired with the camera aimed directly

down. The tops of objects such as buildings appear to “lean”

away from the principal point, or optical centre, of the

photograph. The amount of displacement increases at greater

radial distances from the centre and reaches a maximum at

the corners of the photograph. (Fig. 2)

Fig.1: Vertical aerial photograph of Long Beach,

California, showing relief displacement. Courtesy J. Van

Eden.

Fig. 2: Geometry of displacement due to topographic

relief

Measurement of Relief Displacement from

Vertical Photograph

Sunita Devi1, Veena

2


ISSN: 2278 – 7798 All Rights Reserved © 2014 IJSETR 2801

Fig. 3A shows the geometry of image displacement, where

light rays are traced from the terrain through the camera lens

and onto the film. Prints made from the film appear as

though they were in the position shown by the plane of

photographic print in Fig. 3 A.

The vertical arrows on the terrain represent objects of various

heights located at various distances from the principal point.

The light ray reflected from the base of object A intersects the

plane of the photographic print at position A, and the ray

from the top (or point of the arrow) intersects the print at A’.

The distance A-A’ is the relief displacement (d) shown in the

plan view in Fig. 3 B.

Fig. 3: Geometry of relief displacement on a vertical

aerial photograph

The effect of relief displacement on a photograph taken

over varied terrain. In essence, an increase in the elevation,

of a feature causes its position on the photograph to be

displaced radically outward from the principal point. Hence,

when a vertical feature is photographed, relief displacement

causes the top of the feature to lie farther from the photo

center than its base. As a result, vertical feature appear to

lean away from the center of the photograph. (Fig. 4)

(a) Map (orthographic projection) (b) Photo (perspective projection)

Constant Scale varied scale

No relief displacement relief displacement

Fig. 4 Comparative geometry of (a) map and (b) a

vertical photograph, differences in shape, size and

location of the two trees.

The scale of an aerial photograph is a function of flying

height. Thus, variations in elevation cause variation in scale

on aerial photographs. The higher the elevation of an object,

the object will be displaced from its actual position away

from the principal point of the photograph. The lower the

elevation of an object, it will be displaced towards the

principal point.

1. Layout of vertically extended objects within an image.

(Fig. 5)

Fig. 5

2. Relief displacement as found in frame imagery, entire

image captured at same instant, and relief displacement is

always radial with respect to the nadir point. (Fig. 6)


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Fig. 6

3. Relief displacement as found in push broom imagery, the

image is built up over time by the platform motion; relief

displacement only exists within a line. It is still radial with

respect to the nadir point, but there is a different nadir point

for every line. Therefore the only component of relief

displacement is cross-track; there is no along-track

component. (Platform motion is up/down). (Fig. 7)

Fig. 7

III. GENERAL CHARACTERISTICS OF RELIEF

DISPLACEMENT

Relief displacement shows that some important general

relationships are involved. Relief displacement is also known

as topographic displacement. These relationships can be

stated as follows:

1. There is no topographic displacement at Nadir. If r is zero,

then so is d.

2. Assuming datum elevation to be at Nadir, points above the

datum are displaced radially away from Nadir while points

below datum are displaced radially towards Nadir.

3. Topographic displacement varies directly with the radial

distance from the Nadir to the object. A particular elevation

two inches from the Nadir will have half the displacement as

that same elevation four inches from the Nadir.

4. Topographic displacement varies directly with the height

of an object. A 100 ft. tree would be displaced twice as far as

a 50 ft. tree the same distance from Nadir.

5. Topographic displacement varies inversely with the flying

height of the base of the object. As a result there is little

apparent topographic displacement on space photography.

The reason for small relief displacement from space is that to

achieve a given scale a shorter focal length lens requires

flying at a lower altitude. The effect of using short focal

length lenses is to increase topographic displacement,

distortion and the apparent depth of the third dimension

(vertical exaggeration) in stereoscopic images. (Fig. 8)

.

Fig. 8

IV. CAUSES OF RELIEF DISPLACEMENT

The main causes of relief displacement are height of the

object, distance of objects from nadir point, focal length,

flying height or altitude, height of objects in relation to

datum plane and effect of the field of view.

The amount of relief displacement depends upon:

A. Height of the object

When the distance of objects from the nadir point is

remain same. But the object height increased or decreased.

Higher object is more displaced. (Fig. 9)



Fig. 9 Change in height of objects

B. The distance of the objects from nadir point

When the distance of object is more from nadir point, the

relief displacement will be more. In case of less distance of

object from nadir point, the relief displacement will be less.

(Fig. 10)

Fig. 10 Distance of object from nadir point

C. Focal Length

When the focal length of camera lens is increased, the

relief displacement will be more. On the other hand, when

the focal length of camera lens is decreased, the relief

displacement will be less. (Fig. 11)

Fig. 11 Change in focal length

D. Flying height or altitude

The average scale determined by the altitude of the

aircraft. If the focal length of the camera lens remain

constant. When the flying height increased, the relief

displacement will be increased. (Fig. 12)

Fig. 12 Change in flying height or altitude

E. The height of the object in relation to datum plane.

(Fig.13)

Fig. 13 Height of object in relation to datum plane

F. Effect of the field of view

Normal angle of view will result in smaller relief

displacement (shift on the photograph of a point because of

its relief (height). (Fig.14)

Fig. 14 Effect of the field of view


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V. MEASUREMENT OF RELIEF DISPLACEMENT

The measurement of relief displacement depends upon:-

A. The amount of relief displacement that is d, on a vertical

photograph is directly proportional to the difference in the

elevation h, between the object whose image is displaced on

the datum.

B. It is directly proportional to the radial distance that is r

between displaced image and the principal point.

C. It is inverse proportional to the altitude H of the camera

above the datum. (Fig.13)

Fig.13 Inversely proportional to flight altitude above the

datum.

D. The relief displacement is outward from points whose

elevations are above datum and inward from points whose

elevations are below datum. (Fig.14)

Fig.14 Inward and Outward displacement

E. The direction of the relief displacement is radial from the

nadir point of the photograph. (Fig.15)

Fig.15 Directly proportional to the distance of the

displaced image from the photo nadir

VI. RELIEF DISPLACEMENT CAN BE CALCULATED

Relief displacement is expressed mathematically as:

d = hr/H

d = Relief Displacement

h = Height of the object

r = Radial distance from nadir point

H = Total altitude of the camera or flying height

Example

An aircraft was flying height of 25000 feet above the

ground and takes a vertical aerial photograph of an object

which is 30 meters height. The image of the object is at a

distance of 6 inches from the nadir point.

Solution

H = 25000 feet or 25000 x 30 = 750000cms

h = 30 meters or 30x100 = 3000cms

r = 6 inches or 6 x 2.5 = 15.0cms

d =hr/H

d = 3000 x 15.0/ 750000

d = 0.06cms

VII. CONCLUSION

The surface of the earth is not smooth and flat. As a

consequence, there is a natural phenomenon that disrupts

true orthogonality of photo image features. In this respect, an

orthogonal image is one in which the displacement has been

removed, and all of the image features lie in their true

horizontal relationship. Displacement is any shift in the

position of an image on a photograph that does not alter the

perspective characteristics of the photograph. Displacement

results mainly from the perspective viewing of the camera

resulting in a perspective or central projection on the

photograph. Relief displacement is the shift or displacement

in the photographic position of an image caused by the relief

or topography. Due to terrain relief, the images of ground



positions are shifted or displaced, in the central projection of

an aerial photograph. If a photograph is truly vertical, the

displacement of images is in a direction radial from the

photograph center. This displacement is called also the radial

displacement due to relief. The amount of displacement

increases at greater radial distances from the centre and

reaches a maximum at the corners of the photograph. The

amount of relief displacement is depends height of the object,

distance of objects from nadir point, focal length, flying

height or altitude, height of objects in relation to datum plane

and effect of the field of view. The reason for small relief

displacement from space is that to achieve a given scale a

shorter focal length lens requires flying at a lower altitude.

The effect of using short focal length lenses is to increase

topographic displacement, distortion and the apparent depth

of the third dimension (vertical exaggeration) in stereoscopic

images.

REFERENCES

[1] Thomas M. Lillesand and Ralph W. Kiefer: University of Wisconsin-

Madison, Third Edition, Remote Sensing and Image Interpretation.

[2] Floyd F. Sabins, Jr., Chevron Oil Field Research Company and University

of California, Los Angeles, Second Edition, Remote Sensing: Principles

and Interpretation.

[3] Kimerling, A. Jon, Muehrcke, Juliana O. (2005). Map Use Reading

Analysis Interpretation, Fifth Edition. JP Publications.

[4] Jensen, J.R. 2007. Remote Sensing of the Environment: An Earth

Resource Perspective. Pearson Prentice Hall.

[5] Wolf, P.R. 1974. Elements of Photogrammetry, McGraw-Hill, Inc.

[6] Pateraki, M.2006. Digital Aerial Cameras. International Summer School

“Digital Recording and 3D Modelling”.Crete Greece.

Sunita Devi has passed MSc. in Geography from Kurukshetra University in

2008 and P.G. Diploma in Remote Sensing and GIS from Panjab University,

Chandigarh in 2009, and currently working as a Research Associate in

HARSAC, Department of Science and Technology, CCS, HAU Campus, Hisar.

Veena has passed Msc. in Geography from Kurukshetra University in 2010 and

M.Tech. in Geo-Informatics from Guru Jambheswar University, Hisar in 2012,

presently working as researcher in HARSAC, Department of Science and

Technology, CCS, HAU Campus, Hisar.

Documents

Measurement of Relief Displacement from Vertical Photographijsetr.org/wp-content/uploads/2014/10/IJSETR-VOL-3-ISSUE-10-2800... · International Journal of Science, ... consequence,