Measurement of Relief Displacement from Vertical Photograph

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

Sunita Devi1, Veena2

 photograph. The amount of displacement increases at greater Abstract —The surface of the earth is not smooth and flat. As a radial distances from the centre and reaches a maximum at consequence, there is a natural phenomenon that disrupts true the corners of the photograph. (Fig. 2) 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 Fig.1: Vertical aerial photograph of Long Beach, California, showing relief displacement. Courtesy J. Van differences within any one photograph, and for this reason a Eden. 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 Fig. 2: Geometry of displacement due to topographic relief

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.

(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. 3: Geometry of relief displacement on a vertical aerial photograph

The effect of relief displacement on a photograph taken Fig. 5 over varied terrain. In essence, an increase in the elevation, of a feature causes its position on the photograph to be 2. Relief displacement as found in frame imagery, entire displaced radically outward from the principal point. Hence, image captured at same instant, and relief displacement is when a vertical feature is photographed, relief displacement always radial with respect to the nadir point. (Fig. 6) 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)

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

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. 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 Fig. 8

Relief displacement shows that some important general relationships are involved. Relief displacement is also known IV. CAUSES OF RELIEF DISPLACEMENT as topographic displacement. These relationships can be stated as follows: 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 1. There is no topographic displacement at Nadir. If r is zero, datum plane and effect of the field of view. then so is d. The amount of relief displacement depends upon:

2. Assuming datum elevation to be at Nadir, points above the A. Height of the object datum are displaced radially away from Nadir while points When the distance of objects from the nadir point is below datum are displaced radially towards Nadir. remain same. But the object height increased or decreased. Higher object is more displaced. (Fig. 9) 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.

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. 9 Change in height of objects

B. The distance of the objects from nadir point Fig. 12 Change in flying height or altitude When the distance of object is more from nadir point, the relief displacement will be more. In case of less distance of E. The height of the object in relation to datum plane. object from nadir point, the relief displacement will be less. (Fig.13) (Fig. 10)

Fig. 10 Distance of object from nadir point

Fig. 13 Height of object in relation to datum plane C. Focal Length When the focal length of camera lens is increased, the F. Effect of the field of view relief displacement will be more. On the other hand, when Normal angle of view will result in smaller relief the focal length of camera lens is decreased, the relief displacement (shift on the photograph of a point because of displacement will be less. (Fig. 11) its relief (height). (Fig.14)

Fig. 14 Effect of the field of view

Fig. 11 Change in focal length

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

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.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 Fig.13 Inversely proportional to flight altitude above the distance of 6 inches from the nadir point. datum. Solution D. The relief displacement is outward from points whose elevations are above datum and inward from points whose elevations are below datum. (Fig.14) 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 Fig.14 Inward and Outward displacement orthogonal image is one in which the displacement has been removed, and all of the image features lie in their true E. The direction of the relief displacement is radial from the horizontal relationship. Displacement is any shift in the nadir point of the photograph. (Fig.15) 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.