Lecture 5. Relief displacement. Parallax. Monoscopic and stereoscopic height measurement. Photo Project. Soft-copy Photogrammetry.

Transcription

1 NRMT 2270, Photogrammetry/Remote Sensing Lecture 5 Relief displacement. Parallax. Monoscopic and stereoscopic height measurement. Photo Project. Soft-copy Photogrammetry. Tomislav Sapic GIS Technologist Faculty of Natural Resources Management Lakehead University

2 Geometry of a Vertical Aerial Frame Photograph and the Terrain It Represents Source: Jensen (2007).

3 Relief Displacement on a Vertical Frame Photography Relief displacement is the shift or displacement in the photographic position of an image caused by the relief of the object (Wolf 1974) and the perspective projection based on which images are captured by lens cameras. The amount of relief displacement, d, is: directly proportional to the difference in elevation, h, between the top of the object whose image is displaced and the local datum. directly proportional to the radial distance, r between the top of the displaced image and the principal point. inversely proportional to the altitude, H, of the camera above the local datum. h d H r Source: Jensen (2007).

4 Relief Displacement Based Height Measurement on Vertical Frame Photos Source: Jensen (2007).

5 Relief Displacement on a Vertical Frame Photography Relief displacement causes straight roads, fence lines, etc., on rolling ground to appear crooked on a vertical photograph. Not corrected (not orthorectified) photo Corrected (orthorectified) photo

6 Relief Displacement on a Vertical Frame Photography and Film Strip (Linear Scanner Camera) Analog or digital aerial camera Digital aerial (linear scanner) camera Line of flight Courtesy of Earth Data

7 Relief (radial) displacement in a frame vertical aerial photo Relief displacement direction

8 Relief Displacement in a Linear Scanner Vertical Aerial Photo Relief displacement direction Backward Nadir Direction of flight Forward From:

9 Height Measurement Based on Shadow Length Source: Jensen (2007). The Sun s elevation angle, a, above the local horizon can be determined using a solar ephemeris table. This requires knowing the longitude and latitude of the site, the acquisition date, and time of day.

10 Height Measurement Based on Shadow Length Alternatively, heights can be measured first determining the tan a based on a shadow of an object with a known height. Example: The height of the bottom building, h, is known to be ft. It casts a shadow that measures in on the photo. The photo scale is measured to be 1:5,957, which means that the ground distance of the shadow, L, is ft. That means that: h tana L tana can now be used with other objects after their shadow lengths are measured. For example, the top building, having a shadow of 59.1 ft on the ground, has the height of: h L tana 59.1' ' Source: Jensen (2007).

11 Parallax on Stereo Photos Parallax is the apparent displacement in the position of an object, with respect to a frame of reference, caused by a shift in the position of observation. (Wolf 1974). Objects closer to the position of observation (camera, eyes) have a greater parallax and object further away, smaller. By using geometry and triangulation, one can use parallax to determine the distance to various objects. Utilization of the parallax effect to measure distances has been used in other disciplines as well, such as astronomy. On stereo photos, parallax can be used to measure heights of objects. Greater p. Smaller p. Source: Wolf (1974).

12 Parallax on Stereo Photos p a = x a x a L 2 and L 1 photos superpositioned through their principal points. p b = x b x b p a > p b Point A is higher than point B. Source: Jensen (2007). a change in position, along or parallel to the flightline, of an image of an object from one photo to the next caused by the plane motion is called x-parallax.

13 Parallax on Stereo Photos On stereo photos parallax is created by the movement of the plane along the flight line. The flight line becomes the x-axis in the measurements of the parallax. The parallax on stereo photos, used for stereo viewing and parallax based measurements is also called x-parallax. Stereo photos need to be aligned along the flight line and at a proper baseline distance for a proper stereo viewing. Source: Wolf (1974). So called y-parallax is created when the photos are not aligned along the flight line. Viewing photos in stereo with an existent y-parallax causes eye strain and should be avoided.

14 Height Measurement on Stereo Photos by Using Parallax ho ( H h) dp ( P dp) h o the height of the object H-h the altitude of the aircraft above ground level (AGL). P the absolute stereoscopic parallax (the air base is usually used for P). dp the differential parallax. The following conditions need to be satisfied: the vertical aerial photos have 3⁰ tilt; the adjacent photos are exposed from almost exactly the same altitude above ground level; the principal points (PPs) of both photographs lie at approximately the same elevation above ground level. the base of the objects of interest are at approximately the same elevation as that of the principal points.

15 Height Measurement on Stereo Photos by Using X- Parallax Two out of several ways of doing it: Measuring distances from target points to the point of reference on separate photos belonging to a stereopair. Measuring distances between target points on a stereopair s photos fixed and aligned along the flight line. Using a parallax bar. Monoscopic Stereoscopic

16 X-Parallax Based Height Measurement on Separate Photos Parallax for the top of the building: P a = x a -x a = ( ) = = 3.55 Parallax for the bottom of the building: P b = x b -x b = ( ) = = dp ho ( H h) ( P dp) dp = P a P b = = P = (A-base A-base 4.4 )/2 = ( ) /2= 3.4 Source: Jensen (2007).

17 X-Parallax Based Height Measurement on Separate Photos Close-up of measurement on actual photos. Source: Jensen (2007).

18 X-Parallax Based Height Measurement on Separate Photos ho ( H h) dp ( P dp).211' ' ho ' (3.4'' 0.211'') 0 174' The actual height of the building used in the example is 172. Known from the flight

19 X-Parallax Based Height Measurement on Separate, Fixed Photos Stereo photos need to be properly positioned for stereo viewing (usually done under a mirror stereoscope). p b = x b (- x b ) p b = D - d b Source: Wolf (1974).

20 Parallax on Stereo Photos In humans and many other animals, parallax allows seeing the viewing field depth and perspective. Exact shape images of the real objects can be drawn on a transparent medium and the perception of depth can be preserved even when the real objects are removed. Objects that are closer to the eyes (i.e. higher on a photo in a photogrammetry analogy) are closer to each other on the transparent medium (plane). Source: Wolf (1974). Objects rise as their images are moved closer to each other on the plane. Meaning, their parallax becomes larger.

21 Height Measurement Using a Parallax Bar The principle of floating mark. Two half marks fused into one make a floating mark. By moving the half marks, the floating mark appears to move vertically and can be landed on the objects on the photos. The effect is the same as if the half marks existed on the terrain. If the half marks are moved closer together, the floating mark appears to rise, and vice versa. Half marks are found on the parallax bar, along with a micrometer measurer. Source: Wolf (1974).

22 measuring parallax with a parallax bar Source: Wolf (1974). p a parallax for point a p a = x a x a = D (K r a ) = (D K) + r a The term D K is C -- the parallax constant for the setup. p a = C + r a

23 Ground x, y, and z coordinates can be calculated by u using a paralax. h A = H Bf/p a X A = B * x a /p a Y A = B * y a /p a Source: Wolf (1974).

24 Y Parallax Y parallax is created in stereo viewing when corresponding images fail to lie along a line parallel to the flight line. Y parallax causes eyestrain. Photos properly oriented no y parallax Improper orientation of the photos Photos with y parallax Photo tilt Source: Wolf (1974) Variation in flying height

25 Aerial Photography Project Planning Stereo aerial photos are usually taken as part of a stereo coverage of an area. To accomplish the stereo coverage a flight plan needs to be created and executed. A flight plan usually contains two items: o A flight map shows where the photos are to be taken. o Specifications list specific camera and film/sensor requirements, scale, flying height, end lap, side lap, tilt and crab tolerances, etc.

26 Aerial Photography Project Planning End and Side Laps are overlaps between neighbouring photos either along a flightline (End Lap) or between flightlines (Side Lap). End Lap Side Lap Source: Jensen (2007).

27 End Lap Source: Wolf (1974). PE ( G ) 100 G B PE percent end lap per photo G distance of ground coverage per a photo along the axis parallel to the flight direction. B air base distance, i.e., distance between exposure stations. To avoid possible gaps, aerial photos are normally taken with about 60 % end lap.

28 Side Lap Source: Wolf (1974). PS ( G ) 100 G W PS percent side lap per photo G distance of ground coverage per a photo along the axis perpendicular to the flight direction. W spacing between adjacent flight lines. To avoid possible gaps, aerial photos are normally taken with about 30 % side lap.

29 Flying planes are never constantly in a same position regarding the three axes defining the 3D space. This then changes the relative positions between the aerial photos as well Source: Wikipedia, Author: ZeroOne

30 Causes of Gaps Between Aerial Photos Drift Crab Tilt Flying height variations Terrain variations

31 Causes of Gaps Between Aerial Photos Drift Failure to fly along planned flight lines. Often caused by high winds. Excessive drifts are the most common cause for gaps in photo coverage; when this happens, re-flights are necessary (Wolf 1974). Crab Deviation in the aircraft s actual travel direction from its direction of heading (Wolf 1974). Crab Crabs can be corrected during the flight by rotating the camera to make the sides of the photo format parallel to the actual direction of the flight. Source: Wolf (1974).

32 Causes of Gaps Between Aerial Photos Tilt (Pitch) Source: Wolf (1974).

33 Causes of Gaps Between Aerial Photos Flying Height Variations Source: Wolf (1974).

34 Causes of Gaps Between Aerial Photos Terrain Variations Source: Wolf (1974).

35 Pitch, roll, and yaw movements of the plane also become evident when aerial photos are assembled into a mosaic. Source: Jensen (2007).

36 En example of an aerial photo flight project and the resulting photo alignment.

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38 Time, Season, Direction, Weather Aerial photos should be taken when the sun is between 30 and 50 degrees above the horizon. > 30 deg to avoid underexposure due to low illumination and long shadows that obscure the terrain (although, shadows are also desirable when it comes to, e.g., identifying tree species). < 50 deg to avoid so called hotspots unusually bright areas. Photos are almost never taken while the snow is on the ground. Can be taken leaf-on (for easier tree species identification) or leaf-off (for greater visibility of the ground features). Photos can be flown in any direction. Windy and humid days should be avoided to ensure stable flying and to avoid atmospheric scattering of light in humid conditions, respectively.

39 Soft-copy Photogrammetry Contemporary photogrammetry is mainly practiced as soft-copy photogrammetry. Soft-copy means that a digital image is analyzed, not a hard copy image. The first photogrammetric soft-copy system was developed in the early 1980s, by James Case. Soft-copy photogrammetry includes: o Processing of digital aerial imagery o Stereo-viewing of digital aerial imagery o *Measuring above-terrain heights, deriving digital elevation/surface models (DEMs/DSMs) o Producing orthophotos and ortho mosaics o Extracting planimetric features Stereo aerial imagery required. It can be done with individual or stereo imagery, in mono or in stereo. *In certain circumstances above-terrain height measurements can be done in mono imager y as well rarely practised.

40 In order to use photos as true spatial representations of the real-world, geometric relations need to be established between the camera s, photo s and real-world s coordinate systems. Source: Jensen (2007)

41 In stereo photogrammetry geometric relations need to be established between the adjacent photos as well. Source: Wolf (1974)

42 Three aspects are fundamental to (soft-copy) photogrammetry: Interior orientation Exterior orientation Aerial triangulation

43 Interior Orientation The procedure whereby the geometric characteristics of an aerial photograph are mathematically related to the geometric characteristics (including deformities) of the camera system that took the photograph. The relationship is established between the camera internal coordinate system and the image pixel coordinate system. The information on the camera system is usually found in the camera calibration report, created when the camera was produced or recalibrated. Typical information required for interior orientation that is available in the camera calibration report includes: x,y location of the principal point (e.g., x,y = 0,0) x,y location of all fiducial marks (analog cameras) lens focal length lens distortion Radial distortion Tangential distortion (considered negligible) Source: ERDAS (2009)

44 The relation between the geometry of the camera systems and the aerial photograph is calculated and fixed in digital aerial cameras, there are no fiducial marks involved and no need to manually establish this relation. Interior Orientation It is manually established between chemical film-based aerial photos and aerial cameras by using fiducial marks. Fiducial marks are recorded on the chemical film by the camera at the moment of exposure. Source: Jensen (2007)

45 Exterior Orientation Relates image (photo) coordinates to real-world (exterior) map coordinates. Reference real-world points are called Ground Control Points (GCP) and their position is expressed in the X, Y, Z coordinates in a chosen map coordinate system. All aerial photographs are somewhat tilted and this tilt has to be calculated in the model to be able to derive useful measurements from aerial photos. There are six elements of exterior orientation that express the spatial location and angular orientation of a tilted photograph: X L, Y L, Z L the three dimensional coordinates of the aircraft (camera) at the moment of the exposure, expressed in a ground coordinate system. Omega, phi, and kappa (ω, φ, κ) rolling, pitch, and yawning of the camera at the moment of exposure. All the methods developed to determine these six parameters require identification and X, Y, Z coordinates of at least 3 Ground Control Points on the photo. The GCP points need to form a triangle on the photo, they cannot lie in a straight line.

46 Exterior Orientation

47 Exterior Orientation Ideally, GCPs are marked on the ground and precisely measured (e.g. with GPS), but another method of obtaining their location is by using Geographic Information System layers which share identifiable points with the aerial photo (a particular point can be located on both sources). In addition to GCP points, pass (tie) points identifiable on multiple photos and with unknown real-world coordinates can be used as well. Exterior orientation can also be directly derived when GPS and Inertial Measurement Unit (IMU) are onboard (e.g., ADS camera system). IMU is an electronic device that detects changes in pitch, roll and yaw in the aircraft and, by extension, the camera. Source: Jensen (2007)

48 Ground Control Points (GCPs) Preferred configuration of GCPs. If possible there should be at least one GCP on every third image of a block to calculate the exterior orientation parameters for each photo. When working with one photo only, at least three GCPs are needed to calculate the exterior orientation parameters for it. Source: ERDAS (2009)

49 Tie Points A point that can be recognized on multiple overlapping photos but whose ground coordinates are not known before the block triangulation. Ground coordinates for tie points are computed during the block triangulation. Tie points can be determined manually and automatically. Manual determination in block images typically involves nine points in each image.

50 References: ERDAS LPS Project Manager. Viewed March Gehrke, S., Morin, K., Downey, M., Boehrer, N., and Fuchs, T Semi-global matching: An alternative to LIDAR for DSM generation. In Proceedings of the 2010 Canadian Geomatics Conference and Symposium of Commission I. Jensen., J. R Remote Sensing of the Environment: An Earth Resource Perspective. Pearson Prentice Hall. Mikhail M., J. S. Bethel, J. and C. McGlone Introduction to Modern Photogrammetry. John Wiley & Sons. Wolf, P. R Elements of Photogrammetry. McGraw-Hill, Inc.