Chapters 1-4: Summary

Transcription

1 Chapters 1-4: Summary So far, we have been investigating the image acquisition process. Chapter 1: General introduction Chapter 2: Radiation source and properties Chapter 3: Radiation interaction with the lens system Factors affecting the precision and the accuracy of the image coordinate measurements Chapter 4: Radiation interaction with the light sensitive material along the focal/image plane Analog & digital imaging systems 1

2 CE59700: Chapter 5 Vertical Photography 2

3 Overview Image versus map characteristics Vertical photography: definitions and characteristics Image scale Mathematical relationship between corresponding image and ground coordinates Relief displacement 3

4 An Image Versus a Map ed c b a Image Plane a b c d e Map Perspective center A B C D E A B C D E A B C D E Image Datum A B C D E Map Datum 4

5 An Image Versus a Map Images have the following properties: Perspective projection, and Non-uniform scale. Maps, on the other hand, have the following characteristics: Orthogonal (parallel) projection, and Uniform scale. 5

6 Perspective Versus Orthogonal Projection Cone Cone Building Cylinder Building Cylinder Perspective Projection Orthogonal Projection 6

7 Perspective Versus Orthogonal Projection Perspective Projection Orthogonal Projection 7

8 Perspective Versus Orthogonal Projection Perspective Projection Orthogonal Projection 8

9 Perspective Versus Orthogonal Projection Perspective Projection Orthogonal Projection 9

10 Vertical Photography Optical axis coincides with the plumb line vertical image. 10

11 Vertical Photography Vertical images are taken with the camera optical axis coinciding with the plumb line (True Vertical Image). Nearly Vertical Image: There is a tilt angle between the camera optical axis and the plumb line of ±3. 11

12 Basic Elements of a Vertical Aerial Image y-axis Flight direction Format size x-axis x p y p Fiducial mark Fiducial center (F.C.) Principal point (p.p.) Principal distance Focal length Nadir point (n) Perspective center Flying height above datum (H) 12

13 Fiducial Marks in Analog Metric Cameras 13

14 Basic Definitions Nadir Point (n): The intersection of the plumb (gravity) line through the perspective center with the image plane. Principal Point (PP): The intersection of the normal to the image plane through the perspective center with the image plane. The normal to the image plane is assumed to coincide with the optical axis. Principal Distance (c): The normal distance between the perspective center and the image plane (compare with the focal length - refer to the lens equation). Sometimes, it is denoted as the camera constant. 14

15 Basic Definitions Flying Height (H): The elevation of the perspective center above the stated datum. X-axis of the image coordinate system: The line in the image plane through opposite fiducial marks that are almost parallel to the flight direction. Y-axis of the image coordinate system: The line in the image plane through opposite fiducial marks that are almost normal to the flight direction. 15

16 Image Scale b a Focal length f Perspective center Flying height H Ground A B Average terrain h 1 h (average) 16

17 Image Scale Image scale: It is the ratio between a distance on the image and the corresponding distance on the ground. Since the image is a central projection, it does not have a uniform scale (only one exception exists). Image Scale = ab / AB = c / (H - h) Assuming vertical photography Exception: Vertical image over a flat horizontal terrain has a uniform scale (i.e., it can be used as a map). 17

18 Tilt Effect on Image Scale 18

19 From Image to Ground Coordinates 19

20 From Image to Ground Coordinates Objective: Derive the ground coordinates of object points from the measured coordinates of the corresponding image points. Assumptions: We are dealing with a vertical image. We are dealing with an image captured by frame camera: Captured by analog or digital camera Analog or digital format Diapositive 20

21 Frame Camera Focal Plane Perspective Center Footprint The image footprint is captured through a single exposure. 21

22 Negative Versus Positive Negative Diapositive Perspective Center Footprint 22

23 Image Coordinate Systems Flight Direction z Perspective Center y x a ya a x Assumption: principal point coincides with the Fiducial center. 23

24 Analog Camera: RC

25 Fiducial Marks in Analog Metric Cameras 25

26 Image Coordinate System: Digital Images Digital images can be acquired through either: Scanning analog images Direct use of digital cameras For scanned analog images, the image coordinate system is defined in the same way as analog imagery captured by metric cameras. For digital images captured by digital cameras, the image coordinate system is defined by the central row(s) and the central column(s). 26

27 Example of Photogrammetric Scanner 27

28 Digital Camera: DMC TM _24870/Photogramm%C3%A9trie%20- %20cam%C3%A9ras%20num%C3%A9riques.jpg 28

29 Digital Images captured by Digital Cameras y` y x x` Pixel Coordinates Image Coordinates 29

30 Pixel to Image Coordinate Transformation x ( y nc / 2.0 ) y _ y ( n / 2.0 x ) x _ where n n c r r pix _ pix _ size size : Number of columns Number of rows x _ pix _ size Pixel size along the y _ pix _ size Pixel size along the row direction column direction 30

31 Ground Coordinate System Z Y A X A Z A Y A X 31

32 Ground Coordinates from Image Coordinates PC z Z y x Y A X A Z A Y A X 32

33 Ground Coordinates from Image Coordinates Assumptions: Vertical imagery, The image and ground coordinate systems are parallel, The origin of the ground coordinate system is vertically below the perspective center, and The principal point coincides with the Fiducial center From similar triangles, one gets: X A = x a (H - h A ) / c Y A = y a (H - h A ) / c 33

34 Ground Coordinates from Image Coordinates a b c Negative plane f f y c b Perspective center x a Positive diapositive contact print Flying height (H) Y X p A C Ground level B 34

35 Question: Single Photo Positioning? Can we derive the three-dimensional coordinates of an object point from a single photo? Answer: No We assumed that we know the height of the object point under consideration. 35

36 Single Photo Positioning? a (image point) Perspective Center (Single Light Ray) h A 36

37 Relief Displacement 37

38 Relief Displacement a a o f Focal length H H-h A r' r d (Relief displacement) A A o h A A P Datum R 38

39 Relief Displacement The shift in the photographic position of an image point caused by the height of the corresponding object point above or below the datum. From similar triangles, one gets: d a = r h A / H Relief displacement occurs along the radial direction from the nadir point. For vertical imagery over flat horizontal terrain, the effect of relief displacement simulates a uniform change in the scale. 39

40 Relief Displacement Assumption: nadir point coincides with the Fiducial center. 40

41 Relief Displacement 41

42 Relief Displacement Patch from the left image Patch from the right image PP PP Where are the principal points? 42

43 Relief Displacement Light pole 43

44 Relief Displacement Relief Displacement increases with the radial distance. 44

45 Relief Displacement Relief Displacement is directly proportional to: Radial distance from the nadir point, and Object height above the datum. Relief Displacement is inversely proportional to: Flying height above the datum. Relief displacement causes occlusion. 45

46 Relief Displacement: Characteristics Relief displacement is outward for points whose elevations are above the datum (diapositive). Relief displacement is inward for points whose elevations are below the datum (diapositive). Relief displacement occurs along radial direction from the nadir point of the image. For vertical photographs: The nadir point (n), the principal point (PP), and the Fiducial center (FC) are very close to each other. 46

47 Relief Displacement: Characteristics Inward displacement Outward displacement 47

48 Relief Displacement & Occlusion Occluded Area 48

49 Relief Displacement & Occlusion 49

50 Relief Displacement & Occlusion Occluded Area 50

51 Relief Displacement & Occlusion 51

52 Relief Displacement & Occlusion Occluded Area 52

53 Relief Displacement & Occlusion Patch from the left image Patch from the right image Where are these patches relative to the original images? 53

54 Relief Displacement & Occlusion 54