Basic Principles of Photogrammetry

Transcription

1 Basic Principles of Photogrammetry Annual Conference of PSLS January 13 16, 2019 Hershey, PA Frank Derby, PhD Penn State University Lehman, PA 18627

2 Workshop Content General Principles of Photogrammetry Applications of aerial photogrammetry UAV Flight planning Applications of UAV Digital photography Photo control points Geo-referencing Geo-rectification Deliverables

3 Expected Outcomes Upon completion, participants will understand: Applications of aerial photogrammetry Analog Photography Digital photography UAV Flight planning considerations Georeferencing Georectification Procedures for creating orthophotographs

4 What is Photogrammetry A procedure for acquiring data to map a region of the earth s surface or some phenomenon without making direct contact with the feature or phenomenon. Also called remote sensing, data acquisition is accomplished with sensors mounted on platforms such as aircraft, drones, helicopter, satellites, balloons, etc. Sensors may be photo cameras, infrared sensors, charge coupled devices Sensors operate using the visible region of the electromagnetic spectrum.

5 Photogrammetric Sensors Two main types of sensors Passive Sensors detect energy from the physical environment. Passive sensors gather target energy through the detection of light, radiation, heat or other phenomena occurring in the subject's environment. Active Sensors have their own source of energy. They actively direct wave signals onto targets and measure the backscatter reflected back to it.

6 Photogrammetric Sensors Active Sensors Radar EDM LiDar Lasers Passive Sensors Camera Human eye UV Imagers Thermal IR sensors Masers

7 The Electromagnetic Spectrum

8 Photogrammetric Principles Ground coverage Area of the ground that is captured in a single frame.

9 Photogrammetric Principles End lap the overlap area between adjacent photos on a flight line Air Base the distance between consecutive exposure stations.

10 Photogrammetric Principles Side lap The overlap are between photos on adjacent flight lines.

11 Large Area photogrammetric Project Manned aircraft platform Analog Film format = 9 inch x 9 inch Flying Height = 1000 ft ft. Fixed Focal length camera

12 Applications of Traditional Photogrammetry Topographic mapping Digital elevation mapping Ortho-photo maps Computing volumes of Earthwork Historical preservation Tax maps Cadastral base maps Zoning and planning Etc.

13 Flat Terrain SSSSSSSSSS = PPPPPPPPP dddddddddddddddd = aaaa GGGGGGGGGGGG dddddddddddddddd AAAA Photo scale = FFFFFFFFFF LLLLLLLLLLL FFFFFFFFFFFF HHHHHHHHHHH =ff HH H = Height above ground f = Focal Length ab = Photo distance AB = Ground distance

14 Variable Terrain Use Average Photo scale (S av ) Photo Scale S av = ff HH h aaaa H = Height above Datum H = Height above ground h av = Average height of the terrain

15 Ground Coverage Assuming a camera whose focal length is 152.4mm Flying height = 1000m Frame format of m square, The ground coverage is given by aaaa AAAA = ff HH ; AAAA = aaaa HH ff AAAA = mm xx 1000mm mm = m For a square format the ground coverage = = 3395sq. m

16 Displacement (ab) Relief Displacement aaaa = rrr HH Height of pole (h) h = aaaa HH rr

17 Photo Scale Scale selection depends on the purpose of the project. Finished scale of the deliverables The smallest detail that needs to be shown Dictated by the resolving power of the sensor.

18 Resolving Power of Analog Cameras The resolving power of an objective lens is measured by its ability to differentiate two lines or points in an object. The greater the resolving power, the smaller the minimum distance between two lines or points that can still be distinguished. Given in number of lines per millimeter. E.g. 80 lines/mm

19 Resolving Power and Photo Scale Supposing that in a photogrammetric mapping project, the road marking on a highway need to be shown. Given that the width of the marking is 4 inches (100 mm), what should the minimum photo scale be, if the power of the camera is 80 lines/mm? Solution: The smallest object that the camera can capture is: 1 80 mmmm = mmmm Min. Photo scale = mmmm 100 mmmm =

20 Resolving Power and Photo Scale Assuming that the focal length of the camera is 6 inches (0.5 ft), what should be the maximum flying height? Solution: 1 = H Maximum Flying Height (H) = 4000 ft

21 Small Area Photogrammetric Platforms Aircraft Helicopters Blimps Kites Drones Balloons Pigeons

22 Applications in Small Area Mapping Aerial photography Mapping Volumetric Surveys Contour Mapping Topographic Mapping Digital Terrain Modelling Temporal/Spatial Correlation for Terrain Reconstruction Geophysical Survey

23 Civilian Applications Security awareness; Disaster response, including search and support to rescuers; Communications and broadcast, including news/sporting event coverage; Cargo transport; Spectral and thermal analysis; Critical infrastructure monitoring and inspection, including power facilities, ports, bridges, and pipelines; Commercial photography, aerial mapping for small areas, and advertising.

24 Resolution of Digital Cameras Resolution refers to the number of pixels a camera can capture (in Megapixels). One Megapixel approximates a million pixels. Each pixel contains a digital number (DN) which corresponds to a digital color representation of the features within the corresponding ground.

25 36mm x 24mm (Full format) 23.6mm x 15.7mm (1.5x) 22.2mm x 14.8mm (1.6x) 17.3mm x 13mm (2x) 13.2mm x 8.8mm (2.7x) Sensor Frame Formats

26 Pixel Resolution Pixel size is determined in metric units For a full fame camera, frame size in 36mm x 24mm Surface Area is 36 x 24 = 864 sq. mm. For a 20 MP camera, a pixel size is = 6.42µm x 6.42µm xxxxxxxxxxxx = mm For a frame size of 13.2mm x 8.8mm, the pixel size is 2.4µm x 2.4µm.

27 Pixel Resolution If the UAV camera has a focal length of 28 mm and flies at 390 ft. above ground, then the ground resolution will be: 390 ft. = m ~ 119 m ff = aaaa HH AAAA then AAAA = aaaa xx HH ff AB = mmmm xx mmmm 28 mmmm = mmmm on the ground For a square pixel, the ground resolution is 2.7 cm x 2.7 cm

28 Ground Coverage Length ff = aaaa HH AAAA AB = AB = m HH aaaa ff = xx 24mmmm 28mmmm 24 mm 36 mm Width WW = mm xx 36mmmm 28mmmm = m Total Area = x = 15,606 sq. m

29 End Lap Assuming 75% End lap, End lap = 0.75 x m = m Air base = m Air Base = m Air base End lap

30 Intervalometer Setting Assuming the aircraft travels at 10 meters per second, the intervalometer setting will be: Air base IS = mm 10 mm = 2.55 sec. ~ 2 sec. The UAV will take a picture every 2 seconds. Note: The average UAV travels art 13m/sec. End lap

31 Image Size For a 20 MP camera, the size of a color photograph will be: Assuming 1. Three color bands (Red, Green, Blue) per pixel 2. Each pixel requires 1 byte of memory, 20 MB x 3 color bands = 60 MB for the raw image Therefore the type of storage medium becomes important.

32 Maximum Height of Features Assuming 75% End lap, End lap = 0.75 x m = m Air base = m Air Base = m Air base End lap

33 Maximum Height of Features Still using 75% End lap, End lap = 0.75 x m = m; Air base = m Air base (B) Tallest Feature (h) HH = h ; h = HH(GG BB) GG GG BB GG H h = HH = m G h Remember that tree tops are not pointed End lap

34 Maximum Feature Height Assuming 70% End lap, and Flying of Height of 80 m, Then we can find the maximum height of features. Still using f = 28 mm Ground coverage is ff HH = aaaa AAAA G = 24 mmmm xx 80 mm 28 mmmm = 68 m AAAA = aaaa HH End lap =0.7 x 68 m = 48 m ; Air Base (B)= = 20 m ff h = HH GG BB GG ; h = 80mm xx 48 mm 68 mm = m

35 Sources of Error Internal Lens distortion Film shrinkage Atmospheric refraction Relief Displacement External Rotations in x, y, z of the aircraft in relation the ground Shifts in X, Y, Z, in relation to a geographic coordinate system Errors in the ground control points

36 Relating Image points to Ground Coordinates Premarking or Paneling artificial points are placed at strategic locations on the ground in the project area prior to taking the aerial photography. Provides excellent control quality Useful in areas where there are scant details to be used as ground controls Use for controlling most precise photogrammetric work Extra work and expense incurred in acquiring and placing targets Targets could be moved between time of survey and photography Targets may not appear in favorable positions on the photograph

37 Relating Image points to Ground Coordinates Natural Targets Well defined identifiable points on the photograph are used as control points. The points are then surveyed and used as control points. Control points can be located at suitable locations in the project area. No extra cost for acquiring or placing targets

38 Photogrammetric Image Processing Georeferencing (Ground Registration) the process of aligning the pixels in the image to ground coordinate system. Accomplished through coordinate transformation process (Affine transformation in particular) Remote sensing specialists refer to georeferencing as georectification but the term has a different meaning in photogrammetry Georectification the process of removing effects of tilt, lens distortion and other errors form the the aerial photograph. The process is more complicated than georeferencing. Accomplished by applying mathematical principles of collinearity or coplanarity conditions and aerotriangulation processes

39 Affine Transformation A six parameter transformation which accounts for Unequal scale distortion, non-orthogonality of the axes, angular rotation, and translations in Eastings and Northings. The equations may be expressed using simpler notation of the form: EE = aa 0 + aa 1 xx + aa 2 yy NN = bb 0 + bb 1 xx + bb 2 yy When applied on a feature, the Affine transformation changes all characteristics including shape, scale orientation and size. Note that variations in elevations of points in the photograph are not accounted for.

40 Affine Transformation Given that x, y are in the photographic coordinate system, E, N are in the ground coordinate system, and ε is the lack of orthogonality in the axis. s x, s y are the scale factors for x and y axes respectively, and E 0, N 0 are the translations. ε, θ, s x, s y, E 0, N 0 are the six independent parameters which may be determined if at least three points (preferably more) have known coordinates in both systems.

41 Affine Transformation Determination of unknown parameters θθ = tan 1 aa 2 bb 2 ; εε θθ = tan 1 bb 1 aa 1 ; εε = εε θθ +θθ ss xx = aa 1 cos εε cos εε θθ ; ss yy = bb 2 cos εε cos θθ EE 0 = aa 0 ; NN 0 = bb 0

42 2-D Projective Transformation An eight parameter transformation XX = aa 1xx + bb 1 yy + cc 1 aa 3 xx+ bb 3 yy +1 YY = aa 2xx + bb 2 yy + cc 2 aa 3 xx+ bb 3 yy +1 x and y are tilted photo coordinates Since the transformation is non-linear, it is better to solve by least squares, after linearization.

43 2-D Projective Transformation Unknown parameters: a 1, b 1, c 1, a 2, b 2, c 2, a 3, b 3, are eight transformation parameters to solve for. These are functions of the eight unknowns: x 0, y 0, ω, φ, κ, X L, Y L, and H

44 Image Rotation and Translation

45 Collinearity Equations If there are a number of ground control points whose coordinates XYZ are known, then the process of analytical rectification can be performed based on the parameters derived from these coordinates. Satisfies the condition that the exposure station, any object point and its photo image all lie along a straight line in three dimensional space.

46 Creating Tie Points STA 4 WIL 1A STA 41 RD GYM WIL 1B

47 Collinearity Equations xx aa = xx 0 ff mm 11 XX AA XX LL + mm 12 YY AA YY LL + mm 13 ZZ AA ZZ LL mm 31 XX AA XX LL + mm 32 YY AA YY LL + mm 33 ZZ AA ZZ LL yy aa = yy 0 ff mm 11 XX AA XX LL + mm 12 YY AA YY LL + mm 13 ZZ AA ZZ LL mm 31 XX AA XX LL + mm 32 YY AA YY LL + mm 33 ZZ AA ZZ LL Where: mm 11 = cos φφ cos κκ mm 12 = sin ωω sin φφ cos κκ + cos ωω sin κκ mm 13 = cos ωω sin φφ cos κκ + sin ωω sin κκ mm 21 = cos φφ sin κκ mm 22 = sin ωω sin φφ sin κκ + cos ωω cos κκ mm 23 = cos ωω sin φφ sin κκ + sin ωω cos κκ mm 31 = sin φφ mm 32 = sin ωω cos φφ mm 33 = cos ωω cos φφ

48

49 Interior Orientation Exterior Orientation Digital Elevation Models Mosaics and color balancing Analytical Rectification

50 Digital Elevation Model (DEM) A digital elevation model is a bareearth raster grid referenced to a vertical datum. Elevation data from non-ground points such as bridges and roads, are excluded from digital elevation model. Elevation data from structures such as powerlines, buildings and towers, trees and other types of vegetation are also excluded from a DEM.

51 Digital Elevation Model A bare-earth elevation model is particularly useful in: Hydrologic modelling: Hydrologists use DEMs to delineate watersheds, calculate flow accumulation and flow direction. Terrain stability: Areas prone to avalanches are high slope areas with sparse vegetation. This is useful when planning a highway or residential subdivision. Soil mapping: DEMs assist in mapping soils which is a function of elevation (as well as geology, time and climate).

52

53 Mosaicked Ortho-photo

54 Digital Elevation Models Most users often feel that DEM derived using softcopy photogrammetric instruments will be free from error. User should be aware of several trade-offs: the process works well when the terrain is devoid of trees, buildings, overpasses, bridges, etc., which extend above the nominal terrain. The algorithm assumes these objects are terrain and computes the differential parallax and the resultant height of such surfaces which are then placed in the DEM.

55 Accuracy of DEMs The accuracy of the orthophoto is a function of the quality of the imagery, the ground control, the photogrammetric Aerotriangulation and the DEM. The DEM can have errors associated with it. The orthophoto may be derived from a DEM with building rooftops cleaned up, or even DEM with buildings and trees removed. The analyst should always have access to the metadata of how the DEM was generated.

56 Digital Surface Model A DSM captures the natural and built features on the Earth s surface. Digital Surface Model (DSM) Extruding features are tree canopy.

57 Digital Surface Model

58 DSM is particularly useful in: Digital Surface Model Runway approach zone encroachment. In aviation, DSMs can determine runway obstructions in the approach zone. Vegetation management. Along a transmission line, DSMs can see where and how much vegetation is encroaching. View obstruction. Urban planners use DSM to check how a proposed building would affect the views of residents and businesses. Inspecting Power lines and pipe lines for hazards

59 Thank You!