Geomatics_Lab3_EliasZamora

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❶ Lab Teaching Assistant Aser Eissa (eissaa@purdue.edu) Assignment date: 01/24/2024 Submission date: 02/04/2024 Purdue University Lyles School of Civil Engineering CE 203 – Principles and Practice of Geomatics Photogrammetric Mission Planning, Relief Displacement, and Parallax Computations Elias Zamora (zamora14@purdue.edu) Fall 2024

CE 203 – Principles and Practice of Geomatics Lab–3: Photogrammetric Mission Planning, Relief Displacemenet, and Parallax Computations Objectives The first objective of this assignment is practicing the computation procedure for designing a photogrammetric mission plan over an area with specified dimensions, camera specifications, and overlap/sidelap requirements. It will also introduce a commercial implementation of the mission planning – DJI Ground Station Pro app (https://www.dji.com/ground-station-pro). This application allows you to execute a complex flight mission, where images will be captured at preset waypoints by a UAV-based imaging system. The second objective aims at practicing the derivation of quantitative information (object heights) from image measurements (relief displacement in single images and x-parallax in stereo-images). Given Data : Mission Planning Givens Part A: Mission Planning (40% of total grade) 1. Given the following camera specifications for the imaging sensor and covered area, design a mission plan for image acquisition with 85% overlap and 85% sidelap: ● Area extent is 935 m and 535 m in the East/West and North/South directions, respectively, ● Flying height above ground is 95 m, ● Camera array dimensions 5000 x 4000 pixels, ● Pixel size 0.0045 mm, and ● Camera principal distance is 28 mm. Need to find Number of Strips, and Numbers of Images per strip: ● To find the # of strips, use the equation: N s = D 1 - 0.4W L / D L , As well as the GSD of the image (pixel size * Scale) ● To find the # of images / strips, use equation: N i = (D 2 /D F ) + 4 2

o D 1 = 535, D 2 = 935, W L = w l (H/c), D L = (1-SL%)W L , and the process for D F and W F are Similar, but Side Lap Percentage (SL%) will be replaced with Overlap Percentage (OL%) ● The findings are listed below: The GSD of the image is 15.268mm, meaning we have a high resolution image and we will require more time for data processing. The number of strips of the image is 2, and the number of images per strip is 5. 2. Download the user manual for the DJI Ground Station Pro app (https://dl.djicdn.com/downloads/groundstation_pro/20181102/GS_Pro_User_Manual_v2 .0_EN_201811.pdf). Prepare a short summary that explains your understanding of how DJI has designed this app for mission planning in light of your computational workflow for the above subtask. Looking at the user manual for the DJI Ground Station Pro app (Create Mission Planning on pg. 16), you can customize every part of the mission, with up to 99 waypoints–which will probably be positioned on the flight lines–and the flight path will be created based off of the waypoints. You can also create boundary areas and way points by tapping. The aircraft will use its own software to calculate the Range and Bearing from a selected object/building on the map, meaning you don’t have to calculate height, ASL, MSL, or angle. The mission planning app takes away a lot of the computations and does it for you. Part B: Relief Displacement and Object height Calculations (20% of total grade) • At the bottom of a valley, the scale of a vertical photograph is 1:9700. The principal distance of the lens used to capture the photograph is 6". A road intersection on the same photograph is 485 ′ above the valley floor and 3.98" from the principal point. What is the relief displacement of the road intersection with respect to the bottom of the valley? The height of the camera is 4850 ft. The relief displacement of the road intersection with respect to the bottom of the valley is found using d, which is 0.398 inches. • A vertical photograph captured at a flying height of 3700 ′ above sea level shows a radio tower with a base elevation 590 ′ above the same datum. The image of the tower has a relief displacement of 1.34". The distance from the photographer's principal point to the top of the tower is 5.87". What is the height of the tower? We need use this equation: displacement = (building height * distance of building to principle point) / Flying height Using this equation, we can find that the building is 844.6 ft tall. 3

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Part C: X-Parallax and Object Height Calculations (40% of total grade) Using images DSC03032 .jpg and DCS03033.jpg – which were provided in the previous assignment, carry out the following tasks: 1. Measure the pixel coordinates (row and column) of the top and bottom points of the highlighted building façade edge in Figure 1. a. The pixel coordinates for the Left Image: i. Bottom: (2112.5, 1101.6) col, row ii. Top: (2224, 924.5) col, row b. The pixel coordinates for the Right Image: i. Bottom: (968, 1400) ii. Top: (945.5, 1222.8) 2. Using the image dimensions and pixel size, derive the image coordinates of top and bottom points of that building façade edge (refer to Appendix A for pixel to image coordinate transformation). a. Image coordinates for Left Image: i. Top: -0.039669, 1.07977 mm ii. Bottom: -0.2376, 0.87059 b. Image coordinates for Right image: i. Top: -1.67859, 0.67018 mm ii. Bottom: (-1.68504, 0.46533) mm 3. Derive the height of this building façade edge using the relief displacement equation (for each a. Using the relief displacement equation, we can find that h = 58 m. image separately). Comment on the similarity/difference of these heights. 4. Using the parallax equation, derive the heights of the top and bottom points of the highlighted building façade edge. From the estimated heights, derive the height of this building façade edge. a. Parallax of images tops x-coord: i. 1.63892 mm b. Parallax of images bottoms x-coord: i. 1.44744 mm c. Using the given equation and information, we can find that h = 60m. 4

5. Comment on the similarity/difference of the derived heights from steps 3 and 4 as well as the similarity with the results from the previous assignment for the neighboring building façade edge. a. The similarities between the heights of step 3 and step 4 are close, but not exact. I believe that the measurement for step 4 is more accurate than step 3, since there are less unknowns that we need to find. Appendix A: Pixel to image coordinate transformation Pixel to image coordinate transformation can be established using the following equations (refer to Figure A1): 1. 𝑥 𝑎 = (column 𝑎 – 𝑁 columns /2 ) ∗ pixel_size 2. 𝑦 𝑎 = ( 𝑁 rows / 2 − row 𝑎 ) ∗ pixel_size 𝑁 rows and 𝑁 columns are the number of rows (up-down direction) and columns (left- right direction) of the input image. row 𝑎 and column 𝑎 are the row and column numbers of the point in question. 5

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