Understanding Photogrammetry & Structure from Motion
The Science Behind Photogrammetry
​The science behind photogrammetry and SfM involves principles of geometry, optics, computer vision, and optimization. These techniques leverage the mathematical relationships between images, camera parameters, and 3D coordinates to transform 2D photographs into accurate 3D models, enabling applications in various fields, from archaeology to robotics. Advances in computer vision algorithms and hardware have greatly improved the accuracy and efficiency of these processes, making them indispensable tools in modern imaging and spatial analysis.
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Geometry and Triangulation: At the heart of photogrammetry lies the principles of geometry and triangulation. Triangulation is the process of determining a point's location in space by measuring angles to it from known points at either end of a fixed baseline. In photogrammetry, this involves identifying corresponding points on multiple photographs (often referred to as "tie points") and using their angles of view to calculate the 3D coordinates of the point.
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Epipolar Geometry: Epipolar geometry is a fundamental concept in photogrammetry. It relates the positions and orientations of two cameras capturing the same scene. When you take two pictures of an object from different viewpoints, the epipolar geometry helps establish a relationship between corresponding points in these images. This relationship is crucial for accurate 3D reconstruction.
Introduction to Photogrammetry
Photogrammetry is a technique and science of extracting precise geometric information, measurements, and three-dimensional data of objects, environments, or scenes from a series of two-dimensional images. By analyzing the visual and spatial relationships between these images, photogrammetry utilizes computational algorithms to reconstruct the three-dimensional structure and characteristics of the subject, facilitating the creation of accurate 3D models and maps.
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What is Photogrammetry?
Structure from Motion (SfM): The Photogrammetry Process
One of the key techniques within photogrammetry is Structure from Motion (SfM). SfM is a photogrammetric method that enables the reconstruction of three-dimensional structures from a series of two-dimensional images taken from multiple viewpoints
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Image Acquisition: The first step in SfM is capturing a set of photographs of the object or scene you want to reconstruct. These photos should be taken from varying angles and positions, covering the entire subject.
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Feature Detection: SfM algorithms analyze the images to identify and track distinct features or keypoints, such as corners, edges, or unique patterns, which can be consistently matched between images.
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Camera Calibration: To ensure accurate reconstruction, SfM software also calibrates the cameras used to capture the images, correcting for any lens distortions or variations in camera parameters.
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Sparse Point Cloud Generation: The software triangulates the keypoints across images, creating a sparse point cloud. This cloud represents the 3D positions of the features in the scene relative to the camera positions.
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Bundle Adjustment: To refine the 3D structure, bundle adjustment techniques optimize the camera positions and orientations while minimizing the reprojection errors of the keypoints.
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Dense Point Cloud and Mesh Generation: Once the sparse point cloud is refined, it's used to create a dense point cloud, which provides a more detailed representation of the object's surface. This dense cloud can then be used to generate a 3D mesh or surface model.
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Texture Mapping: The final step involves mapping the original images onto the 3D mesh, creating a realistic textured 3D model of the object or scene.
Resources Used
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Mikhail, E. M., Bethel, J. S., & McGlone, J. C. (2001). Introduction to modern photogrammetry. McGraw-Hill Education.
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Hartley, R., & Zisserman, A. (2004). Multiple view geometry in computer vision. Cambridge University Press.
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Kraus, K., & Haala, N. (2000). Photogrammetry: Geometry from images and laser scans. Walter de Gruyter.
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Bierman, P. R., Wilcots, J. K., et al. (2012). Structure-from-motion (SfM) photogrammetry: A low-cost, effective tool for geoscience applications. Geosphere, 8(4), 935-947.
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Remondino, F. (2011). Digital photogrammetry in archaeology: New perspectives for recording of cultural heritage. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 38(5), 537-542.
Photogrammetry Applications
A Brief History of Photogrammetry
Photogrammetry has a rich and fascinating history that spans over a century. The development of photogrammetry has been driven by technological advancements, scientific discoveries, and a wide range of applications across various fields.
Early Experiments (19th Century)
Photogrammetry's origins can be traced back to the 19th century. French inventor Joseph Nicéphore Niépce produced some of the earliest photographic images in the 1820s, laying the foundation for the use of photography in the field. In the 1850s, French photographer Aimé Laussedat began experimenting with applying geometric principles to photographs. He is often considered one of the pioneers of photogrammetry.
World War I and Aerial Photogrammetry
World War I played a significant role in the advancement of photogrammetry. Aerial photography became a crucial tool for military reconnaissance, mapping, and targeting. The stereoscope, which allowed for the viewing of overlapping aerial photographs in 3D, was widely used during this period to create topographic maps.
Post-War Developments
After World War I, photogrammetry gained recognition as a valuable scientific and engineering discipline. Researchers and professionals began to refine techniques and develop dedicated photogrammetric instruments. The American Society of Photogrammetry (now known as the American Society for Photogrammetry and Remote Sensing, ASPRS) was founded in 1934, further advancing the field.
Aerial Photogrammetry in World War II
World War II saw further advancements in aerial photogrammetry, particularly for military mapping and intelligence purposes. The technology continued to evolve, with improved cameras and instruments.
Photogrammetry Goes Digital
The digital revolution in the latter half of the 20th century had a profound impact on photogrammetry. The transition from film-based to digital cameras, along with the development of powerful computers, transformed data acquisition and processing. Digital photogrammetry allowed for more efficient and accurate 3D reconstruction, enabling a broader range of applications.
Modern Photogrammetry and SfM
In recent years, the advent of Structure from Motion (SfM) techniques, coupled with the proliferation of consumer-grade digital cameras and drones, has democratized photogrammetry. SfM enables 3D reconstruction from a series of 2D images and has found applications in archaeology, cultural heritage preservation, construction, and more. The fusion of photogrammetry with LiDAR (Light Detection and Ranging) technology has further expanded the capabilities of 3D data acquisition, especially in surveying and geospatial applications.
Ongoing Advancements
Photogrammetry continues to advance with the integration of artificial intelligence, machine learning, and computer vision algorithms. These technologies enhance automation, accuracy, and speed in 3D reconstruction. Today, photogrammetry is a vital tool in fields such as archaeology, cartography, civil engineering, environmental monitoring, entertainment, and autonomous navigation.
Resources Used
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Newhall, B. (1982). The history of photography: From 1839 to the present. The Museum of Modern Art.
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Travers, L. (2012). Surveying and mapping in colonial British America. University of North Carolina Press.
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Paine, D. P., & Kiser, J. D. (2017). Aerial photography and image interpretation. Wiley.
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Van Leusen, M. (2003). A history of aerial photography and archaeology: Mata Hari's glass eye and other stories. Antiquity, 77(297), 273-285.