Overview

Photogrammetry, a fascinating blend of art and science, has emerged as a powerful technique in the realm of spatial data acquisition. This innovative methodology, rooted in the principles of geometry and optics, allows the creation of accurate 3D models and maps from photographic images. In this detailed article by Academic Block, we will unravel the intricacies of photogrammetry, examining its history, underlying principles, contemporary applications, and future prospects.

Historical Roots

Early Beginnings

The roots of photogrammetry can be traced back to the mid-19th century when the first aerial photographs were captured from hot air balloons. Pioneers like Nadar and Arthur Batut played crucial roles in laying the foundation for this discipline. However, it was not until the 20th century that advancements in technology, such as the development of aircraft and cameras, propelled photogrammetry into new dimensions.

Father of Photogrammetry

Albrecht Meydenbauer. a German engineer, played a significant role in the development of photogrammetry during the early 20th century. In 1907, he introduced the analytical plotter, a device that revolutionized the field by allowing for precise measurements from aerial photographs.

The analytical plotter facilitated the extraction of geometric information from overlapping aerial images, enabling the creation of detailed topographic maps. Meydenbauer’s contributions marked a crucial advancement in photogrammetry, establishing it as a distinct and valuable discipline for surveying and mapping.

Evolution of Technology

The mid-20th century witnessed a significant leap with the advent of stereophotogrammetry and the use of analytical plotters. Stereophotogrammetry involves the interpretation of overlapping pairs of aerial photographs to extract 3D information. The introduction of computers further revolutionized the field, automating processes and enhancing accuracy.

Key milestones in the field of photogrammetry:

1. Early Aerial Photography: Nadar and Arthur Batut

1A. Nadar’s Balloon Photography (1860)

The earliest form of aerial photography can be attributed to Gaspard-Félix Tournachon, better known as Nadar, a French photographer and balloonist. In 1858, Nadar began experimenting with aerial photography using a tethered balloon. His most famous aerial photograph, taken in 1860 over Paris, captured the cityscape from an elevated perspective. While not true photogrammetry, Nadar’s work laid the groundwork for understanding the potential of aerial imagery.

1B. Arthur Batut’s Kite Photography (1888)

French inventor and photographer Arthur Batut took a different approach by using kites to lift cameras. In 1888, he successfully captured aerial photographs using this method. Although Batut’s work was not photogrammetry in its modern sense, it demonstrated the feasibility of obtaining images from elevated perspectives, setting the stage for future developments.

2. Development of Stereophotogrammetry: Carl Pulfrich and Albrecht Meydenbauer

2A. Pulfrich’s Contributions (Late 19th Century)

In the late 19th century, Carl Pulfrich, a German mathematician and physicist, made significant contributions to stereophotogrammetry. He developed methods to measure terrain and objects in three dimensions using pairs of overlapping aerial photographs. Pulfrich’s work laid the foundation for stereoscopic analysis, a fundamental principle in modern photogrammetry.

2B. Meydenbauer’s Analytical Plotter (1907)

Albrecht Meydenbauer, a German engineer, introduced the analytical plotter in 1907. This device allowed for the precise measurement of objects in photographs and the creation of detailed topographic maps. The analytical plotter marked a crucial advancement, enabling accurate geometric computations from aerial imagery.

3. World War I and Aerial Photogrammetry

3A. Military Applications

The outbreak of World War I in 1914 propelled the development of aerial reconnaissance, creating a significant demand for accurate mapping and surveying. Aerial photography became an indispensable tool for military intelligence. The wartime use of aerial cameras and the subsequent need for precise measurements fueled the evolution of photogrammetry.

3B. Photogrammetric Society (1920)

In the aftermath of World War I, the Photogrammetric Society was founded in the United Kingdom in 1920, reflecting the growing recognition of photogrammetry as a distinct discipline. The society aimed to foster collaboration and exchange knowledge among professionals interested in the application of photogrammetry.

4. Post-World War II Technological Leap: Analytical Plotters and Computers

4A. Analytical Photogrammetry

The mid-20th century saw the advent of analytical photogrammetry, which replaced manual methods with the use of computers. Analytical plotters, such as the Wild A7, allowed for the automated extraction of geometric information from aerial imagery. This marked a significant leap forward in terms of efficiency and accuracy.

4B. Digital Photogrammetry

The latter half of the 20th century witnessed the transition from analog to digital photogrammetry. The integration of computers into the photogrammetric workflow facilitated the processing of large datasets and improved the precision of measurements. Digital technology brought about a paradigm shift, making photogrammetry more accessible and adaptable to various applications.

Principles of Photogrammetry

Stereoscopy

Central to photogrammetry is stereoscopy, the ability of the human brain to perceive depth and dimension from the overlapping images captured by two cameras. This principle is harnessed to create 3D models by exploiting the parallax between corresponding points in the stereo pair.

Ground Control Points

To achieve accuracy in photogrammetric outputs, ground control points (GCPs) are essential. These are precisely measured points on the Earth’s surface whose coordinates are known. GCPs serve as reference points, enabling the photogrammetric software to align and scale the generated models accurately.

Photogrammetric Workflow

1. Image Acquisition: The process begins with the acquisition of overlapping images, whether from aerial platforms, satellites, or ground-based cameras.
2. Camera Calibration: Calibration ensures accurate measurement by accounting for lens distortions and camera parameters.
3. Orientation and Bundle Adjustment: The software determines the spatial relationship between images, refining the positions and orientations of the cameras in a process known as bundle adjustment.
4. Point Cloud Generation: Using the stereoscopic information, a dense point cloud is generated, representing the 3D coordinates of the object’s surface.
5. Surface Reconstruction: The point cloud is processed to create a detailed 3D mesh or surface model, capturing the object’s form and structure.
6. Texture Mapping: High-resolution images are draped onto the 3D model, providing realistic surface details.

Mathematical concepts behind Photogrammetry

1. Basic Geometry in Photogrammetry

1A. Collinearity Equation: The collinearity equation is a fundamental concept in photogrammetry that relates the image coordinates (pixel locations) to the object coordinates (real-world positions). It can be expressed as follows for a single camera perspective:

x=f⋅[Z/X]+x_O; y=f⋅[Z/Y]+y₀;

where:

• x and y are the image coordinates,
• X,Y, and Z are the object coordinates,
• f is the focal length of the camera, and
• (x₀,y₀) is the principal point offset.

1B. Epipolar Geometry:

• In the case of multiple images (stereo pairs), the epipolar geometry helps describe the relationship between corresponding points in different images. It involves the epipolar lines, which are the intersections of the image planes with the epipolar plane. The essential matrix E and the fundamental matrix F are key components in epipolar geometry.

2. Camera Calibration and Distortion Models

2A. Camera Calibration Matrix:

• The intrinsic camera parameters are often represented by a calibration matrix K. For a simplified case (without lens distortion), it can be expressed as:

K= [f 0 x₀ ; 0 f y₀ ; 0 0 1]

where f is the focal length, and (x₀,y₀) is the principal point offset.

2B. Lens Distortion Models:

• Lens distortions, such as radial and tangential distortions, are common in real-world camera systems. Distorted image coordinates (x_d,y_d) can be corrected using distortion models:

x=x_d⋅(1+k₁r²+k₂r⁴+k₃r⁶)

y=y_d⋅(1+k₁r²+k₂r⁴+k₃r⁶)

where k₁,k₂ and k₃ are distortion coefficients, and r is the radial distance from the principal point.

3. Bundle Adjustment

Bundle adjustment is a critical step in refining the parameters of the photogrammetric model. It involves minimizing the differences between observed and computed image measurements. The adjustment equations can be formulated as a least-squares problem, aiming to minimize the residuals between the observed and predicted image coordinates.

min⁡∑_i=1 ⁿ ∑_j=1 ^mi∥observed_ij−predicted_ij∥²

where n is the number of images, m_i is the number of tie points in image i, and observed_ij and predicted_ij are the observed and predicted image coordinates, respectively.

4. Coordinate Transformation

The transformation between image coordinates and object coordinates involves a series of rotations, translations, and scaling. This transformation can be represented by a matrix:

[x; y; Z] = R [X; Y; Z]+[Tx; Ty; Tz]

where R is the rotation matrix, (Tx,Ty,Tz) is the translation vector, and (X,Y,Z) are the object coordinates.

Above mathematical equations provide a glimpse into the underlying principles of photogrammetry. However, it’s important to note that the actual implementation and complexity can vary based on the specific photogrammetric techniques, software, and algorithms employed.

Ethical Considerations

As with any technology, photogrammetry raises ethical considerations. Privacy concerns, especially in urban areas, and the responsible use of data are crucial aspects that must be addressed. Striking a balance between technological innovation and ethical considerations is imperative for the sustainable development of photogrammetry.

Final Words

Photogrammetry, born from the marriage of photography and geometry, has evolved into a transformative force across various domains. Its ability to convert 2D images into rich, detailed 3D models has far-reaching implications for industries ranging from cartography to entertainment. As technology continues to advance, the future promises even more exciting possibilities, pushing the boundaries of what photogrammetry can achieve. However, it is essential to navigate the ethical landscape carefully, ensuring that the benefits of this remarkable technology are realized responsibly and sustainably. In the intricate dance between pixels and precision, photogrammetry continues to shape our understanding of space, form, and the world around us. Please comment below, it will help us in improving this article. Thanks for reading!