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How Does Triangulation in Photogrammetry Work?

Photogrammetry is a combined art and science that acquires reliable data without physical contact. It helps surveyors determine the X, Y, and Z ground coordinates of surface points from the photograph itself.

When conducting a photogrammetric study of an object or area, it’s necessary to have the newest tools for digital photogrammetry. Whatever images are taken can be processed to produce highly detailed byproducts such as planimetric and topographic maps. How well that end product turns out depends on the understanding of the triangulation process.

Positions and Angles

Triangulation Positions and Angles

Traditional triangulation methods require ground control points around the perimeter and in the center of the block area. Global positioning systems (GPS) have changed the way these are established, but a separation in position and angle is needed.

A given project works with multiple overlapping photographs to achieve accurate photogrammetric measurements. The system’s algorithm won’t have trouble reconstructing an area’s geometry on angles up to 90 degrees. However, this works if the coordinates are known. When working with automated matching, it’s best to use small angles between photographs.

Image Quality

Image Quality

An image’s orientation information can be determined by the value of pixel sizes in the X and Y directions. The accuracy of the data collected is relative to the quality of the photographs.

Whether the camera is attached to a tripod or a drone, the resolution must be kept as high as possible. Each image will be taken to cover as much of the area based on the size and position. The photos will be overlapped later to conflate all images from varying positions and angles.

Point Matching

Separate images can be linked together by tie points to create accurate mosaics of the area. Tie points represent the same location in adjacent image. Each point defines a light ray in 3D space that starts at the camera and extends to the real object.

Point matching occurs when two or more points of light correspond to the same 3D location. These points can be connected either manually, but photogrammetry software like PhotoModeler makes it possible to conduct this step automatically. The software takes the camera’s characteristics- focal length, pixel size, lens distortion- to calibrate the geometric intersection of the light rays.

Bundle Adjustment

Bundle Adjustment

When working with software, there are two algorithms to use – camera auto-calibration and bundle adjustment. Out of the two, the “bundle adjustment” algorithm will be necessary for triangulation.

The name is derived from the bundle of light rays that pass through each lens position. Through the algorithm, all photos are adjusted simultaneously to create an intersection of all light rays at each pass point and ground control points. This, in turn, solves the unknown quantities consisting of X, Y, and Z object space coordinates. Once completed, the software creates a 3D model of the area or object complete with lines, surfaces and textures.

The final product should still be reviewed for measurements in real units. A simple ruler and reference scale will suffice for determining the amount of light per distance.

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