Photogrammetry

Photogrammetry ( rarely also photogrammetry or photogrammetry ) is a group of methods of measurement and evaluation of remote sensing to determine from photographs and exact measurement images of an object 's spatial position or three-dimensional shape. Normally, the images are taken with special measuring cameras.

The field emerged in 1900 from geodesy and for about two decades, remote sensing (FE, English Remote Sensing or RS) assigned. Like the majority of remote sensing, photogrammetry method is also a passive remote sensing and surveying method, since it allows the contactless reconstruction of spatial objects from their radiation photographically held. The objects are usually added in the natural light, and of a plurality of positions of the camera (or the same time from multiple cameras ). The light coming from the object in the measuring camera light can be reflected or emitted radiation, artificial lighting is used but usually only for small objects.

• 2.1 Central projection
• 2.2 Camera Calibration
• 2.3 photogrammetry
• 2.4 Resection
• 2.5 Forwards section
• 2.6 Model Block compensation
• 2.7 bundle block compensation

• 4.1 aerial photogrammetry
• 4.2 Nahbereichsphotogrammetrie

• 9.1 Trade associations

Overview

Name and spelling

The name was first 1867 Photogrammetry in the weekly Journal of the architects association in Berlin, German Bauzeitung later used as the title of the anonymously published article. The editors of the weekly paper commented: "The name of photogrammetry is decidedly better chosen as Photometrographie, although not quite significant and satisfactory. "

Since Wilhelm Jordan for, took the decision to have the name of Photogrammetry first published, the editors of the German Bauzeitung said in a note to { 26 (1892 ) 50:300 } that in 1867 published article by Albrecht Meydenbauer came.

Tasks in photogrammetry

Tasks and methods of the subject - which is usually taught at technical universities in the framework of geodesy - are according to Meyers Lexicon as follows:

Recording and evaluation originally only photographic images measured for the determination of texture, shape and position of arbitrary objects. Photogrammetry is now experiencing a significant expansion thanks to a new video recording equipment and digital image processing as a consequence of the possibilities of optoelectronics, computer technology and digital mass storage devices. The main application of photogrammetry is the → geodesy.

These today are, inter alia, the production of maps, digital GIS landscape models and special tasks such as architectural and Unfallphotogrammetrie as well as in medical applications (eg Virtopsy ).

The terrestrial photogrammetry ( Erdbildmessung ), in which the measurement images are taken of geographically referenced points of view ( Fototheodolit ), is used in the geodetic field for example, topographic surveys in the high mountains and engineering surveys. When aerophotogrammetry (aerial measurement), the measurement images are used primarily for the production of topographic maps for cadastral measurements and Aerotriangulationen with a → measuring chamber from the air included (→ Aerial Photography ). According to the number of images used, the methods of single-screen, Zweibildphotogrammetrie ( stereophotogrammetry ) and multi-image measurement can be distinguished. The measured images are equalized in Einzelbildauswertegeräten or measured in stereoscopic dual image evaluation devices in three dimensions.

Among the non - geodetic applications include the measurement of architecture and works of art, the ballistics (see also satellite camera ), agriculture and forestry, radiology, as well as engineering and technical experimentation.

Methodological overview of the technical terms

The figure gives an overview of the methods of photogrammetry from the point of view of the input and output variables.

The 3D coordinates are the location coordinates of object points in three dimensional space. The image coordinates specify the location of the image of the object points on the photographic plate, film or an electronic imager. The exterior orientation of a camera refers to its location in the room and its view direction. The inner orientation defines the illustration relevant parameters of the camera. The most important of these parameters is the focal length of the lens, but it also includes the description of the lens distortion to it. Furthermore, the additional observations play an important role: by standards, so the known spatial distance between two points, or control points, ie, the known 3D coordinates of points in the locality ( object points ), the connection to defined length units and coordinate systems.

Each of the four main variables can be viewed as a prerequisite and as a result of a photogrammetric method. The individual methods are described in the following sections.

Basics

The goal of a photogrammetric analysis is to restore the spatial position of images in which they were located at the time of recording each other. This restoration is done according to the laws of the central projection in compliance with the Komplanaritätsbedingung. Basically, you can perform this calculation in a cast as part of a common adjustment, process engineering, however, breaks this calculation process into several separate steps that are combined according to the given measurement situation to another,

• Absolute Orientation: The model composite of the relative orientation already corresponds to the geometry of the points in the locality, however, determines the spatial orientation of the model network is not consistent with the location and the scale is still unknown. As part of a three-dimensional Helmert transformation, the model coordinates of the model network are transformed to the known control points in the locality. The Helmert transformation fits the points as in the existing point field that the residual discrepancies in the coordinates are minimal. When using a Restfehlerinterpolation Also consider these misclosures it removed.
• Exterior orientation: In contrast to the relative orientation in which only a mutual restoration of the spatial position of two images is done, allows the exterior orientation of the spatially unambiguous reconstruction of the image position in the recording. The prerequisite for this is that one has visible in the image control points in the locality to which we include iteratively the image coordinates in the course of a spatial resection.
• Interior orientation: To measure within an image must be known where the principal point ( ideally corresponds to the center of the image ) is located. This point is defined by the beam passing through the focal point perpendicular to the standing plane of the lens in the image. This point, and adventitious even the camera constant (usually the focal length ) and the lens distortion is determined by measurement and allows the transformation of a measured point in the image coordinate system.
• Relative orientation: Restoration of the relative position of two images in each room and calculate a so-called model. From the coordinates of the two images and the model coordinates are calculated. In practice, can be so many pictures, for example, from aerial photographs, add up to a model network

Previously, the evaluation of two aerial images Luftbildauswertegeräten, which reached the relative and absolute orientation by physical restoration of the beam. Today, the evaluation is usually done in the comparators, where image coordinates are measured directly. The other steps are then method transitions the numerical photogrammetry, with model block and Bündelblockausgleichungsverfahren used.

Central projection

With a known internal and external orientation and known 3D coordinates of the object points to their image coordinates can be calculated therefrom. This corresponds to the photographic image of the object points with known camera position. The calculation is based on the model of a pinhole camera which is the technical implementation of the central projection in the ideal case. The mathematical formulation of the central projection, are the so called collinearity equations, which represent the main equations of photogrammetry simultaneously:

The meanings of the symbols are explained below:

• I - index for numbering the different cameras
• J - index for numbering the different object and image points
• C - constant chamber, roughly equivalent to the focal length of the lens
• R - 3 × 3 rotation matrix to define the viewing direction of the camera
• - Vector to describe the asymmetry of the pixels of array sensors
• - Vector defining the projection center
• - Vector to define the 3D coordinates of the object points
• - Vector defining the position of the image principal point on the film or sensor
• And - functions to specify the distortion corrections

Alternatively, the image coordinates by means of projective geometry to calculate (homogeneous coordinates). It is equivalent to the classical Kollinearitätsgleichung.

With

• - Homogeneous image coordinates (2d)
• - Homogeneous space point (3d)
• - Projection matrix (3x4 matrix )
• - Calibration matrix with camera constant, principal point, shear and scale difference ( 3x3 matrix )
• - Rotation matrix
• - Identity matrix
• - Position of the projection center ( homogeneous)

Camera Calibration

Wherein the camera calibration, the imaging characteristics, that is, the inner orientation of the camera and the external orientation is calculated from the known image and the 3D coordinates of the object points.

Image measurement

The image measurement determines the exact image coordinates of the image of an object point in an image. In the simplest case, the image measurement is carried out manually. The position of the object point of interest from a human with a measurement device is determined on a negative or positive. Since this method is very error-prone and slow, you used today almost exclusively computer-based method for searching and measuring of objects in images. Here, methods are digital image processing and pattern recognition are used. Can greatly simplify this task by using artificial signal marks. These can be identified by automated methods and localized very precisely to 1/ 50 to 1/ 100 pixels in the image.

Resection

The resection calculates the camera position, thus the exterior orientation of the known interior orientation, the 3D coordinates of the object points and their image coordinates. In classical geodesy at least three fixed points are required for it, while usually approach attracts a larger number of points in measurement images for better accuracy. (Note: Normally 6 control points for orientation of a measurement image are required).

Next section

With a forward section, one can calculate the 3D coordinates of the object points at least two known external orientations and the corresponding image coordinates. Requirement is that at least two photographs of an object taken from different directions, whether concurrently or sequentially with multiple cameras with a camera plays for the principle of no importance.

Model block compensation

Two images in an analog or analytical evaluation are to orient relative. The resulting three-dimensional model coordinates are concatenated using three-dimensional Helmert transformations in a common adjustment to the soil surface transforms ( absolute orientation ). The numerical analysis of the equations to be solved consists only of rotations, translations and a scale. With respect to the coordinates on their disintegrate focus the normal equations of the Ausgleichungssystems and necessary for the adjustment of a model 7 unknowns are reduced to two normal equations with 4 unknowns and 3. Since the numerics is not too demanding, this calculation method became widespread. One end of the 70s, developed at the University of Stuttgart program system resulted in the designation of PAT - M43 ( program system aerotriangulation - Modellblockausgleichung with 4 or 3 unknowns ). The achievable accuracies Modellblockausgleichungen result mean error for the position of ± 7 microns and the height of ± 10 microns. Similar program systems originated with the Orient ( photogrammetry) Vienna University of Technology and other universities.

Bundle block compensation

The bundle block matching is the most important method of photogrammetry. With it, you can of coarse approximations for exterior and interior orientation simultaneously calculate all the unknown quantities of the collinearity equations. As a known quantity only, you need the image coordinates of object points, as well as additional observations in the form of a length scale or the spatial coordinates of control points. This method is the most commonly used methods of photogrammetry in static measurement objects. The main advantage lies in the possibility of a simultaneous calibration. This means that the measurement camera is calibrated during the actual measurement. Measurement and calibration images are thus identical which reduces the cost of the measurement and at the same time guaranteed that the measurement camera is always calibrated. However, not all are suitable configurations of object points for a simultaneous calibration. Then either additional object points must be included in the measurement or separate calibration images are made.

The bundle block compensation is based, as the name says, on the common calculation of bundle blocks. From the theoretical side, it is the more rigorous procedure in comparison with the model block adjustment. The procurement of the output data is, however, easier. The further calculation of the modeling to the absolute orientation is performed in a single curve fitting. The demands on the numerics, however, are much higher than bem model block adjustment: the normal equations do not decompose and the number of unknowns is up to several thousand considerably higher.

Classification

After the used method of image measurement and subsequent evaluation by dividing the Photogrammetry in analog photogrammetry with optical-mechanical Photography and evaluation, analytical photogrammetry with optical-mechanical photography and computer- aided evaluation, digital photogrammetry with digital photography and computer-based offline analysis, as well as digital Onlinephotogrammetrie with a digital photography and online photo measurement.

Applications

Photogrammetry can be divided aerial photogrammetry and terrestrial and close-range photogrammetry in the two main areas of application.

Aerial photogrammetry

In aerial photogrammetry photographs with airborne, digital or analog measuring cameras are added. It usually occur regularly, in strips arranged image associations to which overlap significantly neighboring images. The image associations are based, thus transformed into a common coordinate system. The orientation of the image is based associations of pass and tie points as part of a bundle. From the oriented images can secondary products such as 3D points, digital terrain models ( DTM), orthophotos, etc., are derived.

The results of the aerial photography used to produce and update topographic maps and orthophotos, the großmaßstäbigen point determination in land survey and land consolidation. It can also digital terrain models (DTMs ) can be derived from the data. The land use survey and environmental and land management will also benefit from the results of aerial photogrammetry.

Close-range photogrammetry

The close-range photogrammetry deals with objects ranging in size from a few centimeters up to 100 meters. In the close-range photogrammetry there, unlike in aerial photogrammetry, no restrictions on recording arrangement. Any number of recording positions are used as they arise, when photographing an object with a handheld camera from several directions. In general, today we used to high-resolution digital cameras.

The most common applications of close-range photogrammetry are the industrial metrology (see fringe projection ), medicine and biomechanics, as well as to record the accident. In architecture and archeology makes use of the close-range photogrammetry for building survey, so the documentation as a basis for alterations and historic preservation measures.

An important by-product of close-range photogrammetry are equalized photographs. These are photographs of nearly planar objects such as building facades, which are projected onto a surface such that the gaps in the image with a simple metric scale lengths and distances can be converted.

In recent times, the modern cinematography techniques acquired from photogrammetry. In the movie Fight Club have been using this technique, for example, interesting camera movements possible.

History

The theory of photogrammetry was developed in the mid -19th century in France and Prussia in parallel with the rise of photography. The French officer Aimé Laussedat published in 1851 his writing Métro photography, the German architect Albrecht Meydenbauer published in 1858 his photogrammetric method for building surveying. He gave the Photogrammetry her name and founded in 1885 the first photogrammetric operating authority in the world, the Royal Prussian measurement image Institution. Edouard Gaston Deville and Paul also guest were some of the pioneers of this method. Invented in 1907 by Eduard Orel stereo autographs, which was manufactured by Carl Zeiss in 1909 commercially. With this enabled device ( stereo image pairs ) were the contour lines are drawn automatically by optically scanning the photos.

In the 1930s, the bundle was (based on the devised by Carl Friedrich Gauss compensation calculation ), as he published in 1930 in his book Lectures on Photogrammetry, developed, used since the 1960s on a large scale computers by guest. As at the end of the 1980s, large-format photo scanner for aerial photos or video and digital cameras were available for short-range shots, the analog methods of photogrammetry in most applications have been replaced by digital evaluation. In the first decade of the 21st century, the last step took full digitization by the conventional film -based cameras have been increasingly replaced by digital sensors in aerial photogrammetry.