POMPEII

Photogrammetry is the theory, science and art of obtaining reliable information from photographs.  It can provide both interpretative particulars (identification of features) and metric data (dimensions of features).  An important aspect of photogrammetry is that accurate information may be obtained from images of objects rather than from the objects themselves.[1]

Historically, photogrammetry has concentrated on creating two-dimensional representations of three-dimensional subjects.  Aerial photogrammetric techniques have been extensively researched and used by industry and governments to produce topographic, planimetric and other types of maps from long-range aerial photographs.  Terrestrial photogrammetry employs ground-based close-range photography to produce drawings of existing structures and terrain.

Two-dimensional photogrammetric techniques produce geometrically accurate images of subjects that are orthogonal (i.e., at right angles) to the plane that is being recorded.  An orthographic projection assures consistency of scale and removes perspective distortions.   Three photogrammetric process were identified that could possibly improve the photomosaic methodology:

• Image acquisition
• Photogrammetric control
• Image adjustment

Image Acquisition - A variety of equipment and techniques are used to capture photogrammetric imagery.  When horizontal surfaces such as areas of the earth are recorded, photographs are taken from above.  When vertical surfaces such as walls are recorded, photographs are taken horizontally.  Aerial cameras are generally large format (23 X 23 cm), which capture high-resolution long-range images, and may be either film or digital instruments.  Most terrestrial imagery is now accomplished with digital cameras.  Photogrammetric cameras are broadly classified as either “metric” or “amateur”.[2]

Metric cameras are precision instruments that are robustly constructed and incorporate special low distortion, fixed focal length and fixed focus lenses.  The objective of the design is for the optical parameters of the camera to be known, to remain constant and to provide a geometry that enables the photographs to be analyzed, processed and adjusted accurately.  Metric cameras are bulky, expensive and periodically must be calibrated to maintain required standards.  The design of the lens also dictates a fixed depth of field, which in turn establishes how close or far away the camera may be from a subject and still capture images that are in focus.  Budget considerations, as well as the difficulties of air transportation made it unlikely that a metric camera would ever be available to produce images for photomosaics in Pompeii.  In addition, it was uncertain if a metric camera would function properly at very close range.

“Amateur camera” is a term of art describing a non-metric photographic instrument whose internal optical parameters are not known or may change; it is not an inferior device.  The evolution of high-resolution digital photography has resulted in the development of several successful strategies to utilize commercially available professional and consumer cameras, especially for close-range terrestrial photogrammetry.  The equipment is more affordable than metric hardware, and the resulting accuracy is acceptable for producing photomosaics of the facades in Pompeii.

Photogrammetric Control - Unprocessed photographs can only provide relative size information about a subject, rather than absolute dimensions.  However, if the measured locations (coordinates) of points on a subject are known and can also be identified on its photograph, the ratio of the distance between points on the image and the distance between corresponding points on the subject can be determined.  This ratio is the scale of the photograph, which can then be used to ascertain any absolute length on the subject from its image.

Photogrammetric control is the process of establishing and measuring the coordinates of points on a subject.  In aerial photogrammetry, the coordinates of “ground control points” are obtained by total station survey or GPS.  In terrestrial photogrammetry, the coordinates of the control points on the surface of structures or features are obtained by total station survey, hand measurement or by placing objects of known length on the subject when it is photographed.  The points may either be identifiable locations on the subject or attached targets.  Control points are used not only to determine scale, but also to correct distortions in the photographs.[3]

One of the shortcomings of the first photomosaic was the absence of an absolute scale.  Also, the lack of verifiable spatial data made it difficult to combine the photographs accurately.  The techniques of photogrammetric control were, therefore, incorporated into the photomosaic methodology.  Control points would be defined and measured on the structures and later used to combine the images and to determine its scale.

Image Adjustment - Orthographic maps and drawings show two-dimensional images of three-dimensional subjects as they would be viewed from infinity.  In theory, parallel lines are projected from the surface of a subject onto an imaginary plane that is perpendicular to the projected lines, thereby creating a replica of the subject.  Any variation in the third dimension of the subject does not affect the two-dimensional projection.  A camera cannot be located at an infinite distance from a subject.  Its finite position with respect to the subject will affect the geometry of the image.  Photographs taken with even the highest quality equipment may contain several types of distortion that can result in inaccurate measurements and alter the relative position of objects.  Image adjustments may, therefore, be required to eliminate or minimize the distortion.[4]

A single photograph of any subject may contain distortions due to the features of the subject itself.  If a subject has considerable surface relief, the areas closer to the camera will appear displaced and proportionally larger than those further away due to perspective. For example, objects on hills viewed from above would appear larger than similar features in adjacent valleys.  Protruding balconies, porches and bay windows will appear at a larger scale than the buildings from which they project.  These inaccuracies must be removed to create drawings that are true orthographic representations.  Multiple photographs may be utilized to make these corrections.

Where high precision is required, a metric camera is used to take a series of sequential images of the same subject from different positions.  If two adjacent photographs (a stereo pair) are correctly overlapped and viewed simultaneously through a stereoscope, the subject will be perceived in three dimensions.  Stereoscopic viewing optically corrects perspective relief displacement. Specialized optical or analytical stereoplotters utilize the stereo images along with the parameters of the camera and control point coordinates to create true orthographic drawings and maps. A variety of digital, or “softcopy” stereoplotters are now available that utilize the same principals.

Images will contain distortions if the camera is not positioned normal (at right angles) to the plane of the subject.   The resulting oblique or tilted photographs are perspective views and must be adjusted.  Rectification is a process that removes the distortion by optically or mathematically adjusting the image plane to match that of the subject in order to create orthogonal images or drawings.  Stereoplotter analysis can also use the parameters of the camera, control point coordinates and the stereo images to remove tilt as well as relief displacement.  Budget limitations would also prohibit the use of Stereoplotter analysis on this project.  Further research was required in order to identify a simplified image adjustment strategy.

A single photograph is not usually sufficient to produce a geometrically accurate map or drawing of a subject.  However, techniques have been developed to generate orthographic images of a subject from individual photos, which are called orthophotographs.  They are created by photogrammetrically removing relief and tilt distortion and scale variation from images with either differential rectification or simple rectification.[5] The process is usually accomplished with digital images and computer software.  Orthophotos have the advantage of showing details that are not present in maps or drawings, and may be less expensive to generate.  They are frequently included in geographic information system (GIS) databases as a supplement for or complement to map data.  The orthophoto concept seemed promising for incorporation into the photomosaic methodology.

If a subject has medium-to-high surface relief, an orthophoto is produced with differential rectification.  The process requires high-resolution digital images that are taken with a metric camera, control point coordinates and a preexisting digital elevation model of the subject.  A specialized Orthophoto Workstation utilizes the control points and computer software to remove the effects of camera tilt (rectification) and scale variation.  Relief displacement is removed with pixel-by-pixel calculations that compare the image to the digital elevation model.  The procedure is complex and expensive but can produce true orthogonal photographic images that are very accurate.[6] Budget limitations again would prohibit the use of an Orthophoto Workstation for the adjustment of images on this project.

Further research indicated that a non-metric camera could be utilized to produce orthophotographs in some situations.  If a subject is flat, there is no surface relief, and simple rectification can be used to create orthophotos.  Single photographs taken with an uncalibrated non-metric camera can be rectified if the coordinates of at least four control points on the surface of the subject are known and can also be identified on the image.[7] Specialist software applications based upon projective geometry are available to make corrections to digital images.  A number of non-specialist image-editing software applications[8] have perspective correction tools that allow oblique (keystone) images to be adjusted, but only by eye.  It is even possible to create simple rectified drawings by tracing an image from a digital projector that has been inclined to remove (most) of the tilt in the original photograph.[9]

If a subject does have some surface relief, but it is moderate in comparison to overall size, the surface can be assumed to be planar (flat) and its image considered as having negligible surface distortion.  In this case, only rectification is required to remove any distortion caused by camera tilt.[10]

If an uncalibrated non-metric camera is positioned such that the photographs are taken normal (at right angles) to the surface plane of the subject, the resulting image of that plane will be orthogonal and rectification is not necessary.[11] The distance between only two control points on the surface plane of the subject can be measured and compared to the corresponding distance on the image to determine its scale.[12]

Although the building frontages in Pompeii are not flat, the surface relief is generally low.  Therefore, photographs taken with the camera lens carefully positioned and aligned to be normal to the plane of a facade will have negligible surface relief distortion and also will not require rectification. All surfaces on the plane of the facade are orthogonal and appear at the same scale.  However, any features not on the surface of the plane of the facade will appear slightly displaced.  The resulting images are more accurately called “pseudo-orthophotos" but still provide reasonable accuracy in a cost-effective manner.

Photographs taken with an uncalibrated non-metric camera utilizing these simplified orthophoto techniques could then be combined into a single photomosaic image using the control point data to assist in their placement.  It was determined that the alignment of the images could be better accomplished if more comprehensive control information were available.  The concept of defining control points on the building frontages was, therefore, later expanded into the creation of control elevation line drawings for more precise photo placement.

The photogrammetric research produced several useful techniques that were incorporated into the methodology for producing photo-realistic and dimensionally accurate photomosaics of the facades in Pompeii.

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