A Photogrammetric Triple Constraint: Time, Distance, Camera Cost

A Photogrammetric Triple Constraint: Time, Distance, Camera Cost

Tutorials October 26. 2020

Written by Owen Murray, photographer at the Epigraphic Survey of the Oriental Institute, University of Chicago

Introduction

With the rise of photogrammetry in digital epigraphy, so has the ability to produce quality, to-scale photographs without expensive field equipment. Although lighting is, has been, and always will be, a major factor in the quality of said photographs — rectified, to scale documentation is no longer dependent on medium and large format cameras cable of changing the orientation and/or position of their lens in relation to the film or image sensor of the camera (i.e. tilt shift and levelling).

It’s not that this type of equipment, knowledge or techniques are no longer useful, it’s that photogrammetry has shifted the paradigm and levelled the playing field, so to speak. 

A Project Management Triple Constraint: Time, Quality & Budget (Cost)

In the world of Project Management (PM), one variant of the PM Triangle known as the Scope Triangle deals with the triple constraint of Time, Quality & Cost (Budget). Pick any two, and the other can be determined. 

Something quick and cheap is generally of poorer quality (red)

Something cheap and of good quality will generally take more time (blue)

Something on time and of good quality will generally cost more (green)

Photogrammetry relies on multiple overlapping photos shot from different camera positions (angles), regardless of the size of the sensor in the camera used or the focal length of the lens. That said, insofar as photogrammetry is concerned there are specific millimeter to pixel ratios that can be used to determine the scale ratio of a desired overall photograph, or orthomosaic, at a specific resolution (dpi) in flat 2 dimensional space (x,y), as well as the number of points per meter squared that correlate with the quality of desired result/physical geometry, in 3 dimensional space (x,y,z). 

e.g. A standard Epigraphic Survey (Chicago House) background photograph for epigraphy requires a scale of 1:4 @1200dpi. To achieve this, one needs a 0.085mm/px ratio. For physical facsimile creations such as the Tomb of Tutankhamoun or Seti IFactum Arte relied/rely on a Lucida Scanner that is capable of 100,000,000 points per square meter, which in turn allows them to rout panels with sub millimetric precision

*As epigraphy is a foremost concern, the first example above focuses on the scale ratio of a desired photograph (orthomosaic) at a specific print resolution, though the general concept articulated can be applied to both 3D virtual and physical facsimiles as well, as reflected in the second example.*

Since the results in photogrammetry for scale and resolution are directly related to predetermined mm/px ratios, quality, in effect, can be predetermined, too. (Disclaimer: A poorly taken photo, is a poorly taken photo regardless of camera or operator: focal point, aperture, and slow shutter/shake even at the smartphone level are now all factors within control of the user.)

A Photogrammetric Triple Constraint: Time, Distance, Camera Cost 

Photogrammetry may have levelled the playing field in terms of the ability to produce quality, to-scale photographs without expensive field equipment, but what it hasn’t done is change the sensor size or quality of lenses in various cameras, so although one can now use anything from a smartphone to a large format view camera with a digital back to produce rectified photographs, a set of constraints still apply. 

Like the Project Management Triple Constraint of Time, Quality & Cost (Budget), one can consider the photogrammetric triple constraint as: Time, Distance (Camera Position from Object) & Camera Cost (Sensor Size/Lens Quality); pick any two, and the other can be determined.

Lower camera cost (e.g. smart phone; smaller sensor (smaller/cheaper lens), will require a closer distance (camera position from object) and thus more time. Less expensive camera = closer distance = more time.

Higher camera cost (e.g. medium format Hasselblad; large sensor, sharper lenses) means further distance (camera position from object) and thus less time. More expensive camera = further distance = less time.

Mid-range camera cost (e.g. Nikon/Canon 35mm full frame DSLR) means a mid-range distance (camera position from object) and a median amount of time. Mid-range camera = mid-range distance = median time

It should be noted that the amount of time involved for the photographs above is based purely on the number of individual photos (camera positions) needed to achieve a desired mm/px ratio as related to the sensor size of the camera. In practical application, an object’s physical geometry and complexity (e.g. depth discrepancy and intricacy of the surfaces involved) may necessitate more photos, regardless of the camera involved.

Conclusion

Before embarking on a documentation project, determining the desired output (scale and resolution) and publication venue/s and mediums can help inform choices about equipment and the amount of time, cost and personnel involved. 

As mentioned above, although rectified, to-scale photography can now be produced without expensive field equipment, lighting will always play a major factor in the quality of the end result, and as such should be considered alongside camera choices. There are a number of different options ranging from available light, to mirrors, to continuous light such as LED panel/Halogen work lamps, to photography studio strobes; all with their advantages and disadvantages. This will be explored in a further article. 

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