Photo by Charles 🇵🇭 on Unsplash

Understanding Photogrammetry

The science of measuring objects from its images

In this write up, we shall do an in-depth analysis of the field of Photogrammetry, what is has to offer, the developments leading to this point and how you can get started. This article was prepared in preparation for a (possible) Lightning talk at PyCon India 2019 (October 12–13 at Chennai).

Kindly note that this is the culmination of existing resources on the web — organized as per my research. I, by no means, claim to be an expert of this field and I would urge you to take my pointers with a pinch of salt. Sources have been cited at the end.

I hope you find this useful and feel convinced to dive deep into the world of Photogrammetry.

What is it?

We all have certainly taken photographs at some point in our life — especially since we now live in the 21st century and a camera can be spotted in everyone’s pockets.

A camera captures a moment in the real world in the form of an image. In this process, we convert real world entities into what appears to be a hyper realistic drawing on a surface.

If we were to take a more abstract view of this process, one might say we convert a 3 dimensional object on to a 2 dimensional image. Which means we give up a dimension — the depth of the image.

The objective of Photogrammetry techniques is to go reverse — that is to convert a 2D image in to a 3D object. But how would that be possible — especially since we gave up one dimension entirely?

Why is it relevant?

With a bit of imagination, one can understand the potential that exists in reversing the process. To be able to create real world objects from images means we can encode objects and create it later — similar yet different from a hologram.

To state a few interesting use cases, we can reconstruct a situation if we have the images to analyze and derive further conclusions. Also, 3 dimensions mean we can derive volume of objects from images — which in it self can prove to be of vital important in numerous cases — such as resource management, surveying etc.

A grand yet imaginative case would be to recreate an entire system — even at the scale of cities, nations or planets — from mere images taken from different angles thus creating different perspectives.

Have we not already solved this?

For those of you who have spent time learning graphics would understand the math behind estimation of true lengths from apparent views in perspectives. In many ways, Photogrammetry is similar. However, one is not explicitly provided with the angle at which an image is captured thus challenging this pursuit even today.

You could also argue that a CT scan in hospital is similar in the sense that a near accurate render of the brain is created using the radiations and it would be a justified example but this would be a rather narrow case of application and it is believed that radiations are harmful in the long run — thus encouraging us to find alternative routes to this problem.

Evolution over time

The exploration for photogrammetry was the natural route once photography was made possible. In fact, it is believed that several centuries earlier, the early Greeks spent considerable amount of time developing this idea.

Notable versatile artist Leonardo Da Vinci made the following remark in 1480:

“Perspective is nothing else than the
seeing of an object behind a sheet of
glass, smooth and quite transparent, on
the surface of which all the things may
be marked that are behind this glass.
All things transmit their images to the
eye by pyramidal lines, and these
pyramids are cut by the said glass. The
nearer to the eye these are intersected,
the smaller the image of their cause
will appear”

Following Da Vinci’s pursuits and findings, several others took up the challenge over time to understand both the principles and the approaches necessary to make measurements from apparent lengths.

The key challenge in the initial stages was to understand the principles of projective geometry from a graphical perspective. This relationship was developed by R. Sturms and Guido Hauck in Germany in 1883.

While examining the growth of the field of Photogrammetry, the following four stages are worth taking note of (known as the development cycle):

  1. Plane Table Photogrammetry (1850–1900)
  2. Analog Photogrammetry (1900–1960)
  3. Analytical Photogrammetry (1960 — present)
  4. Digital Photogrammetry (present day standard)

While this write up focuses on the latest standard, we need to elaborate a little more of the past to better understand the developments that lead to the latest form.

Aimé Laussedat (1849) is known as the father of Photogrammetry for his approach of using terrestrial photographs for topographic map compilations. These photographs were taken by aerial objects with a knowledge of heigth apriori — thus enabling him to determine the scale of the map. This approach — better known as plane table photogrammetry — though worked, proved to be an arduous procedure in the long term, considering the primitive state of image capturing devices themselves. Several notable individuals developed several notable devices after this initiation — such as Photographic plane table, errecting lens imaging system, panaromic camera etc.

A point came when stereoscopy became widely used and airplanes were possible. This marked the beginning of analog photogrammetry. Edouard Deville is known as Canada’s father of photogrammetry for creating stereomodel via Wheatstone Stereoscope — which he used to map the Canadian Rocky Mountains.

Deville’s Stereo Planigraph

Following this triumphant moment was another set of commendable inventions by commendable inventors — few mentionable are Perspektograph, radial and aero triangulation concept multi-lens camera’s, stereocomparator, besides the rest. A lot of notable papers on Analytical Photogrammetry was published by Sebastian Finsterwalder — he explained the conditions under which rays intersect. Also, the application of this field in wars encouraged support from the military to further advance research work.

Analytical Photogrammetry rose from the works of notable researchers of the past. The development of computers nudged for the change in the approach of photogrammetry. Duane Brown served a notably important role in advancing the field by developing mathematical formulations to calibrate the camera. He formed his own organization and pioneered short range and analytical photogrammetry. His work included adjusting for decentering distortion, principal point calibration, and film unflatness. Softwares helped in bundle adjustment. Digital transformation of coordinates between image and map was made possible by computers, besides driving instrumers around the stereomodel.

When speaking of Digital Photogrammetry, one cannot miss Gilbert Louis Hobrough. Over the course of decades, he developed notable instruments such as Automatic Registration Electronic Stereoscope (ARES), Gesalt Photo Mapper (GPM) etc. Other notable mention-worthy developments include Charge-Coupled Devices (CCD), Landsat, Digital Camera, Flash Memory, Matching, Projective Geometry, 5-point relative orientation.

Principles involved

  • Non-contact measurement: In photogrammetry, our measurements cannot be made directly due to perspective shifts that may occur to the true length of the object.
  • Collinearity: Assumption that Object points (Q), projection center (C) and projected points (q) are all collinear
  • Triangulation: We need at least two measurements of the same point taken at different positions to determine the depth (z-axis) measurement of an image (along x and y axises). We determine the depth by trigonometry and the angle the rays make relatively.

Applications

<paused for now. Shall add more details in the future>

Sources

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