View from above: Obtaining volumetric data

By |  August 8, 2015

PQ1508_airgon-photo1Using a drone and low-cost camera, producers can make accurate
 volumetric computations.

Volumetric data is a critical piece of information for aggregate operations. Yet economical, accurate and timely collection of such data remains elusive for most operators.

Several major developments in technology during the past eight years have enabled a new approach to collecting volumetric data for surface mining and stockpiling. Bearing a digital camera, a small unmanned aerial system (sUAS, or drone) can rapidly collect imagery that can be subsequently processed into a very accurate 3D model of the imaged area.

From this sUAS-collected model, volumetric information can be computed, along with ancillary data such as image maps of the collected area. This new technique provides, at a substantially lower cost, faster and more accurate information than do traditional techniques.

Even better, these new drone-based collection methods are amenable to owner-operator deployment models, enabling mine owners a new level of control over the volumetrics management process.

In this overview article, we will introduce a bit of the technology behind volumetrics, review current methods for volumetric analysis and provide a case for migrating to sUAS technology.

Measuring volume

A stockpile with a highly conformant mesh. The mesh is defined by the vertices, often termed model key points.

A stockpile with a highly conformant mesh. The mesh is defined by the
vertices, often termed model key points.

A volumetric computation consists of measuring the shell of a volume (also called the “hull”) in three dimensions and then differencing this hull to a base surface described by a polygon called the “toe.” Generally the hull is defined by a series of connected triangles. The incremental volume between each of these triangles and the base is then summed to compute the overall volume.

The key challenge in deriving volumetrics is the measurement of the vertices of the defining triangles. There are two issues involved: deriving the three-dimensional coordinates of the vertex and defining enough vertices to accurately model the surface. This second component is by far the most difficult and most violated principle of volumetric computations.

We term the ability of the triangulated surface to model the actual shape of the stockpile “conformance.” The photo on the next page shows a stockpile with a highly conformant mesh. The vertices, often termed “model key points,” define the mesh.

All stockpile volume computations today that are based on point measurement use this triangulated-irregular-network approach to computing the model. The variable between the techniques is the method by which the model key points are collected.

A note about positioning

The most common collection technique is to simply walk the toe and pile with a global navigation satellite system receiver.

The most common collection technique is to
simply walk the toe and pile with a global
navigation satellite system receiver.

Positioning of data involves both relative (also called local) accuracy and absolute accuracy. Good local accuracy means the stockpile to be measured is accurately modeled in terms of dimension and scale, but its position relative to a coordinate reference system is not well known.

This will provide an accurate volumetric computation, but you will not be able to position the result in the “real world.” The impact is that you could not accurately position the toe polygon on a map nor could you do analysis over time of the data, because, even if modeling a static pile, its location will move relative to the reference system.

Ancillary data can often be obtained from a stockpile volumetrics data collect (especially if you are using a camera or laser-scanning mapping technique). With local accuracy only, you will not be able to produce useful derivative results such as digital elevation models, contours and project-spanning cross-sections.

Equally important is the fact that data exhibiting good local accuracy but poor absolute accuracy cannot be merged. For example, without good absolute accuracy you could not use your results in a geographic information system or even superimpose the stockpile toes in Google Earth.

Current methods of computing volumes

There are several methods of stockpile modeling in use today that one would term “traditional.” These involve various methods of measuring the model key points of the pile and then feeding these data to an off-the-shelf computer program to construct the triangles and compute the volume.

The most common collection technique is to simply walk the toe and pile with a global navigation satellite system receiver, collecting real-time kinematic model key points. The triangulated irregular network is then constructed from these data and the volumes computed.

A composite view of a stockpile from a sand-and-gravel operation.

A composite view of a stockpile from a sand-and-gravel operation.

This is the least desirable method of obtaining volumes. It is dangerous to the surveyor, placing that person in harm’s way. Owing to the fact that the surveyor cannot reach all of the locations that require a model key point and the pile is disturbed by the walk itself, this is the least accurate of the available methods for obtaining volumes.

A survey total station moves the surveyor off the stockpile for collecting model key points. There are two problems with this technique. The first is that of defining the model key points. The surveyor chooses these by “eyeball experience” because there are no automated techniques for doing so.

The second problem with this approach (and most other terrestrially based approaches) is that key points of the stockpile under measurement can be obstructed from view by other parts of the pile. This occurs not only for tall stockpiles but also for more complex geometries where, for example, interior depressions exist.

This is illustrated in a page 16 photo. Note the cross-section cut through the stockpile, with two occluded depressions encircling the peak of the pile. This type of geometry is more common than not.

Terrestrial laser scanning (tripod laser scanning) solves the problem of model key points by simply saturating the stockpile with sample points. This results in a very dense cloud, eliminating the issue of locating correct model key points. However, the occlusion problem still exists due to the terrestrial placement of the scanner.

Notice in a page 16 photo that the entire top of the stockpile has been missed by the scan. Triangulating software will typically interpolate across this void, producing a flat top. Obviously this adds significant error to the volume computation and is unacceptable.

This problem is generally addressed by placing the scanner on a platform that can be elevated. This approach adds significant time and complexity to the on-site data-collection process. As a result of these complexities, terrestrial laser scanning has had very limited acceptance as an accurate and economical technique for stockpile volumetrics.

Fixed-wing aircraft

Key points of the stockpile under measurement can be obstructed from view by other parts of the pile. This occurs not only for tall stockpiles but also for more complex geometries where interior depressions exist.

Key points of the stockpile under measurement can be obstructed from view by
other parts of the pile. This occurs not only for tall stockpiles but also for more
complex geometries where interior depressions exist.

In traditional airborne photogrammetry, a fixed-wing aircraft is used to acquire several large format (usually digital) images from different perspectives over the stockpile area. Photogrammetric stereo extraction techniques are used to collect so-called “mass points” over the area to be modeled. These mass points form the model key points for creating the triangulated irregular network that is used in modeling the stockpiles.

Note that airborne photogrammetry does address the occlusion and safety issues associated with ground modeling techniques and, thus, it is a much-preferred method. The biggest objection to traditional airborne stockpile techniques is the cost. A typical manned airborne data collection is in the range of $4,000 to $8,000, depending on site size and complexity (complexity being overhead structures such as conveyors).

Airborne laser scanning provides a distinct advantage over photogrammetric techniques in that it provides single ray measurements of the surface. In photogrammetric methods, an algorithm (or human stereo operator) must deduce the surface from two or more images. For this reason, laser scanned data generally provides a more accurate set of model key points.

Most stockpiles require model key point sample spacing on the order of 4 in. or so to construct an accurate model. This translates to a point density of about 100 points per square meter. Data at densities above about 16 points per meter must be collected via helicopter rather than a fixed wing aircraft owing to the slow sensor movement necessary to collect at high density. The use of manned helicopters equipped with laser scanners for volumetric computations is simply cost prohibitive.

New techniques

Obviously, a new approach to volumetrics is needed if these data are to be collected in an accurate yet economical fashion. Fortunately, a confluence of new technologies that includes, as mentioned earlier, small unmanned aerial systems (sUAS) and new approaches to extracting 3-D models from non-metric cameras are now enabling low-cost, accurate data extraction.

Here, the entire top of the stockpile has been missed by the scan. This adds significant error to the volume computation and is unacceptable.

Here, the entire top of the stockpile has been missed by the scan. This adds
significant error to the volume computation and is unacceptable.

As is evident from the popular news, sUAS – drones – have made tremendous technical advances in the past 10 years. While remote-controlled model aircraft have been around since the 1930s, performing engineering work with these models was not really practical due to a number of factors.

The first issue of using an sUAS for engineering work is precise control of the flight pattern. This precise control is necessary in order to correctly position a camera for image collection. This was not really practical until low-cost autopilots became available about 10 years ago.

The factor that made this possible was low-cost position-sensing equipment. A global navigation satellite system receiver was necessary for determining the approximate X, Y, Z location of the aircraft, and a gyroscope system was required for measuring pitch, yaw and roll. While both have been available for the past 30 years, it has only been since the advent of the smartphone that prices have dropped to a level that has made this technology viable for controlling and positioning commercial sUAS.

Today, a complete autopilot, including both a satellite system receiver and an inertial measurement unit, can be purchased for as little as $500. An example is the PX4 open design from the Computer Vision and Geometry Group of the Swiss Federal Institute of Technology in Zurich, Switzerland. This device is half the size of a deck of playing cards with a weight of only 1.31 oz.

The second major development (particularly for multirotors) has been the development of low-cost, high-energy-density batteries and efficient, lightweight motors. These developments have enabled fixed wing sUAS to stay aloft for periods up to an hour and multirotor to stay aloft for about 25 minutes.

Structure from motion, dense image matching

In the traditional photogrammetric technique of collecting mass points, the same location in object space (e.g., a point on the stockpile) is measured in two images taken from different, known positions. The X, Y and Z model key points are computed using a stereo triangulation technique. These techniques have historically been performed using imagery from large-format, metric cameras.

These cameras are not practical for sUAS work due not only to their size and weight, but also their high cost (hundreds of thousands of dollars). In addition, because only two match points are used to construct a 3D model point, it is easy to encounter blunders; that is, 3D points with incorrect coordinates owing to a mismatch in the images.

A new technique has emerged from the computer science and robotics field called Structure from Motion and dense image matching. The robotics community was interested in figuring out the location of a moving robot using economical, small-format cameras.

Rather than using stereo matching from a pair of images, Structure from Motion matches thousands of points from many overlapping images of the same location. From the 3D model space of all of the participating images, the precise location of the camera at the moment of image exposure is recovered (this is called the camera exterior orientation or EO).

This EO can be determined in a relative way, even with no knowledge of the location of the camera at the time of exposure. Once these EO locations are known, a technique called dense image matching is used to create a 3D point cloud model of the imaged space.

The Structure from Motion algorithm also includes routines for camera self-calibration. This means that for each exposure of the camera, the algorithm computes the mathematic relationship between the camera exposure station and each pixel of the captured image. This allows accurate mapping using low-cost consumer cameras.

The end result of all of this is that, using a low-cost consumer camera, a relatively accurate, dense 3D point model of the object space can be computed from the individual images. By relatively accurate, we mean the overall 3D model is accurate when measuring from point to point. To make the model absolutely accurate, we will need to introduce scale and ground truth through conventional surveying techniques.

A composite view of a stockpile from a sand-and-gravel operation is depicted above. The ortho image is shown in the view of the upper left (the map view). The right window shows a 3D model of the point cloud data obtained by dense image matching. The points in red are overhead structures that have been tagged to exclude them from the volumetric computation.

The bottom view shows a cross section, cut through the pile at the location of the overhead conveyor. Note that because of the depression (caused by a reclaim conveyor at the base of the pile), this pile could not be accurately modeled by terrestrial systems.

In summary, we see that new technologies have come together to enable high-accuracy, aerial volumetric computations (and general site mapping) using low-cost hardware and software. And there are no barriers to entry. The complete volumetric system of hardware (primarily the sUAS) and processing software can be learned in about one week of training.

There are a number of options for deployment, including the owner/operator model wherein the mine/quarry operator purchases the equipment and training and deploys the technology at will. Over the next three years, we will see a complete migration of technology to sUAS for many aggregate operations.


Take note

New technologies have come together to enable high-accuracy, aerial volumetric computations (and general site mapping) using low-cost hardware and software.


Lewis Graham is the president and CTO of GeoCue Group Inc., supplier of lidar production and workflow tools and consulting services for airborne and mobile laser scanning. GeoCue’s subsidiary, AirGon, provides technology for drone-collected stockpile volumetrics and mine site mapping. www.airgon.com

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