Is it a bird... or a plane... or superman? Neither, it is perspective distortion

Is it a bird? or a plane? Or Superman? ... If all you have is observed size then you cannot answer that question.

And its a key reason why 2D imaging (photo based imaging) is fundamentally unsuited to particle size distribution measurement of piled particles

Perspective distortion means the observed size of an object in a 2D camera is inversely proportional to the distance to the object.

So a bird nearby can appear the same size as a plane far away.

So why would we use a 2D camera if you wanted to measure the size of objects?

If you could guarantee the objects were always the same distance away from the camera, then you can "calibrate" the observed size versus the actual size

So with a mono-layer of separated rocks on a solid surface, go for it, sizing the rocks is no problem with a well calibrated setup.

But if you are looking at a pile of rocks, where the height of the rock pile varies and therefore the distance from the camera varies, then your observed size is going to vary, and it can vary extremely.

In this simple example, the same green particle at 600mm distance looks 33% larger in the camera than at 800mm distance from the camera

Increasing the production rate increases the pile height 100mm then the green rock in the center of the pile becomes only 500mm from the camera and now looks 60% larger than the same rock at 800mm

Alternatively if the production rate drops so the pile height drops 100mm then the rock in the center is 700mm from the camera and looks 14% larger than the rock at 800mm distance.

So the rock at 800mm can vary in observable size up to 60% based on distance to the camera. Clearly measuring particles with a 2D camera in this example is subject to extreme error (between 0 and +60% for the rock at 800mm distance) based on only perspective distortion.

2D camera imaging (photographic) is subject to many more errors;

Photo based imaging is poorly suited for image segmentation (delineating all the individual particles correctly from each other) because of image color variation not corresponding to the boundaries of the particles. This can happen for many reasons; insufficient color variation causing merging of particles in the image, or additional color variation from material changes/shadows/wet vs dry splitting up particles.

Photo based imaging has limited or no capacity to distinguish between overlapped and non-overlapped particles resulting in an undersize error of many rocks

And photo based imaging has limited or no capacity to correctly identify areas of fines in the image, typically mistaking them for a single particle and adding a large oversize error.

If you want to learn more about the issues facing particle size distribution measurement of fragmented rocks, and bulk particles get in touch with our Principal Scientist Matthew Thurley

If you want a robust automated system for measurement on conveyor belt that overcomes all of these errors then consider 3DPM from Optimation and Innovative Machine Vision

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