Can one use an Artificial Neural Network to determine the size of an object in a photograph? My question relates to but doesn't duplicate a question that has been asked here.

I've Googled a lot for an answer to the question: Can you find the dimensions of an object in a photo if you don't know the distance between the lens and the object, and there are no "scales" in the image?

The overwhelming answer to this has been "no". This is, from my understanding, due to the fact that, in order to solve this problem with this equation,

$$Distance\ to\ object(mm) = \frac{f(mm) * real\ height(mm) * image\ height(pixels)}{object\ height(pixels) * sensor\ height(mm)}   $$

you will need to know either the "real height" or the "distance to object". It's the age old issue of "two unknowns, one equation". That's unsolvable. A way around this is to place an object in the photo with a known dimension in the same plane as the unknown object, find the distance to this object and use that distance to calculate the size of the unknown (this relates to answer from the question I linked above). This is an equivalent of putting a ruler in the photo and it's a fine way to solve this problem easily.

This is where my question remains unanswered. What if there is no ruler? What if you want to find a way to solve the unsolvable problem? Can we train an Artificial Neural Network to approximate the value of the real height without the value of the object distance or use of a scale? Is there a way to leverage the unexpected solutions we can get from AI to solve a problem that is seemingly unsolvable?

Here is an example to solidify the nature of my question:

I would like to make an application where someone can pull out their phone, take a photo of a hail stone against the ground at a distance of ~1-3 ft, and have the application give them the hail stone dimensions. My project leader wants to make the application accessible, which means he doesn't want to force users to carry around a quarter or a special object of known dimensions to use as a scale.

In order to avoid the use of a scale, would it be possible to use all of the EXIF meta-data from these photos to train a neural network to approximate the size of the hail stone within a reasonable error tolerance? For some reason, I have it in my head that if there are enough relevant variables, we can design an ANN that can pick out some pattern to this problem that we humans are just unable to identify. Does anyone know if this is possible? If so, is there a deep learning model that can best suit this problem? If not, please put me out of my misery and tell me why it it's impossible.
Can one use an Artificial Neural Network to determine the size of an object in a photograph?


Yes: Learning Depth from Single Monocular Images

In the end, depth is just one special form of size.

Of course, you need something partially known, e.g. another car. You don't need to know the exact size of the car, but you know which size cars in general have. If you have an image without any reference, it is impossible.