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How do these work?
In little kid language how do these work?

I will take a swing at this...

If I have a photograph and I cut it in half, it is fairly obvious if one lines the two halves together how to put it back together.  If I hand you the two halves, you can most likely figure out how to make them one photograph or image.  You would be "stitching" the two halves together.

If I were to cut the photograph into 100 pieces, it would be much more difficult to stitch them together, but it would be like a puzzle that you could eventually figure out.

With 3D scanning, there is something called photogrammetry.  Photogrammetry takes this from the 2D world into the 3D realm.

If I gave you a single photograph of a carton of milk and asked you to make it into a 3D model it would be very difficult.  You would not know what the back or at least one other side of the carton look like.  You would not know if there was a hole in the back, if the back was cut out, or really anything about the back other than assumptions.  However, if I gave you four photographs, one from each side of the carton of milk, it would still be challenging to stitch together but much easier.  If I then gave you six photographs, the four sides plus the top and bottom, you would know what the entire outside of the carton looks like and could probably have a good chance of recreating it.  One challenge in recreating the carton is we are not certain of the size of the carton.

In photogrammetry the size is often an unknown so an initial scale is set then from that initial scale, or reference point, the rest of the image is determined.  So, if I included a ruler in the image of the carton laying next to the edge of the carton from each angle, that would help you a lot.  (Multiple reference points.)  In 3D scanning, or photogrammetry, we try to get an initial reference point measurement then go from there.  This initial reference point can even be an assumption, so long as we stick with that assumption the entire time.  So if we assume the milk carton is 3 inches across at the bottom, we can then determine how tall the carton is, then we can even the determine the dimensions for the top with the folds and so forth.  The 3D scanning software stitches all the images together then does this math and makes a 3D drawing based on the software's best guess of the dimensions.  Once the software is done it shows you what it thinks the 3D model should look like.  With today's technology it is usually fairly accurate.

When doing this entire process the software actually has a better chance of getting it right if you provide it with more images of the same item from as many different angles as possible.  Just like the milk carton where four images was better than one and six images were better than four.  If you took 20 or 30 images of the milk carton from different angles the software would most likely have a better chance of stitching them all together correctly and building the 3D model of the milk carton.

When 3D scanning items such as jewelry, the items are often very small and relatively ornate.  In these situations it is a good idea to get a bunch of photographs from a bunch of different angles for the software to stitch together.

There are other factors which come into play, such as consistent lighting which can change shadows, as well as texture details which are not ideal for photographs such as super shiny surfaces.  Shadows imply something is covering a spot.  It can be an obvious block, like a prong could be blocking the light from reaching another prong.  Or, it could be a curve in the metal, like a dimple or dome that causes shadows.  Taking a lot of photos from different angles allows the software the opportunity to figure these out by tracking the light and shadows.

Using a single reference point is possible, but if you could provide several reference points it would allow the software to double check itself and make sure all of the dimensions agree with as many of the reference points as possible.

3D scanning works by stitching a bunch of images together and then using at least one reference point to determine dimensions which can then be used to recreate the object on the computer.  This entire 3D scanning process is called photogrammetry.
Take care, and God bless.
Javier Odom - Walt's Jewelers

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