You're right that the feet deform significantly when you stand on them. For that reason you usually measure them load-bearing (i.e. you stand up with even weight distribution on your feet).
I think it's more likely that it's the deformation of the shoe that is uneven than that the shoe affects the deformation of the foot much. An exception would be if it has a built-up sole with support for the arches, preventing the arches from collapsing.
Either way, it's a complex process that is hard to model, just like you say. The way we're getting around it is by collecting various data on what people end up liking and then infer the properties of the shoe, rather than trying to explicitly model it. So the solution is a combination of 3D scanning and machine learning.
Also worth mentioning, by the way: most people actually have slightly different size and shape on their left vs. right foot. For about 50% of the population the length differs by more than half a US size. Being perfectly symmetrical is the rare case.
I think it's more likely that it's the deformation of the shoe that is uneven than that the shoe affects the deformation of the foot much. An exception would be if it has a built-up sole with support for the arches, preventing the arches from collapsing.
Either way, it's a complex process that is hard to model, just like you say. The way we're getting around it is by collecting various data on what people end up liking and then infer the properties of the shoe, rather than trying to explicitly model it. So the solution is a combination of 3D scanning and machine learning.
Also worth mentioning, by the way: most people actually have slightly different size and shape on their left vs. right foot. For about 50% of the population the length differs by more than half a US size. Being perfectly symmetrical is the rare case.