A word for "to proceed inwards from the outside", like "bottom-up"

"Bottom-up" means to proceed upwards from the bottom.

"Top-down" means to proceed downwards from the top.

Then is there a hyphenated word meaning to proceed inwards from the outside? "Outside-in" sounds like it means the outside is turned inwards like how we can turn a glove outside-in, so I'm not sure if it's the correct word.

The following sound perfectly fine to me:

The mortician examined the corpse from top to bottom and from the outside in.
The lab technician conducted an outside-in examination of the sample.

In both cases, I'm able to assume that something started externally and finished internally.

In fact, outside in is used so infrequently, that nobody, especially in the context of the example sentences, would be likely to confuse it with something else.

Incidentally, we turn gloves (and other things) inside out, never outside in.

Similarly, with additional context, the assertion that bottom up means "to proceed upwards from the bottom" is not always the case:

He turned the glass bottom[s] up. [The bottom and top reversed positions.]

It's when you don't use the word turn that the directional phrase takes on the meaning originally ascribed to it:

The company had a bottom-up hierarchy. [Change started at the bottom and went upward.]

The same phrase can be used, but have a different meaning depending on context.