What does the word “register”mean in this sentence? Does it have something connotative meanings?
I peer around, stroke my own skin, look into this baby’s eyes that register me as a blurred self-extension, as a function of her will.

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In this case, the verb "to register" means "to perceive" or "to understand" or "to recognize."

Think about a cash register in a store. The clerk pushes numbers on the register and the register receives those numbers. It's the same way here. The baby is receiving/perceiving the other person "as a blurred self-extension."

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A good synonym would be to recognise him as……

To register in this case means to acknowledge ……

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It simplyeans that the baby's brain thinks the speaker is an extension of herself etc.

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