Nonlinear Mapping - Object to Image Space

I am familiar with collinear mapping from object to image space where
we can map point to point, lines to lines, and planes to planes through
an optical system.

I would like to find the nonlinear? mapping where we can map from say
an elliptical object to the corresponding image space shape, or a
cylinder object surface shape to the corresponding image space shape.

Have googled around a bit looking for answers but didnt find much.
What is this field of math/mapping called?
Any online or book references would be appreciated.

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