Backwards projection from 2D to orthomosaic

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I have a dataset of images and an orthomosaic + DSM that I'm trying to work with.

I can take a point in the ortho and get that same point in the original images via projection through the given camera matrices no problem but what I really need is the inverse of this.

Given a point in the original image, is it possible to get that point in the ortho (specifically get the z value from the DSM). I know that a ray of points in the world will all map to the same pixel but that doesn't matter since I just need a row, column to lookup in the dsm.

Basically if I detect an object in the original set of images I want to get it's height by referencing the dsm.

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