After changing the image, it is re-embedded in the PDF file.The above procedure for editing images can also be used to replace graphics.
In the ‘Touchup’ Preferences of Acrobat you can define which image and object editor you want to use from within Acrobat.
If you looking for a Free (as in 'libre') Software, Ghostscript is surely your best choice.
However, it is not always easy to use -- some of its (very powerful) processing options are not easy to find documented.
Always keep in mind that PDF files are an accurate representation of a document. They are not intended to be intermediate files that can still be edited.
There are programs on the market that allow you to change the content of a PDF file and there are applications or plug-ins that can extract the content of a PDF so that you can insert this data into a new document.
This page focuses on the typical editing needs in a prepress environment.