Also called "Black-out poetry" because of its origins in censorship, this approach involves selectively erasing or redacting a source text so that what remains is a found poem. Erasure as a literary technique can be traced to the Dada movement and even before, though its recent history begins after World War II whenRobert Rauschenberg created an "Erased Kooning", not with black ink but by meticulously erasing the drawing almost back to its paper(1953). With the following decade came what we today would recognize as erasure poems: Dorothy Cross's "Dictionary Columns" and Tom Phillips' altered Victorian novel A Humument.
As a glance at the "Blackout Poetry" page on Pinterest shows, the technique has become very popular for altered books, though recently its best known practitioner may be Austin Kleon, whose book on "newspaper blackout" has led to a Ted talk called "Steal Like an Artist" that frames it within post-modern Appropriation art.
Typically now, the emphasis is on the words that have been reserved, with the redacted spaces drawn or painted so that the words are worked into a whole-page composition. Often the redacted text is not completely obscured, so that a ghost of the old page remains in dialogue with the new. There's a higher difficulty level because the positions of words is fixed while the poetry still depends on a left-to-right/top-to-bottom reading order. Blackout may have its origins in paper but it can also be created digitally. Based on a scanned excerpt from T.S. Eliot's "Ash Wednesday", the following example was created in Photoshop.