Miyaguchi–Preneel
Matyas–Meyer–Oseas plus one more XOR of the previous chaining value — the variant Whirlpool picked.
The formula is Hi = Eg(Hi−1)(mi) ⊕ mi ⊕ Hi−1. Shoji Miyaguchi and Bart Preneel arrived at it independently around 1990. The extra term costs a single XOR and feeds both the message and the chaining value forward, closing a few shortcuts that simpler schemes leave open.
In 1993 Preneel, Govaerts and Vandewalle worked through all 64 ways of building a compression function from one block-cipher call per block and found twelve secure ones — Miyaguchi–Preneel, Matyas–Meyer–Oseas and Davies–Meyer among them. Proofs only arrived in 2002. Whirlpool wraps Miyaguchi–Preneel around its own AES-like cipher, W.