Judge Miller was Buck's original owner in Santa Clara Valley, California. The judge never appeared in the book but was mentioned several times.
Judge Miller originally was the owner of Buck's parents Shep and Elmo, before Buck was born. Judge Miller spoiled Buck and allowed his grandchildren to ride on Buck. Once when he was away on a trip, his gardener's helper Manuel sold Buck.
When Buck woke up on a train, he wasn't afraid because he and Judge Miller traveled a lot by train.
Judge Miller was mentioned again when Buck starts to steal from other dogs because he never stole when he lived with Miller because he had all that he could ever need.
Judge Miller was mentioned later in the book, when Buck remembered his previous lives in California and Alaska.
When John Thornton became Buck's owner, Buck for the last time remembers Judge Miller and his grandchildren because they had never shown love, that John Thorton showed to him.