A processor identifies keypoints on a hand in a two-dimensional image that is captured by a camera. A three-dimensional pose of the hand is determined using locations of the keypoints to access lookup tables (LUTs) that represent potential poses of the hand as a function of the locations of the keypoints. In some embodiments, the keypoints include locations of tips of fingers and a thumb, joints that connect phalanxes of the fingers and the thumb, palm knuckles that represent a point of attachment of the fingers and the thumb to a palm, and a wrist location that indicates a point of attachment of the hand to a forearm. Some embodiments of the LUTs represent 2D coordinates of the fingers and the thumb in corresponding finger pose planes as a function of the locations of the tips of the fingers or thumb relative to the corresponding palm knuckles.