camera extrinsic parameters
Camera extrinsic parameters describe where a camera is and which way it is facing in the world. If the intrinsic parameters are the fixed personality of the lens, the extrinsics are its current address and head tilt — they change the instant the robot moves or turns its head. They are exactly the camera's pose: its position in space plus its orientation.
Concretely, the extrinsics are a rotation and a translation that together carry coordinates from the shared world frame into the camera's own frame, where the camera sits at the origin looking straight down its lens. The translation says how far to slide the world's origin to reach the camera; the rotation says how to spin the world's axes so they line up with the camera's up, right, and forward directions. Apply this pair to any point measured in the room, and you learn where that point sits relative to the camera — the necessary first step before the pinhole projection can turn it into a pixel.
This is why extrinsics are central to a moving robot. As an arm reaches or a rover drives, its onboard camera's extrinsics update every moment, and the robot uses them to fuse what it sees with what it already knows about the room. Get the extrinsics wrong and a perfectly sharp image is pinned to the wrong place in the world; get them right and vision and motion speak the same language.
A camera bolted 1.2 meters above the floor and tilted 30 degrees downward has extrinsics that say so: a translation up the wall and a rotation that pitches its gaze toward the ground, so a tile seen in the image can be placed exactly on the real floor.
Extrinsics = position + orientation: they tell the robot where the camera sits and how it is aimed.
Because they encode a position and an orientation, the extrinsics are exactly a rigid-body transform — the same kind of mathematics used to track any frame attached to the robot.