Camera Intrinsics and Extrinsics - 5 Minutes with Cyrill

so welcome to another episode of five minutes with cyril and i want to talk today about camera intrinsics and extrinsics so what are intrinsics and extrinsics so intrinsics and extrinsics are parameters of a camera model so a camera model with a mathematical description of how a camera works and the extrinsics and intrinsics are the parameters of this model they're sometimes also called interior and exterior orientation of a camera so let's start with the extrinsics because we can very easily describe that the extrinsics basically describe where is my camera in the 3d world so it's basically xyz location where your camera is and a 3d orientation where your camera is actually looking to so it's a 6 degree of freedom vector or 6 dimensional vector so if you want to perform camera localization we want to compute the extrinsics of our camera and typically we use the projection center of our camera so the point according to the pinhole model where all rays intersect and this defines the location of the camera so this point is the point that we want to describe with our extrinsic parameters besides the extrinsics they are the intrinsics so the intrinsics are the parameters that basically sit inside the camera and basically describe how a point in the three bolt is mapped onto the 2d image plane assuming that the camera sits in the origin and has a zero orientation so it basically covers the whole process of getting a point onto the image plane and assuming the camera sits in the origin of our coordinate system and to describe the intrinsics we typically use at least in basic form four or five parameters it depends if you have a digital camera or an analog camera so what are those intrinsic parameters what you typically have you have the camera constant which is basically the distance of your image plane to your production center and a scale difference in x and y and depending on the literature sometimes one also uses for that the focal lengths and x and the focal lengths and y as two parameters but they are basically equivalent one can be very trivially mapped into the other and then we have two parameters for the so-called principle point so the principal point is basically the pixel in your image through which the optical axis of your camera passes and it basically describes where that point sits in your image typically it's somewhere near the center of your image but of course not precisely because your chip is not precisely glued into your camera and if you have an analog camera then you also have a sheer parameter in most digital cameras this sheer parameter should be very close to zero and those four or five parameters described then with a mathematical model how a point from the 3d world is actually mapped onto the image plane and this is described through the so-called direct linear transform so the direct linear transform is a 11 degree of freedom transformation taking the six degrees of freedom from the extrinsics and the five degrees of freedom from the intrinsics into account and basically i used to describe a so-called a fine camera model or the model of the fine camera this is basically a camera which has a perfect lens so there are no lens distortions or other distortions involved in here and it's an approximation of the camera because all our real-world cameras have those and the dlt or those parameters through an approach which is also called dlt can be computed using six or more control points so points with known coordinates in the environment and by picturing those points i can estimate what are the intrinsics of the camera and i can also estimate where that camera is in practice we have a few more parameters involved for example for lens distortion for example if you have a barrel distortion or a cushion distortion or any other form of distortion in your lens this is something which adds additional parameters so-called non-linear parameters to your model and that you need to estimate additionally and once you have all those parameters you can actually map any point from the 3d volt onto the 2d image plane with this equation x equals p x where capital x is a point in the 3d world p is a projection matrix and lowercase x is the point in your image plane here expressed in something which is called homogeneous coordinates and all the intrinsics and extrinsics sit in this matrix p so these are the different elements in this matrix p that you need to know in order to describe how a 3d point is mapped onto the 2d image plane and so this matrix p what it does it typically takes into account the extrinsic so where the camera it encodes a projection from the 3d world to the 2d world and then also takes the intrinsic parameters of your camera into account so several parameters are kind of merged together in this matrix and we can estimate those intrinsics and extrinsics using calibration patterns so if you want to compute the intrinsics we typically call that camera calibration if you want to compute only the extrinsics then the something which would typically refer to as camera localization because we only want to know where the camera in the world and where is it looking to and estimating those parameters is something that you do if you want to perform measurements or perform geometric estimations with your camera then typically calibrate your camera beforehand to get rid of the distortions of errors that your lens introduces to this mapping so that you then can work with the so-called calibrated camera i hope that was useful and thank you very much for your attention

Channel: Cyrill Stachniss

Views: 7,615

Rating: 4.9741936 out of 5

Keywords: robotics, photogrammetry

Id: ND2fa08vxkY

Length: 5min 59sec (359 seconds)

Published: Thu Feb 18 2021