Camera resectioning

Camera resectioning is the process of estimating the parameters of a pinhole camera model approximating the camera that produced a given photograph or video. Usually, the pinhole camera parameters are represented in a 3 × 4 matrix called the camera matrix. Camera resectioning is the process of estimating the parameters of a pinhole camera model approximating the camera that produced a given photograph or video. Usually, the pinhole camera parameters are represented in a 3 × 4 matrix called the camera matrix. This process is often called camera calibration, although that term can also refer to photometric camera calibration. Often, we use [ u   v   1 ] T {displaystyle ^{T}} to represent a 2D point position in pixel coordinates. Here [ x w   y w   z w   1 ] T {displaystyle ^{T}} is used to represent a 3D point position in World coordinates. Note: they were expressed in augmented notation of homogeneous coordinates which is the most common notation in robotics and rigid body transforms.Referring to the pinhole camera model, a camera matrix is used to denote a projective mapping from World coordinates to Pixel coordinates. The intrinsic matrix K {displaystyle K} contains 5 intrinsic parameters. These parameters encompass focal length, image sensor format, and principal point. The parameters α x = f ⋅ m x {displaystyle alpha _{x}=fcdot m_{x}} and α y = f ⋅ m y {displaystyle alpha _{y}=fcdot m_{y}} represent focal length in terms of pixels, where m x {displaystyle m_{x}} and m y {displaystyle m_{y}} are the scale factors relating pixels to distance and f {displaystyle f} is the focal length in terms of distance. γ {displaystyle gamma } represents the skew coefficient between the x and the y axis, and is often 0. u 0 {displaystyle u_{0}} and v 0 {displaystyle v_{0}} represent the principal point, which would be ideally in the center of the image. Nonlinear intrinsic parameters such as lens distortion are also important although they cannot be included in the linear camera model described by the intrinsic parameter matrix. Many modern camera calibration algorithms estimate these intrinsic parameters as well in the form of non-linear optimisation techniques. This is done in the form of optimising the camera and distortion parameters in the form of what is generally known as bundle adjustment. [ R 3 x 3 T 3 x 1 0 1 x 3 1 ] 4 x 4 {displaystyle {}{egin{bmatrix}R_{3x3}&T_{3x1}\0_{1x3}&1end{bmatrix}}_{4x4}} R , T {displaystyle R,T} are the extrinsic parameters which denote the coordinate system transformations from 3D world coordinates to 3D camera coordinates. Equivalently, the extrinsic parameters define the position of the camera center and the camera's heading in world coordinates. T {displaystyle T} is the position of the origin of the world coordinate system expressed in coordinates of the camera-centered coordinate system. T {displaystyle T} is often mistakenly considered the position of the camera. The position, C {displaystyle C} , of the camera expressed in world coordinates is C = − R − 1 T = − R T T {displaystyle C=-R^{-1}T=-R^{T}T} (since R {displaystyle R} is a rotation matrix). Camera calibration is often used as an early stage in computer vision. When a camera is used, light from the environment is focused on an image plane and captured. This process reduces the dimensions of the data taken in by the camera from three to two (light from a 3D scene is stored on a 2D image). Each pixel on the image plane therefore corresponds to a shaft of light from the original scene. Camera resectioning determines which incoming light is associated with each pixel on the resulting image. In an ideal pinhole camera, a simple projection matrix is enough to do this. With more complex camera systems, errors resulting from misaligned lenses and deformations in their structures can result in more complex distortions in the final image.The camera projection matrix is derived from the intrinsic and extrinsic parameters of the camera, and is often represented by the series of transformations; e.g., a matrix of camera intrinsic parameters, a 3 × 3 rotation matrix, and a translation vector. The camera projection matrix can be used to associate points in a camera's image space with locations in 3D world space.