Abstract
The transformation of the three-dimensional coordinates of a point to the two-dimensional coordinates of its image can be expressed compactly as a 4 × 4 homogeneous coordinate transformation matrix in accordance with a particular imaging geometry. The matrix can either be derived analytically from knowledge about the camera and the geometry of image formation, or it can be computed empirically from the coordinates of a small number of three-dimensional points and their corresponding image points. Despite the utility of the matrix in image understanding, motion tracking, and autonomous navigation, very little is understood about the inverse problem of recovering the projection parameters from its coefficients. Previous attempts have produced solutions that require iteration or the solution of a set of simultaneous nonlinear equations. This paper shows how the location and orientation of the camera, as well as the other parameters of the image-formation process can easily be computed from the homogeneous coordinate transformation matrix. The problem is formulated as a simple exercise in constructive geometry and the solution is both noniterative and intuitively understandable.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call