2 Vector Spaces and Projective Spaces 3 2.1 Vector spaces and their duals . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Projective spaces and homogeneous coordinates . . . . . . . . . . . . . . . 5 2.2.1 Visualizing projective space . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Homogeneous coordinates . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Linear subspaces . . . . ....

|This paper presents a linear algorithm for recovering 3D a ne shape and motion from line correspondences with uncalibrated a ne cameras. The algorithm requires a minimum of seven line correspondences over three views. The key idea is the introduction of a one-dimensional projective camera. This converts 3D a ne reconstruction of \line directions" into 2D projective reconstruction of \points". ...

In this study, all embeddings that map each line of projective plane order 4 to an oval Projective Space dimensional will be investigated and it was shown the image these maps generate spaces P G(4, 4).