Linear Structure From Motion

Determining the structure of the world and the motion of the observer from image changes has been a central problem in computer vision for over fteen years Since the early work on Structure from Motion SFM by Longuet Higgins and Pradzny several techniques have been developed to compute the motion of the camera the shape of moving objects or distances to points in the world However the image changes are non linearly related to camera mo tion and distances to points in the world Thus solving the problem typically requires non linear optimization techniques that can be unstable or computa tionally ine cient Linear algorithms are preferable since they are computa tionally advantageous and since linear estimation is much better understood than non linear estimation Our paper describes an unbiased completely linear algorithm for Structure from Motion This work is similar to that of Jepson Heeger except that we employ spherical projection The use of a spherical imaging geometry allows a simpler and more intuitive derivation of the algo rithm and produces an unbiased estimator Experimental results are provided that demonstrate the performance of the algorithm