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 fifteen years. Since the early work on Structure from Motion (SFM) by Longuet-Higgins [4] and Pradzny [6], 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 motion and distances to points in the world. Thus, solving the problem typically requires non-linear optimization techniques that can be unstable or computationally inefficient. Linear algorithms are preferable since they are computationally 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 [3] except that we employ spherical projection. The use of a spherical imaging geometry allows a simpler and more intuitive derivation of the algorithm, and produces an unbiased estimator. Experimental results are provided that demonstrate the performance of the algorithm.