Structure from motion: determining the range and orientation of surfaces by image interpolation

A new scheme is presented for determining the range and orientation of arbitrarily oriented surfaces directly from the apparent image motion captured by a moving camera. The mean range, slope, and tilt of the surface are computed by decomposition of the image motion into components representing translation, compression, and shear. These motion parameters are computed directly from intensity changes in the images by the solution of a set of linear equations, the coefficients of which are derived from the raw image data by a novel process of linear image interpolation. The advantages of this scheme over those of existing schemes are that (1) it involves no identification or tracking of features and therefore avoids the correspondence problem, (2) it does not require measurement of high-order spatial or temporal derivatives of the image and is therefore robust to noise, and (3) the three parameters characterizing the surface (mean range, slope, and tilt) are recovered in a noniterative calculation. The scheme is ideal for applications such as autonomous robot navigation in which information about slope and tilt can be used to determine the traversability of the surrounding terrain.