Perspective approximations

In recent years, researchers in computer vision working on problems such as object recognition, shape reconstruction, shape from texture, shape from contour, pose estimation, etc., have employed in their analyses approximations of the perspective projection as the image formation process. Depending on the task, these approximations often yield very good results and present the advantage of simplicity. Indeed when one relates lengths, angles or areas on the image with the respective units in the 3D world assuming perspective projection, the resulting expressions are very complex, and consequently they complicate the recovery process. However, if we assume that the image is formed with a projection which is a good approximation of the perspective, then the recovery process becomes easier. Two such approximations, are described, the paraperspective and the orthoperspective, and it is shown that for some tasks the error introduced by the use of such an approximation is negligible. Applications of these projections to the problems of shape from texture, shape from contour, and object recognition related problems (such as determining the view vector and pose estimation) are also described.