Accuracy Limits for 3-D Rigid Body Motion Estimation under Perspective Projection

In this paper we investigate accuracy limits for 3-D rigid body motion estimation under perspective projection. Our approach is based on the observation that due to the discrete pixel nature of the image data the epipolar lines in real images can be represented by corresponding discrete line segments. We employ the theory of Farey series to derive subspaces in the motion parameter space that can be covered by a single representative. The size and arrangement of these cells depend on the camera geometry, the image resolution and the feature point correspondence accuracy. Our results support the observations made by many other researchers that the accuracy not only depends on the above mentioned factors, but also strongly depends on the actual motion itself. Simulation results show the accuracy limits derived for di erent cameras when working at varying image resolutions.