Error Analysis of SFM Under Weak-Perspective Projection

Despite the long history of studies on weak-perspective projection and the intuitive notion that this model has better numerical stability compared to the perspective model under appropriate conditions, there lacks a deep understanding about the error characteristics of motion and depth recovery process under this model. In this paper, we present the differential approach to SFM under weak-perspective projection. Based on this approach, error behavior which governs the formation of motion ambiguities under weak-perspective is investigated. Recovery of depth information and its distortion are also discussed. Regions where ordinal depth can be extracted is shown to be following a simple relationship under all types of motion, a different result compared to the case of perspective projection.