Active Structure From Motion: Application to Point, Sphere, and Cylinder

In this paper, we illustrate the application of a nonlinear active structure estimation from motion (SfM) strategy to three problems, namely 3-D structure estimation for 1) a point, 2) a sphere, and 3) a cylinder. In all three cases, an appropriate parameterization reduces the problem to the estimation of a single quantity. Knowledge of this estimated quantity and of the available measurements allows for then retrieving the full 3-D structure of the observed objects. Furthermore, in the point feature case, two different parameterizations based on either a planar or a spherical projection model are critically compared. Indeed, the two models yield, somehow unexpectedly, to different convergence properties for the SfM estimation task. The reported simulative and experimental results fully support the theoretical analysis and clearly show the benefits of the proposed active estimation strategy, which is in particular able to impose a desired transient response to the estimation error equivalent to that of a reference linear second-order system with assigned poles.