  Recovering the 3D structure of the surrounding environment is an essential
task in any vision-controlled Structure-from-Motion (SfM) scheme. This paper
focuses on the theoretical properties of the SfM, known as the incremental
active depth estimation. The term incremental stands for estimating the 3D
structure of the scene over a chronological sequence of image frames. Active
means that the camera actuation is such that it improves estimation
performance. Starting from a known depth estimation filter, this paper presents
the stability analysis of the filter in terms of the control inputs of the
camera. By analyzing the convergence of the estimator using the Lyapunov
theory, we relax the constraints on the projection of the 3D point in the image
plane when compared to previous results. Nonetheless, our method is capable of
dealing with the cameras' limited field-of-view constraints. The main results
are validated through experiments with simulated data.

Robotics;Computer Vision and Pattern Recognition