Depth Estimation for a Point Feature: Structure from motion & Stability Analysis

This paper presents a new approach to recover the depth information from images of a monocular vision system. The depth estimation of a point is achieved by designing a nonlinear observer based on a polytopic structure. The fulfillment of the conditions of the state estimation, that depends on the applied velocities for the nonlinear system, is required. To this end, the observability analysis is performed to establish the kinematic conditions for the reconstruction of unmeasured states. The stability analysis is carried out using Lyapunuv theory. The observer gains were computed from the resolution of the Linear Matrix Inequality (LMI) constraints. Illustrations and simulation results are given at the end to prove the effectiveness of the proposed approach.