Single Camera Structure and Motion Estimation - Visual Servoing via Advanced Numerical Methods - page 201

Chapter 12
Single Camera Structure and Motion Estimation

Ashwin P. Dani and Warren E. Dixon

Abstract. Two new continuous nonlinear observers are proposed for the problem of
structure from motion (SfM) and structure and motion (SaM) of a stationary object
observed by a moving camera. The observer for SfM, where full velocity feedback
is available, yields global exponential convergence of the states for the structure.
The SaM observer requires only one of the linear velocities as a feedback and iden-
tifies the states asymptotically. The linear velocity is used to derive the scene scale
information. The observer gain conditions are derived to prove the stability of the
proposed observers through a Lyapunov-based analysis.

12.1 Introduction

Provided points of interest can be tracked between multiple images ( i.e. , through
feature point tracking 1 ), image feedback can be used to estimate the motion of the
tracked feature points or can be used to estimate the geometry of the feature points.
The objective of the SfM problem is to estimate the Euclidean geometry ( i.e. ,3D
structure) of the tracked feature points attached to an object provided the relative
motion 2 between the camera and the object is known. The converse of the SfM prob-
lem is the motion from structure (MfS) problem where the relative motion between
the camera and the object is estimated based on known geometry of the tracked