Surface Structure and Three-Dimensional Motion from Image Flow Kinematics

Abstract

This study concerns a new formulation and method of solu tion of the image flow problem. It is relevant to the maneu vering of a robotic system through an environment containing other moving objects or terrain. The two-dimensional image flow is generated by the relative rigid-body motion of a smooth, textured object along the line of sight to a monocular camera. By analyzing this evolving image sequence, we hope to extract the instantaneous motion (described by six degrees of freedom) and local structure (slopes and curvatures) of the object along the line of sight. The formulation relates a new local representation of an image flow to object motion and structure by twelve nonlinear algebraic equations. The repre sentation parameters are given by the two components of image velocity, three components of rate of strain, spin, and six independent image gradients of rate of strain and spin, evaluated at the point on the line of sight. These kinematic variables are motivated by the deformation of a finite element of flowing continuum. A method for solving these equations was devised and successfully implemented on a VAX com puter. A number of examples were explored revealing two classes of ambiguous scenes (i.e., nonunique solutions are ob tained). A sensitivity analysis was conducted to estimate noise levels in the representation parameters that still yield acceptable solutions; indications are that the method is quite stable. Finally, an approach is suggested by which the kine matic variables may be extracted from evolving contours in an image sequence.