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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.

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In the kinematic analysis of time-varying imagery, where the goal is to recover object surface structure and space motion from image flow, an appropriate representation for the flow field consists of a set of deformation parameters that describe the rate of change of an image neighborhood. In this paper we develop methods for extracting these deformation param eters from evolving contours in an image sequence, the image contours being manifestations of surface texture seen in perspective projection. Our results follow directly from the analytic structure of the underlying image flow; no heuristics are imposed. The deformation parameters we seek are actu ally linear combinations of the Taylor series coefficients (through second derivatives) of the local image flow field. Thus, a by-product of our approach is a second-order polyno mial approximation to the image flow in the neighborhood of a contour. For curved surfaces this approximation is only locally valid, but for planar surfaces it is globally valid (i.e., it is exact). Our analysis reveals an "aperture problem in the large" in which insufficient contour structure leaves the set of 12 deformation parameters underdetermined. We also assess the sensitivity of our method to the simulated effects of noise in the "normal flow" around contours as well as the angular field of view subtended by contours. The sensitivity analysis is carried out in the context of planar surfaces executing general rigid-body motions in space. Future work will address the additional considerations relevant to curved surface patches.

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The dynamics of two-dimensional uniform wavetrains on the interface between a viscoelastic compliant coating and a boundary-layer flow are explored theoretically. The coating is treated as a single-layer isotropic Voigt material of finite thickness that is bonded to a rigid half-space. The flow is modelled first by potential theory and then modified to incorporate pressure phase shifts and magnitudes found in boundary-layer flow over wavy walls. The consideration of viscoelastic effects has led to an important dimensionless damping parameter γt = Ct τt/d (where τt is the strain relaxation time, Ct is the elastic shear-wave speed and d is the layer depth) that seems to have been overlooked by experimentalists. The flow and the damping are found to have dramatic effects on wave propagation. Using flow pressure and material-damping parameters typical of experiments, the results show that both upstream- and downstream-propagating waves exist at low flow speeds. At higher flow speeds, shorter waves can no longer propagate upstream. At still higher velocities, two instabilities, ‘static divergence’ and ‘flutter’, are found. Static divergence occurs for flow speeds above 2.86Ct and consists of slow waves moving with speeds of about 0.02Ct. These results compare fairly well with published experimental data. Static divergence is found to be a damping instability for these coating systems. When the flow speed is increased further, the flutter instability appears consisting of waves with phase speeds about equal to Ct.

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