On tracking the motion of rigid bodies through edge detection and least-squares fitting

Abstract

A class of techniques is investigated for determining at least three components (two translational and one rotational) of the motion of a rigid body from silhouette images, with particular emphasis on motion within a fluid. The investigated techniques all employ edge detection followed by some form of least-squares fitting to the detected points in determining the movement of the body. Four techniques are discussed and, through both an artificial image analysis and calibrated sphere measurements, are shown to be capable of measuring displacements down to a few thousandths of a pixel under low image-noise conditions ($\lesssim2\%$). Measurements of two configurations in a high-enthalpy shock tunnel demonstrate the capabilities of the techniques under experimental conditions. In particular, a technique referred to as edge-tracking is introduced, which can be employed in situations where the model profile is unknown and/or only some fraction of it is visible. This latter quality is especially useful for measurements in high-enthalpy facilities, where test-gas luminosity can obscure a significant extent of the model outline. A further advantage of this technique is that, even for complex geometries, the fitting procedure can typically be reduced to solving a sequence of linear least-squares problems, rather than a nonlinear one, with a corresponding benefit in computational efficiency.