Shape analysis of complex profiles - Chen, Jen-Ming; Ventura, Jose A. (International journal of machine tools & manufacture, 1995)
This paper proposes a novel shape representation scheme based on CAD database specifications, and an optimization matching algorithm using the least-squares criterion to determine the pose and scale of objects, and perform out-of-profile inspection. The shapes of interest are two-dimensional (2D) profiles generated by projecting 3D objects onto a 2D inspection plane, the boundaries of which are composed of straight-line segments and circular arcs. This procedure can be applied to automated inspection of machined parts using machine vision systems. The shape model is characterized by four global parameters, based on which all the geometric primitives of the shape are expressed in analytic form. The matching procedure is to find the least-squares error between the true profile of the object and the sensed data, and to satisfy all the geometric constraints among primitives simultaneously. The advantage of the proposed model is that all the primitives of the shape are represented by the same (four) parameters in implicit equations, so that the spatial relationships among them are completely specified by the equations. Based on this representation scheme, the subsequent matching problem is formulated as an unconstrained optimization model, and solved by a gradient-based descent algorithm. In the experimental study, the results generated from the proposed technique are compared with those from two of the most commonly used machine vision approaches: Fourier Descriptors (FDs) and moments. This comparison shows that the method is superior to FDs and moments in error minimization. In addition, a complete procedure for automated design, manufacturing and machine vision inspection of production parts is described.