Non-uniform surface sampling techniques for three-dimensional object inspection

Abstract

While the uniform sampling method is quite popular for point- wise measurement of manufactured parts, we present three novel sam- pling strategies that emphasize 3D non-uniform inspection capability. They are direct and indirect adaptive sampling and local adjustment sampling. The adaptive sampling strategy is based on a recursive sur- face subdivision process that applies two different approaches. One uses the direct triangular patch subdivision while the other uses the in- direct sectional adaptive approach. The direct adaptive sampling ap- proach can distribute points more closely around edges, corners, and vertices as found on the class of machined products. The indirect adap- tive sampling techniques extend optimum 2D sampling methods to 3D applications. The modified 2D adaptive sampling techniques are used sequentially twice; first, the critical cross sections are optimally selected, and then each section is optimally sampled to develop an accurate geo- metric description using a small number of sampling points. Beyond the practical application value of a technique to inspect curved surface ob- jects, this kind of technique is also of value in understanding the principle of optimum sampling in a 3D sense. The local adjustment sampling strat- egy uses a set of predefined starting points and then finds the local optimum position of each nodal point. This method approximates the object by moving the points toward object edges and corners. The pre- defined starting points sets include uniform and non-uniform sampling distribution generated by the direct adaptive sampling approach. The results show that the initial point sets, when preprocessed by the adap- tive sampling using triangular patches, are moved the shortest distance to edges and corners for global optimum approximation, again showing this method's superiority. The performance comparisons of applying uni- form sampling and adaptive sampling are made based on the MSE mean square error value between the real object surfaces and their approximating surfaces. The adaptive sampling methods exhibit better performance than the uniform sampling methods in reducing the MSE values with fewer sample points. In addition to the performance advan- tage over uniform sampling, the non-uniform sampling techniques we propose also proved to be integratable with view planning for the inspec- tion of products by different manufacturing processes. © 2008 Society of