Probabilistic Evaluation of 3D Surfaces Using Statistical Shape Models (SSM)

Abstract

Inspecting a 3D object which shape has elastic manufacturing tolerances in order to find defects is a challenging and time-consuming task. This task usually involves humans, either in the specification stage followed by some automatic measurements, or in other points along the process. Even when a detailed inspection is performed, the measurements are limited to a few dimensions instead of a complete examination of the object. In this work, a probabilistic method to evaluate 3D surfaces is presented. This algorithm relies on a training stage to learn the shape of the object building a statistical shape model. Making use of this model, any inspected object can be evaluated obtaining a probability that the whole object or any of its dimensions are compatible with the model, thus allowing to easily find defective objects. Results in simulated and real environments are presented and compared to two different alternatives.

An Approach to Comparing Multidimensional Geometric Objects

“…In works [8][9], an approach is proposed to compare three-dimensional geometric objects (human and mannequin bodies) using stochastic methods, using form functions. Many articles are devoted to the comparison of 2D and 3D geometric objects based on various approaches, which include the use of: generate specific distance histograms that define a measure of the geometric similarity of the inspected objects [10], a probabilistic method to evaluate 3D surfaces is presented [11], graph matching technique to measure the distance between these graphs [12], Hausdorff distance (HD) and the accumulated distance difference (ADD) [13], graph similarity into PPM and similarity measurement based on Topological Relationship Distribution (TRD) feature [14], a probability distribution function (PDF) produced from spatial disposition of 3D keypoints, keypoints which are stable on object surface and invariant to pose changes [15], a method of sequential application of global descriptors, allowing the first stage to produce a "rough" screening of obviously different objects, and then to apply more accurate algorithms on a significantly reduced object base [16]. Also, there are a number of review articles devoted to research on the problem of comparing 2D and 3D geometric objects [17].…”