Matching for Shape Defect Detection

The problem of defect detection in 2D and 3D shapes is analyzed. A shape is represented by a set of its contour, or surface, points. Mathematically, the problem is formulated as a speciic matching of two sets of points, a reference one and a measured one. Modiied Hausdorr distance between these two point sets is used to induce the matching. Based on a distance transform, a 2D algorithm is proposed that implements the matching in a computationally eecient way. The method is applied to visual inspection and dimensional measurement of ferrite cores. Alternative approaches to the problem are also discussed. In industrial shape defect detection, two types of measurements can be distinguished: (a) Direct, or absolute, measurements, when a dimension, or another quantity to be measured, is speciied with respect to particular shape features (corners, etc.) that are easy to identify and locate. An example of such measurement is obtaining the distance between centroids of two holes. (b) Relative measurements, which are speciied with respect to a reference shape. Most of direct measurements are straightforward, as they usually have precise mathematical deenitions in terms of images. Such computational deenitions are relatively easy to translate into a computer algorithm. Relative measurements are much more challenging, as the deenitions are, in fact, implicit. Here, one compares a measured shape to a reference (ideal) shape. For shift-and rotation-invariant comparison, optimal reference position and orientation (pose) of the measured shape is to be found, which requires invariant matching of the two shapes. The pitfall of matching for defect detection is that no reference pose (e.g., baseline) can be speciied a priori because defects may deteriorate any part of the shape. It is a typicaìchicken-and-egg' problem. What parts of a measured shape should be considered defective? Usually, it is assumed that those parts of the shape that coincide with the reference, or lie within the tolerance limit, are