Global Slope Change Synopses for Measurement Maps

Quality control using scalar quality measures is standard practice in manufacturing. However, there are also quality measures that are determined at a large number of positions on a product, since the spatial distribution is important. We denote such a mapping of local coordinates on the product to values of a measure as a measurement map. In this paper, we examine how measurement maps can be clustered according to a novel notion of similarity - mapscape similarity - that considers the overall course of the measure on the map. We present a class of synopses called global slope change that uses the profile of the measure along several lines from a reference point to different points on the borders to represent a measurement map. We conduct an evaluation of global slope change using a real-world data set from manufacturing and demonstrate its superiority over other synopses.