In car manufacturing, quality management and control are important parts of the series process. In series production, many parts are controlled in various ways in some or all stages of assembly. While tactile measurements are mostly restricted to the points on an inspection plan, this restriction does not apply to optical measurements. We propose a method based on the theory of Pareto sets (multivariate topological analysis) to cope with the large amount of data produced by optical measurements and to find points of interest on the measured surface in addition to the inspection plan. We describe a method which automatically detects areas of systematic errors on a component and visualizes them on the triangulated surface. The visualization can help experts to decide, whether a detected feature is severe enough to be added to the inspection plan.

Topological and structural analysis of multivariate data is aimed at improving the understanding and usage of such data through identification of intrinsic features and structural relationships among multiple variables. We present two novel methods for simplifying so-called Pareto sets that describe such structural relationships. Such simplification is a precondition for meaningful visualization of structurally rich or noisy data. As a framework for simplification operations, we introduce a decomposition of the data domain into regions of equivalent structural behavior and the reachability graph that describes global connectivity of Pareto extrema. Simplification is then performed as a sequence of edge collapses in this graph; to determine a suitable sequence of such operations, we describe and utilize a comparison measure that reflects the changes to the data that each operation represents. We demonstrate and evaluate our methods on synthetic and real-world examples.

Abstract How can the notion of topological structures for single scalar fields be extended to multifields? In this paper we propose a definition for such structures using the concepts of Pareto optimality and Pareto dominance. Given a set of piecewise‐linear, scalar functions over a common simplical complex of any dimension, our method finds regions of “consensus” among single fields’ critical points and their connectivity relations. We show that our concepts are useful to data analysis on real‐world examples originating from fluid‐flow simulations; in two cases where the consensus of multiple scalar vortex predictors is of interest and in another case where one predictor is studied under different simulation parameters. We also compare the properties of our approach with current alternatives.