The increasing use of advanced measurement tools and technology in industry over the past 30 years has ushered in a new set of challenging computational problems. These problems can be broadly classified as fitting and filtering of discrete geometric data collected by measurements made on manufactured products. Collectively, they define the field of computational metrology for the design specification, production, and verification of product geometry. The fitting problems can be posed and solved as optimization problems; they involve both continuous and combinatorial optimization problems. The filtering problems can be unified under convolution problems, which include convolutions of functions as well as convolutions of sets. This paper presents the status of research and standardization efforts in computational metrology, with an emphasis on its classification and synthesis.

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