Using discrete optimization for designing dental shade guides

A key criterion in the design of dental shade guides used for matching tooth color is that the shade tabs cover the natural tooth color space as completely as possible with a manageable number of tabs. Earlier studies have designed hypothetical shade guides from a given population of tooth colors described in the CIELAB system using the goal of minimizing the mean coverage error. In this study, we investigate this topic using the goal of maximizing coverage, meaning that as many measured colors as possible were within a given color difference from the nearest shade tab of the guide. We use techniques of linear discrete optimization to determine the positions of the shade tabs and consider both color difference formulas, CIELAB and CIEDE2000, in an exemplary tooth color population. We obtain coverage error and coverage figures for hypothetical shade guides of various numbers of tabs designed with the goal of either minimizing coverage error or maximizing coverage. Results show that discrete optimization and the goal of maximizing coverage could be used to improve shade guide development. The described technique could be used not only for dental shade guides development, but also for any purpose requiring coverage of as many colors as possible while keeping the number of reference colors manageable.