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Convex reduction of calibration charts

机译：减少校准图的凸度

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Calibration targets are widely used to characterize imaging devices and estimate optimal profiles to map the response of one device to the space of another. The question addressed in this paper is that of how many surfaces in a calibration target are needed to account for the whole target perfectly. To accurately answer this question we first note that the reflectance spectra space is closed and convex. Hence the extreme points of the convexhull of the data encloses the whole target. It is thus sufficient to use the extreme points to represent the whole set. Further, we introduce a volume projection algorithm to reduce the extremes to a user defined number of surfaces such that the remaining surfaces are more important, i.e. account for a larger number of surfaces, than the rest. When testing our algorithm using the Munsell book of colors of 1269 reflectances we found that as few as 110 surfaces were sufficient to account for the rest of the data and as few as 3 surfaces accounted for 86% of the volume of the whole set.
机译：校准目标广泛用于表征成像设备并估计最佳轮廓，以将一个设备的响应映射到另一个设备的空间。本文解决的问题是，校准目标中需要多少个表面才能完美地说明整个目标。为了准确回答这个问题，我们首先要注意反射光谱空间是封闭且凸的。因此，数据的凸包的极端点包围了整个目标。因此，使用极值点代表整个集合就足够了。此外，我们引入了体积投影算法，以将极端情况减少到用户定义的表面数量，从而使其余表面比其余表面更重要，即占更大数量的表面。当使用Munsell的1269色反射色测试我们的算法时，我们发现只有110个表面足以说明其余数据，而只有3个表面就占了整个体积的86％。

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