In color spaces where the chromatic term is given in polar coordinates, the shortest distance between colors of the same value is circular. By converting such a space into a complex polar form with a real-valued value axis, a color algebra for combining colors is immediately available. In this work, we introduce two complex space operations utilizing this observation: circular average filtering and circular linear interpolation. These operations produce Archimedean Spirals, thus guaranteeing that they operate along the shortest paths. We demonstrate that these operations provide an intuitive way to work in certain color spaces and that they are particularly useful for obtaining better filtering and interpolation results. We present a set of examples based on the perceptually uniform color space CIELAB or L*a*b* with its polar form CIEHLC. We conclude that representing colors in a complex space with circular operations can provide better visual results by exploitation of the strong algebraic properties of complex space C.

翻译：在色度项以极坐标表示的颜色空间中，相同明度颜色之间的最短距离呈圆形。通过将此类空间转换为具有实数值明度轴的复数极坐标形式，即可直接建立颜色组合的代数运算。本文基于这一发现引入两种复数空间操作：圆形平均滤波与圆形线性插值。这些操作生成阿基米德螺线，从而确保沿最短路径进行运算。我们证明这些操作提供了在特定颜色空间工作的直观方法，并特别有助于获得更优的滤波与插值结果。基于感知均匀颜色空间CIELAB（L*a*b*）及其极坐标形式CIEHLC，我们展示了一系列实例。结论表明：利用复数空间C的强大代数性质，通过圆形操作进行颜色表示可呈现更佳的视觉效果。