Another way to approach the linear combination is to look at it geometrically. This is where the idea of barycentric coordinates can help. A barycentric coordinate system describes the location of a point as the weighted sum of the regular coordinates of the vertices forming a simplex. In other words, it describes a linear combination with respect to a set of points, where in -dimensional space.
One by-product of weighing the candidates by their distance is that the resulting output image is prone to false contours or banding. Increasing reduces this effect at the cost of added granularity or high frequency noise due to the introduction of ever more distant colours to the set. I recommend taking a look at the original paper if you’re interested in learning a bit more about the algorithm[1].
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