We’ve looked at how we can geometrically find the linear combination using barycentric coordinates, but it is not the only way to do so. Natural neighbour interpolation works by observing what happens when an input point is inserted into a set of points represented by a Voronoi diagram. The Voronoi diagram is simply a partition of space into polygonal regions for each data point, such that any point inside a given region is proximal to its corresponding data point.
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You look at a region of the image. If all the pixels are roughly the same color (below some threshold), you store the average color for the whole region as a single value. If the pixels vary too much, you split the region into four quadrants and try again.