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How to calculate the YUV values of a grayscale image ?

Is it possible to calculate the values YUV of a graycale image ?

I found an article that confuses me: Interactive Image Colorization and Recoloring based on Coupled Map Lattices In which the authors propose an algorithm to color and recolor an image.

First they color grayscale images. The user scribble some regions of the image with the desired color which spreads itself automatically by the algorithm. They use YUV color space to compare the values of Y between the current pixel and its neighbors. If the Y value of a neighbor is stronger than the current pixel sets its U and V values to those of the neighbor (attacker).

My problem: how can I cancluate the YUV values of a given pixel of a grayscale image ?