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I have extracted urban footprints using Landsat ETM+. I am now interested to make rose diagram depicting direction of each pixel to ascertain in which direction urban area has been increased over the study period.

Obviously, this need reference point from where direction of each pixel will be calculated. I can get the results while converting the pixels into polygon and clip the features in four cardinal directions (0-90, 90-180, 180-270 & 270-360 degrees) and plot the resultant data as rose diagram.

But, is there any elegant way to retrieve better results while converting each pixel to assign its direction ranging from 0-359?

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The solution is a small part of the workflow detailed at https://gis.stackexchange.com/a/54002/664: compute the Euclidean distance grid from the reference point, negate its values, and compute the aspect grid of that.

Geometrically, you are creating an inverted cone whose apex is at the reference point. Its aspect gives the direction of the outward Normal vector, which is directed radially away from the reference point (the direction in which distance increases most rapidly).

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