Post date: Nov 7, 2014 7:06:38 PM
Just today I've finished yet another way to explore how changes in layouts lead to changes in impacts and costs for my third chapter. My new metric of differences between layouts is the average distance between corresponding pixels of infrastructure between two different layouts.
What did I just say?
Take these three layouts:
The first two look really similar, right? The only difference seems to be the pad has been moved left in the middle layout, and as a result the road has shifted up. By comparison, the first and last layouts look much less similar: the pad is further away and the pipeline route is much different and the road goes in opposite directions from the pad.
The distance between pads is the easiest to measure: take their centroids, get the distance between them. Between the first and second layouts, that's 42 m. Between the first and last, 201 m. To measure how much the roads and pipelines have changed, I have to do a bit more work. Take the roads. I trace along the road, associating each pixel with a percent along the road. Right at the pad, that's 0% along the road. At the existing roads, that's 100% along the road. Then, at each pixel along the first layout, I get the distance to the corresponding pixel on the second layout. Since roads have a different number of pixels from layout to layout, I have to interpolate between the pixels to get corresponding positions. Once I have all the distances that pixels have been moved from one layout to the next, I can just summarize that with, e.g. a mean. So between the first and second layout, the average distance between corresponding road pixels is 57 m. And the average distance between the pipes is 28 m. Note that despite the fact that most of the pipeline between the first and second layouts is the same, you get a non-zero separation because the starting pixels of one pipe are in different locations than the starting pixels of the other. By the time you get to the end of the pipe, the pixels match up again.
So, in total I get these comparing the second two layouts to the first:
So, as expected, the middle layout is really similar to the first layout (mean distance across all infrastructure of 32 (+/- 20) meters), whereas the right layout looks quite different.
How am I going to use this information? You mean apart from being a really neat way to distinguish spatial differences between two layouts with a single metric. Well, the hope was that I could hook these distances to the variograms I've shown in a previous post and come to some conclusion about how the spatial difference in impacts and costs have something to do with these spatial differences in layouts. So far I'm missing something, but I'm not there yet.
Just something else to note about the methods that was a challenge for me and I am happy with my solution (ask me about it): What about when you have more than one pad that shares a portion of a road/pipeline?