What is a local relief model, and what does it hide?

A barrow half a metre high on a hillside that drops 30 metres across the frame is invisible in a raw elevation image. The hill is the whole dynamic range and the barrow is a rounding error. This is the problem a local relief model solves, and it solves it with subtraction.

The whole method in three steps

• Take the terrain model.
• Blur it, heavily, with a kernel wide enough to smooth away anything you care about. Ours is 45 metres.
• Subtract the blurred copy from the original.

What is left is the difference between the ground and a smoothed version of itself. The hillside cancels out, because a smoothed hillside is still a hillside. The barrow does not, because a smoothed barrow is nearly flat. You get a map of local deviation in metres, and on it a half-metre mound reads the same wherever it sits.

It also removes the lighting problem entirely. There is no sun, so there is no azimuth, so nothing disappears for being parallel to it.

The first thing it hides: anything bigger than the kernel

The kernel width is a decision about what counts as terrain and what counts as archaeology, and it is usually made once and never revisited.

At 45 metres, a barrow is a feature and a hillfort rampart circuit 200 metres across is terrain. The hillfort is not faint in the output. It is absent, subtracted along with the hill, because at that scale it is the hill as far as the smoothing is concerned. Widen the kernel to catch it and you start keeping natural landforms as features, and your candidate list fills with knolls.

There is no correct kernel width. There is a width that suits the size of thing you are looking for, and a survey that reports its detections without reporting its kernel has not told you what it was looking for.

The second thing it hides: the edges of your own tiles

This one cost us a scheduled monument, and it is the reason this page exists rather than a general explainer.

To compute the smoothed value at a point, the kernel needs real ground all around that point. A 45 pixel kernel at 1 metre resolution needs 22 metres of context in every direction. Near the edge of a tile that context does not exist, so the software pads it, usually by mirroring or by repeating the edge value. The smoothed surface there is computed from invented data, so the subtraction is wrong, so the local relief is wrong.

Then the part that should worry anybody running a grid. On a 1,000 metre tile, a 22 metre unreliable border on all four sides is 8.6% of the tile area. Across that survey it came to 0.52 square kilometres of ground where the method quietly did not work, and which ground fell inside it was decided by nothing except where we started the grid. We started at E364000 N93000 because those are round numbers.

The fix is trivial once you have seen it. Fetch tiles with a halo of at least the kernel radius, compute the relief model on the padded tile, then discard detections that fall inside the halo. We do that from run 004 onward. Nothing about it is clever. It is only invisible.