# Difference in vector / raster area measurements

I'm comparing raster and vector distance zones.

So I created a line, calculated the Euclidean distance, and reclassified the raster to two zones: from 0-10m and 10-20m. To compare it with vector distance, I created a Multiple Ring Buffer with the same line and the same two zones, 0-10m and 10-20m.

When I'm calculating the area, for example for the 0-10m zone, the (vector) buffer has an area of 1475 m² while the Euclidean distance raster for the same zone has an area of 1493 m²!

Can someone please explain why those two values differ?

• If you were to select all distances in the raster that are less than or equal to the buffer radius and inspect the boundary of that zone, you would find that it consists of whole cells in the raster, and thereby only discretely approximates the vector buffer. You really should be comparing the raster solution to a rasterized version of the vector solution: any substantial discrepancy between those two would be worth investigating. – whuber Jun 23 '14 at 20:16

## 2 Answers

From what you are explaining the Euclidean Distance would be (a) The buffers would be (b) So the differences would be in the corners (c) The raster buffer is an approximation of the distance with a discretization of the space. Vector buffer nearly exact representation of the buffer (it is exact if the vector model uses parametric curves, but most often those curves are stored as a set of small straightline segments).

You you create a buffer with Euclidian distance, you have 2 issues:

• In ArcGIS, the distance to the line is measured at the center of the pixel, therefore the area of the resulting zone will overestimate the actual buffer extent by half a pixel (on average). This can be solved by considering the buffer area after removing this 1/2 pixel (with one meter pixel, take 9.5 m instead of 10 m).
• After removing the bias, you will still have an unprecise mesure because pixels are represented as squares (if you zoom on your map this will be obvious). You can increase the precision of your raster by reducing the pixel size, but this will increase processing time as well as size on disk.