# ArcGIS backlink raster incorrect

I created a small (4x4) cost raster with a 10m cell resolution, and used the ArcGIS Cost Distance tool to calculate the Output Distance raster and the Output backlink raster, assuming a single source point in the bottom left (SW) corner. Then I used Dijkstra's algorithm to check the output distance raster values; they are all correct. However when checking the backlink raster, it appears to be incorrect. The cell value one east and 2 north in the backlink raster produced is 5, but should be 4 so it goes diagonally. This makes me wonder how often incorrect least cost paths are produced. Am I missing something, or does ArcGIS often produce incorrect backlinks and therefore incorrect least cost paths? I'm using ArcGIS for Desktop 10.3.

The cost raster (from Chang's textbook 7th edition) is:

1 2 2 1
1 4 5 1
2 3 7 6
1 3 4 4

The (correct) Output Distance raster produced by ArcGIS is:

40.0 51.2 71.2 86.2
30.0 55.0 84.9 92.4
15.0 28.3 78.3 125.7
0.0 20.0 55.0 95.0

The (incorrect) backlink raster produced by ArcGIS is:

3 4 5 5
3 5 4 6 <-- 5 should be a 4
3 4 5 4
0 5 5 5

You can see from the output distance raster that the correct direction would be 4: from 55 to 15 rather than to 30. Heck, even a 3 would go to 20 and be better than 30. Or is ArcGIS doing something I don't understand?

• This is really something to discuss with Esri Tech Support. GIS SE is not intended to replace software vendors' support mechanisms. – Vince Mar 2 '16 at 14:57

## 1 Answer

You are wrong, because cost of travel between 2 nodes equal to L*C , where L is distance between them and C is average of 2 node costs. Any diagonal L is approximately 14.14 in your case: Thus travelling ArcGIS GCBA path costs (25+15+15 = 55.00) is cheaper than yours GBA (42.42+15=57.42)

• Thanks FelixIP. I knew that the output distance raster value for the square should be 55. But I guess what you're saying is that ArcGIS doesn't use the output distance raster to compute the backlink raster. Instead it bases it on the pathway used when creating the output distance raster. I always thought you could just follow the smallest values in the output distance raster back to the source when creating the backlink raster and the least cost path. Thanks for clarifying. – flagman Mar 4 '16 at 9:09
• Similar to hydrology (flow direction), backlink raster is first to be computed through analysis od cost surface. The rest, e.g. path cost, derived from it. Elevation is cost surface in hydrology. – FelixIP Mar 4 '16 at 19:38