Geospatial Thinking - it's all about the edge!

In 2014 I was faced with a tricky classification problem. Around that time statewide woody vegetation cover raster datasets at reasonably high resolution (5m) were starting to become BAU thanks to the foresight and investment by the geospatial folks within government. The data being produced was woody cover derived via remote sensing methods with a relatively simple classification (1=presence woody veg and 0= absence of woody veg). This was a fantastic result however what this meant was that we had pixels in the depths of East Gippsland forests with the same value as a strip of roadside vegetation in the Wimmera. This was not a fault in the method of creating the data it was more a challenge in how to use it in decision-making. The remote sensing got you this cool dataset at high-res (for its time) input. The challenge was how to use geospatial methods to transform this into actionable information.

I was doing quite a bit of work in roadside vegetation studies and fire management at the time so thinking a lot about using this info in operations and planning. I was looking to break up the vegetation cover in some way. There were suggestions of creating distance or density surfaces from the binary (1,0) data. However, both of these ideas had a few problems. Let me explain using two thought experiments:

Experiment 1 - the problem of orientation

• Imagine being on a road going north-south

• Image at your present location on the road to your left were lots of trees and to your right it was clear fields

• Now move north up the road to another location. At this point things were the inverse (trees on the right and clear on the left)

• These are not the same landscape clearly however a density function of the data produces the same result at the road. The orientation or direction of tree cover is lost.

Experiment 2 - the problem of mass

• Image you are in the East Gippsland forest in a clearing. You are 20m from the tree line. In the woody cover data, your location is a Zero but you a surrounded by a bucket load of trees (Ones) - you have a very large mass of trees near you but not at your location

• Imagine you are in the Wimmera in a large wheat field. Image you are standing next to a small clump of trees (let's say remnant vegetation) in that field. You are 20m from the clump. You are the same distance, but the mass of trees is a lot lower.

• If you create a "distance from cover" surface both locations will have the same value

Neither distance nor density on their own were going to give me what I was looking for. Along came a thought bubble.

• Image you are at the 1st point in the roadside experiment above.

• Now imaging facing north and asking what the density of cover is in a wedge to the north - keep that value handy

• Now rotate 45 degrees to the east - do the same

• Go around the compass collecting these values at 45 degrees segments

• What you end up with is 8 values for that location

Applying the concept

Applying this idea to the woody vegetation cover raster produces 8 datasets - this was looking a lot like a multi-band image problem at that point. I used a standard remote sensing isoclusting (unsupervised classification) method create a signatures for 10 classes. I then used a Maximum Likelihood Classification function that produced a classified surface based on the signature and the 8 inputs. Two very OOTB functions applied to this novel set of info. What popped out was a big surprise. The example below shows what I mean.

From the original 1's and 0's to this quite interesting, classified space. The only judgments I had to make were:

1. The number of wedges to use - rule of thumb is 45 degree wedges is a good starting point

2. How far out do I look (wedge radius) - in the cover context this is about how far do you walk in a cleared space before you say I am in a cleared space - a thresholding question

3. What value to accumulate in the wedge (if wedges are of equal size a sum is the same as density)

4. The number of classes do I ask for out of the ISOCLUSTER function. Running this many times in many contexts has given me a rule of thumb that 10 classes is usually enough

What had I discovered? Looking at the result I realised it was classifying edge types, that you can think of the original woody cover like a complex edge.

I had, by accident, invented an edge detection filter - I called it Directional Density - the filter uses density values in different direction to classify the central location.

The really nice thing about the workflow was that it could be easily implemented within ArcGIS with out of the box capabilities. Below is an example of the filter implemented in ArcGIS Model Builder

Taking it statewide

I got all excited and applied this to the statewide 5m woody vegetation cover data

Looking up close!

Conclusions

It's great to invent something, it does not happen that often and Directional Density has proved to be very useful over the years. I have applied it to all manner of complex edges from terrain models to multi-criteria cost surfaces it has been a great way to defining boundaries (edges) in a systematic and transparent way.

My take homes on all this:

• don't be afraid to experiment

• look that the full capability of the technology you have, even at those which are not traditionally applied to your area

• thought experiments are a great way to think through the problem you ae trying to solve

• have some fun - the least that can happen is that you will learn something

Feel free to give Directional Density a go I consider it released as Creative Commons with Attribution. Let me know how you go - always interested in hearing about novel applications

Couple of additional things that have come from Directional Density

• you can use those density surfaces coupled with the classes to provide statistically significant summary values

• you can apply this same concept to complex surfaces like terrain models

Ciao