Fuzzy classification in GIS is attractive because it offers new possibilities to quantify spatial variability of categorical objects and analyse spatial confusion between the classes. In the case of fuzzy k-means classification, each class is mapped separately as a single membership ranging from 0 (no membership in the class) to 1 (full membership). Consequently, a variable with k classes will result in k membership maps (plus one map for the extragrade class). There are in principle two different ways to produce membership maps:

• By interpolation of sampled data: the membership values from the point samples can be interpolated using compositional kriging to produce membership maps.
• By direct classification of each pixel in the map: here no interpolation is need; the only requirement is that the attributes used to derive distances are mapped over the whole area of interest.

In this article I will demonstrate how to run supervised fuzzy k-means classification in a raster-based GIS ILWIS to derive generic landform positions from terrain data. In ILWIS, it is also possible to use calculations with table and raster data at the same time. This makes this packages especially powerful for per-pixel computations. For more details about the fuzzy k-means classification of landforms or similar classes, see the following references:

Hengl, T., S. Gruber, and D.P. Shrestha. 2003. Digital Terrain Analysis in ILWIS, pp. 26-27. Lecture notes and users' guide, International Institute for Geo-Information Science & Earth Observation (ITC), Enschede, Netherlands.

Hengl T., Walvoort D.J.J., Brown A. 2004. A double continuous approach to visualisation and analysis of categorical maps. Int. Jou. of Geographical Information Science, 18(2): 183-202.

ILWIS scripts and sample dataset with PLANC, SLOPE and ACV maps (94 KB)

Fuzzy k-means in ILWIS - HOW DOES IT WORK?

It takes five steps to derive memberships from PLANC, SLOPE and ACV maps and based on the class centres defined in the table (LF_class). Input parameters: %1 - table with central values has to have same domain as the class map, %2 standard fuzziness factor = 1.5, %3 - domain, %4 - SLOPE, %5 - PLANC and %6 - ACV.

//Calculate distances from the central value to the attribute band per each class and standardise them according to the standard deviation:

t_d11=abs(%4-TBLVALUE(%1, "SLOPE", 1))/TBLVALUE(%1, "SLOPE_STD", 1)
t_d12=abs(%5-TBLVALUE(%1, "PLANC", 1))/TBLVALUE(%1, "PLANC_STD", 1)
t_d13=abs(%6-TBLVALUE(%1, "ACV", 1))/TBLVALUE(%1, "ACV_STD", 1)
t_d21=abs(%4-TBLVALUE(%1, "SLOPE", 2))/TBLVALUE(%1, "SLOPE_STD", 2)
...
t_d63=abs(%6-TBLVALUE(%1, "ACV", 6))/TBLVALUE(%1, "ACV STD", 6)

//Calculate sum�s of distances for each class:

sum_dc1=t d11^2+t d12^2+t d13^2
sum_dc2=t d21^2+t d22^2+t d23^2
...
sum dc6=t d61^2+t d62^2+t d63^2

//Calculate fuzzy factors per each class:

sum_d1=(sum_dc1)^(-1/(%2-1))
sum_d2=(sum_dc2)^(-1/(%2-1))
...
sum d6=(sum dc6)^(-1/(%2-1))

//Sum all fuzzy factors for all classes:

sum_d=sum_d1+sum_d2+sum_d3+sum_d4+sum_d5+sum_d6

//Calculate memberhsips for each class as sum_dc /sum_d:

GLF_Channel{dom=Value, vr=0.000:1.000:0.001}=sum_d1/sum_d
GLF_Pit{dom=Value, vr=0.000:1.000:0.001}=sum_d2/sum_d
...
GLF_Peak{dom=Value, vr=0.000:1.000:0.001}=sum_d6/sum_d

Figure: Membership maps for six generic landform types.

DO-IT-YOURSELF: EXTRACTING GENERIC MORPHOMETRIC FEATURES

STEP 0: Get the most recent version of ILWIS and install it on your PC. Detailed explanation of GIS operations and ILWIS commands can be found in the ILWIS help documentation or user's guides (both available on-line). If you need more details on how to create and run a script, we advise you to read the ILWIS 3.0 Academic user's guide chapter 12. The ILWIS script consists of set of commands that can be used with up to nine script parameters. These can be either spatial objects, values or textual strings. A script, in principle, consists of two parts: definition of script parameters and list of commands. Sign "//" is used to exclude to insert comments and explanation of formulas.

STEP 1: Download and unzip the ILWIS scripts and sample dataset for fuzzy classification in some working directory (e.g. d:\ILWIS_maps\). If you have your own Digital elevation model, then you first need to derive planar curvature (PLANC), slope map (SLOPE) and Anisotrophic Coefficient of Variation (ACV) from it.

TIPS: *Scripts to derive SLOPE, PLANC and ACV you can find here.

Figure: Definition of generic landforms based on three terrain parameters: SLOPE, PLANC and ACV.

STEP 2: Run the script (G_landforms) that will produce six membership maps for channels, ridges, slopes, pits, peaks and plains.
//Created by: T. Hengl (http://spatial-analyst.net)
//Purpose: Supervised Fuzzy k-means classification based on the methodology described in De Gruijter and McBratney (1988),
//Input parameters: %1 - table with central values has to have same domain as the class map, %2 standard fuzziness factor = 1.5, %3 - domain, %4 - SLOPE, %5 - PLANC and %6 - ACV
//Steps: calculate distances as the difference between the xj(Central) and xj(i) and standardise them according to the sampled variation (sx)
//i = class, j = attribute; d13 means - 1st class, 3rd attribute map,
//SLOPE, PLANC and ACV are default names for input maps - these need to be modified otherwise

TIPS: *Note the values in the LF_CLASS table can be easily modified depending on the type of area.

STEP 3: You can visualize each membership separaterly, or only the most probable class.

SEE ALSO:

Classification of generic landforms in Landserf
Fuzzy k-means classification in FuZZME

 

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