Spatial filtering

The major objective of spatial filtering process is to structure the distribution pattern into two components, a regional and a local one. Low-pass filters are operators that smooth the spatial distribution of properties in order to enhance the regional component. Conversely the local component is extracted by retaining the local variations of properties with high-pass filters that use gradient operators. As seen in the Section 3.3.1 of the Lesson 2 about spatial discrete distributions (I-AN, Lesson 2. Discrete Spatial Variables), the spatial context (the neighbourhood) of any cell can be defined form three parameters:

• The size of the filtering window
• The shape of the filtering window
• The proximity to the central cell

The spatial filtering process can be applied in the following geographic information context:

• Information is in image mode (raster format)
• Properties are estimated for each cell in the image, either from an exhaustive description of space or through a regionalisation process
• Spatial distribution can be either continuous or discontinuous
• Properties can be either qualitative or quantitative

As the principles of spatial filtering methods are supposed to be known, let us illustrate the application of such a filtering process on images of change indices.

First example: Dealing with a continuous spatial distribution, we want to analyse the spatial distribution of vegetation density change between 1984 and 2000 in the surrounding area of Fribourg City in Switzerland. A vegetation density index for the two dates was derived from Landsat TM remotely sensed images acquired during the month of July with a spatial resolution of 30m. The Normalised Difference Vegetation Index (NDVI) expresses the global density of vegetation within each pixel. Although this normalised ratio is aimed to compensate for external influences, its values cannot be considered as fully calibrated. However, the analyst wants to identify areas of significant changes in vegetation density between the two dates in order to interpret if it is either a temporary change due to different seasonal conditions or a permanent one. The animation below shows the process for identifying major areas of interest in this example.

Second example: Dealing with a discontinuous spatial distribution, we want to analyse the spatial distribution of landcover types (qualitative level) during the period 1946-2001 in the area of Bulle in Switzerland. The geographical database was built by K. Al Ghamdi (Al-Ghamdi 2008) for his PhD study on the modelling of landcover change in this area. In order to identify landcover change between 1946 and 2001 we have derived a C index as a change indicator. C takes only two possible values: 0 for no change and 1 for any land cover change during this period of time. The animation below shows the process for the detection of all features corresponding to a change in landcover