# What are some examples of model-based upscaling of raster data?

Remotely-sensed raster data may be too fine-grained for many purposes.

A typical approach to coarsen the grain is to upscale by reducing the resolution. If the data are continuous (e.g elevation, surface temperature) cells on the raster can be aggregated (and therefore reduced in number) by using a mean function. Or if they are discrete (e.g. vegetation) they may be aggregated using the mode of adjacent cells.

Moving windows are a second example of upscaling. Here a "window" is slid across the raster and the cells under the window are replaced using some function of their values (e.g. using a mean or mode).

I believe that model-based approaches to upscaling will simplify a raster by adopting a more complex model of the raster (i.e. the cells and their adjacencies).

Can anyone clarify my definition of model-based approaches, and provide an example? Do the resulting "cells" even need to be regular, could they vary in shape and size?

EDIT: To be more specific about what I mean by model-based upscaling. Here is an example of what I think may be considered a model-based approach.

Consider using a mathematical graph to represent discrete features on a raster. Then use some method to identify components of these features (i.e. groups of vertices). A Voronoi tessellation, for example, using the components as generators, could then be used to produce an irregular tiling that represents an upscaling of the original raster.

... I could give more detail here, but opt not to, as I am interested in mostly whether or not this would be considered a model-based approach to upscaling ... or alternatively how such operations could be described in generic terms. Is this merely a way of doing interpolation (as defined in an answer below)?

I am not clear what you mean by model-based-upscaling because, within your definition, moving-window approaches should be classed as model-based as they account for cells, their neighbours and some function of relationship or association (be it mean, max, min, std or whatever).

Essentially there are two ways to change the resolution of a raster:

1. Interpolation
2. Aggregation - which can sub-divided into simple aggregation (which would appear to be the first method you describe) and moving window statistics (your second method).

So, I must assume that by model-based methods you mean interpolation. Interpolation is a group of methods of resampling a raster that are very common in image manipulation and by no means exclusive to GIS. . The main methods of resampling a raster by interpolation are (roughly in order of decreasing speed and increasing 'quality'):

• Nearest neighbour
• Bilinear
• Bicubic
• Lancoz
• Spline

There are other methods but they tend to be more obscure. By 'quality' I mean the perceived image quality and not how fit the method might be for a given type of geographic data. You will find most of these methods in your GIS and in Photoshop, GIMP or whatever. Have a look in the ESRi documentation for a nice pictoral description of some of these or turn to Wikipedia for the maths.

Other methods of interpolation that are usually used to create a raster from points include kriging etc. You could potentially use these on your raster (it is only a grid of values after all.

There is another approach to resampling a raster that you see more often in Image procesing and not so much in GIS and that is Gaussian processes. Given its lack of prevelance in GIS, I'll leave that there.

Finally, the resulting cells MUST be regular. How could you have a raster otherwise? That does not mean they have to be square. They could be rectangular and theoretically hexagonal or some other stackable shape but I don't know of any system that uses such shapes. If you cell size does not adequately describe your features, it is either at the wrong resolution (be less agressive with your resampling!) or you might be better off using vector data.

• Agreed that the resulting product wouldn't be a raster if cells weren't regular. However, it is still a data structure that could, in theory, be of value. Thanks for your good coverage of this topic from a GIS perspective. I suspect that what I am after may be not really be a GIS question, per se, but rather one of spatial analysis in general. Commented Apr 12, 2012 at 14:12
• qgis has a hexagonal grid plugin, one example use here by our own @underdark. There is also Pyxsis Innovation's DERM, a hex-based Digital Earth Reference Model, which is very intriguing but which I've not looked at for years (their license model was too restrictive for my taste). Commented Apr 12, 2012 at 19:58
• +1 Very interesting! I will have to have a look at the QGIS hex raster plugin! Commented Apr 12, 2012 at 20:55