GRASS raster semantics

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Revision as of 17:33, 4 September 2008 by DylanBeaudette (talk | contribs) (Raster to Vector Conversions)

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A quick summary c/o Glynn Clements:

Region Calculations

Well, the region isn't limited to raster data; it may also affect some vector operations.

The region's bounds describe a rectangle in two-dimensional space. For raster operations, this rectangle is subdivided into a grid of rectangular cells, so the region's bounds are aligned with the edges of the outermost cells.

Cell Locations

Cells are areas, not points, so they don't have locations. Their corners have locations, as do their centres.

A cell with array indices (i,j) (easting, northing) corresponds to the rectangle:

      { (x,y) : west + i * ewres <= x < west + (i+1) * ewres,
                north - (j+1) * nsres <= y < north - j * nsres }

whose centre is at:

      (west + (i+1/2) * ewres, north - (j+1/2) * nsres)

[Subject to wrapping of longitude values in lat/lon locations.]

Raster to Vector Conversions

IIRC, r.to.vect uses the midpoints of the cell's edges (i.e. one coordinate will be on a grid line, the other will be mid-way between grid lines).

Resampling

The built-in nearest-neighbour resampling of raster data calculates the centre of each region cell, and takes the value of the raster cell in which that point falls.

If the point falls exactly upon a grid line, the exact result will be determined by the direction of any rounding error.

[One consequence of this is that downsampling by a factor which is an even integer will always sample exactly on the boundary between cells, meaning that the result is ill-defined.]

r.resample uses the built-in resampling, so it should produce identical results.

r.resamp.interp method=nearest uses the same algorithm, but not the same code, so it may not produce identical results in cases which are decided by the rounding of floating-point numbers.

For method=bilinear and method=bicubic, the raster values are treated as samples at each raster cell's centre, defining a piecewise- continuous surface. The resulting raster values are obtained by sampling the surface at each region cell's centre.

As the algorithm only interpolates, and doesn't extrapolate, a margin of 0.5 (for bilinear) or 1.5 (for bicubic) cells is lost from the extent of the original raster. Any samples taken within this margin will be null.

AFAIK, r.resamp.rst behaves similarly, i.e. it computes a surface assuming that the values are samples at each raster cell's centre, and samples the surface at each region cell's centre.

For r.resamp.stats without -w, the value of each region cell is the chosen aggregate of the values from all of the raster cells whose centres fall within the bounds of the region cell.

With -w, the samples are weighted according to the proportion of the raster cell which falls within the bounds of the region cell, so the result is normally[1] unaffected by rounding error (a miniscule difference in the position of the boundary results in the addition or subtraction of a sample weighted by a miniscule factor).

[1] The min and max aggregates can't use weights, so -w has no effect for those.

General Rules

For the most part, the interpretation is the "obvious" one, given:

1. Cells are areas rather than points. 2. Operations which need a point (e.g. interpolation) use the cell's centre.

Developer Notes Rules

From a programming perspective, the functions:

      G_row_to_northing()
      G_col_to_easting()
      G_northing_to_row()
      G_easting_to_col()

all transform floating-point values.

Passing integer row or column indices to the first two functions will return the coordinates of the cell's top-left corner; for the centre coordinates, pass row+0.5 and/or col+0.5.

Similarly, the last two functions will typically return non-integral values; use floor() to discard the fractional part and obtain the row or column index of the cell within which the point lies.