r.fill.stats(1grass) GRASS GIS User's Manual r.fill.stats(1grass)
NAME
r.fill.stats - Rapidly fills ’no data’ cells (NULLs) of a raster map
with interpolated values (IDW).
KEYWORDS
raster, surface, interpolation, IDW, no-data filling
SYNOPSIS
r.fill.stats
r.fill.stats --help
r.fill.stats [-mkwus] input=name output=name [uncertainty=name] dis-
tance=value mode=name [minimum=value] [maximum=value] power=value
cells=value [--overwrite] [--help] [--verbose] [--quiet] [--ui]
Flags:
-m
Interpret distance as map units, not number of cells
-k
Keep (preserve) original cell values
By default original values are smoothed
-w
Just print the spatial weights matrix
-u
Just print estimated memory usage
-s
Single precision floating point output
--overwrite
Allow output files to overwrite existing files
--help
Print usage summary
--verbose
Verbose module output
--quiet
Quiet module output
--ui
Force launching GUI dialog
Parameters:
input=name [required]
Raster map with data gaps to fill
output=name [required]
Name of result output map
uncertainty=name
Name of uncertainty output map
distance=value [required]
Distance threshold (default: in cells) for interpolation
Default: 3
mode=name [required]
Statistic for interpolated cell values
Options: wmean, mean, median, mode
Default: wmean
minimum=value
Minimum input data value to include in interpolation
maximum=value
Maximum input data value to include in interpolation
power=value [required]
Power coefficient for IDW interpolation
Default: 2.0
cells=value [required]
Minimum number of data cells within search radius
Default: 8
DESCRIPTION
r.fill.stats is a module for fast gap filling and interpolation (with
smoothing) of dense raster data.
The r.fill.stats module is capable of quickly filling small data gaps
in large and high-resolution raster maps. It’s primary purpose is to
improve high-resolution, rasterized sensor data (such as Lidar data).
As a rule of thumb, there should be at least as many data cells as
there are "no data" (NULL) cells in the input raster map. Several in-
terpolation modes are available. By default, all values of the input
raster map will be replaced with locally interpolated values in the
output raster map. This is the equivalent of running a low-pass smooth-
ing filter on the interpolated data and is often desirable, owing to
noisy nature of high-resolution sensor data. With dense data and small
gaps, this should result in only slight deviations from the original
data and produce smooth output. Alternatively, setting the -k flag will
disable the low-pass filter and preserve the original cell values.
Available gap filling modes:
• spatially weighted mean (default)
• simple mean
• simple median
• simple mode
The spatially weighted mean is equivalent to an Inverse Distance
Weighting (IDW; see also r.surf.idw) interpolation. The simple mean is
equivalent to a simple low-pass filter. Median and mode replacements
can also be achieved using r.neighbors.
Note that r.fill.stats is highly optimized for fast processing of large
raster datasets with a small interpolation distance threshold (i.e.
closing small gaps). As a trade-off for speed and a small memory foot
print, some spatial accuracy is lost due to the rounding of the dis-
tance threshold to the closest approximation in input raster cells and
the use of a matrix of precomputed weights at cell resolution (see fur-
ther down for details). Note also that processing time will increase
exponentially with higher distance settings. Cells outside the distance
threshold will not be interpolated, preserving the edges of the origi-
nal data extent.
This module is not well suited for interpolating sparse input data and
closing large gaps. For such purposes more appropriate methods are
available, such as v.surf.idw or v.surf.rst.
Applications where the properties of r.fill.stats are advantageous in-
clude the processing of high resolution, close range scanning and re-
mote sensing datasets. Such datasets commonly feature densely spaced
measurements that have some gaps after rasterization, due to blind
spots, instrument failures, and misalignments between the GIS’ raster
cell grids and the original measurement locations. In these cases,
r.fill.stats should typically be run using the "weighted mean" (de-
fault) method and with a small distance setting (the default is to use
a search radius of just three cells).
The images below show a gradiometer dataset with gaps and its interpo-
lated equivalent, produced using the spatially weighted mean operator
(mode="wmean").
In addition, r.fill.stats can be useful for raster map generalization.
Often, this involves removing small clumps of categorized cells and
then filling the resulting data gaps without "inventing" any new val-
ues. In such cases, the "mode" or "median" interpolators should be
used.
Usage
The most critical user-provided settings are the interpolation/gap
filling method (mode) and the maximum distance, up to which
r.fill.stats will scan for cells with values (distance). The distance
can be expressed as a number of cells (default) or in the current GRASS
location’s units (if the -m flag is given). The latter are typically
meters, but can be any other units of a planar coordinate system.
Note that proper handling of geodetic coordinates (lat/lon) and dis-
tances is currently not implemented. For lat/lon data, the distance
should therefore be specified in cells and usage of r.fill.stats should
be restricted to small areas to avoid large inaccuracies that may arise
from the different extents of cells along the latitudinal and longitu-
dinal axes.
Distances specified in map units (-m flag) will be approximated as ac-
curately as the current region’s cell resolution settings allow. The
program will warn if the distance cannot be expressed as whole cells at
the current region’s resolution. In such case, the number of cells in
the search window will be rounded up. Due to the rounding effect intro-
duced by using cells as spatial units, the actual maximum distance con-
sidered by the interpolation may be up to half a cell diagonal larger
than the one specified by the user.
The interpolator type "wmean" uses a precomputed matrix of spatial
weights to speed up computation. This matrix can be examined (printed
to the screen) before running the interpolation, by setting the -w
flag. In mode "wmean", the power option has the usual meaning in IDW:
higher values mean that cell values in the neighborhood lose their in-
fluence on the cell to be interpolated more rapidly with increasing
distance from the latter. Another way of explaining this effect is to
state that larger "power" settings result in more localized interpola-
tion, smaller ones in more globalized interpolation. The default set-
ting is power=2.0.
The interpolators "mean", "median" and "mode" are calculated from all
cell values within the search radius. No spatial weighting is applied
for these methods. The "mode" of the input data may not always be
unique. In such case, the mode will be the smallest value with the
highest frequency.
Often, input data will contain spurious extreme measurements (spikes,
outliers, noise) caused by the limits of device sensitivity, hardware
defects, environmental influences, etc. If the normal, valid range of
input data is known beforehand, then the minimum and maximum options
can be used to exclude those input cells that have values below or
above that range, respectively. This will prevent the influence of
spikes and outliers from spreading through the interpolation.
Unless the -k (keep) flag is given, data cells of the input map will be
replaced with interpolated values instead of preserving them in the
output. In modes "wmean" and "mean", this results in a smoothing effect
that includes the original data (see below)!
Besides the result of the interpolation/gap filling, a second output
map can be specified via the uncertainty option. The cell values in
this map represent a simple measure of how much uncertainty was in-
volved in interpolating each cell value of the primary output map, with
"0" being the lowest and "1" being the theoretic highest uncertainty.
Uncertainty is measured by summing up all cells in the neighborhood
(defined by the search radius distance) that contain a value in the in-
put map, multiplied by their weights, and dividing the result by the
sum of all weights in the neighborhood. For mode=wmean, this means
that interpolated output cells that were computed from many nearby in-
put cells have very low uncertainty and vice versa. For all other
modes, all weights in the neighborhood are constant "1" and the uncer-
tainty measure is a simple measure of how many input data cells were
present in the search window.
Smoothing
The r.fill.stats module uses the interpolated values to adjust the
original values and create a smooth surface, which is akin to running a
low-pass filter on the data. Since most high-resolution sensor data is
noisy, this is normally a desired effect and results in output that is
more suitable for deriving secondary products, such as slope, aspect
and curvature maps. Larger settings for the search radius (distance)
will result in a stronger smoothing. In practice, some experimentation
with different settings for distance and power might be required to
achieve good results. In some cases (e.g. when dealing with low-noise
or classified data), it might be desirable to turn off data smoothing
by setting the -k (keep) flag. This will ensure that the original cell
data is copied through to the result map without alteration.
Effect of smoothing the original data: The top row shows a gap-filled
surface computed from a rasterized Lidar point cloud (using mode=wmean
and power=2), and the derived slope, aspect, and profile curvature
maps. The smoothing effect is clearly visible. The bottom row shows
the effect of setting the -k flag: Preserving the original cell values
in the interpolated output produces and unsmoothed, noisy surface, and
likewise noisy derivative maps. The effect can be seen in the illus-
tration above: Slope, aspect, and profile curvature are computed using
the r.slope.aspect module, which uses a window (kernel) for computa-
tions that considers only the immediate neighborhood of each cell. When
performed on noisy data, such local operations result in equally noisy
derivatives if the original data is preserved (by setting the -k flag)
and no smoothing is performed.
(Note that the effects of noisy data can also be avoided by using mod-
ules that are not restricted to minimal kernel sizes. For example, as-
pect and other morphometric parameters can be computed using the
r.param.scale module which operates with variable-size cell neighbor-
hoods.)
Spatial weighting scheme
The key to getting good gap filling results is to understand the spa-
tial weighting scheme used in mode "wmean". The weights are precomputed
and assigned per cell within the search window centered on the location
at which to interpolate/gap fill all cells within the user-specified
distance.
The illustration below shows the precomputed weights matrix for a
search distance of four cells from the center cell:
000.00 000.01 000.04 000.07 000.09 000.07 000.04 000.01 000.00
000.01 000.06 000.13 000.19 000.22 000.19 000.13 000.06 000.01
000.04 000.13 000.25 000.37 000.42 000.37 000.25 000.13 000.04
000.07 000.19 000.37 000.56 000.68 000.56 000.37 000.19 000.07
000.09 000.22 000.42 000.68 001.00 000.68 000.42 000.22 000.09
000.07 000.19 000.37 000.56 000.68 000.56 000.37 000.19 000.07
000.04 000.13 000.25 000.37 000.42 000.37 000.25 000.13 000.04
000.01 000.06 000.13 000.19 000.22 000.19 000.13 000.06 000.01
000.00 000.01 000.04 000.07 000.09 000.07 000.04 000.01 000.00
Note that the weights in such a small window drop rapidly for the de-
fault setting of power=2.
If the distance is given in map units (flag -m), then the search window
can be modeled more accurately as a circle. The illustration below
shows the precomputed weights for a distance in map units that is ap-
proximately equivalent to four cells from the center cell:
...... ...... ...... 000.00 000.00 000.00 ...... ...... ......
...... 000.00 000.02 000.06 000.09 000.06 000.02 000.00 ......
...... 000.02 000.11 000.22 000.28 000.22 000.11 000.02 ......
000.00 000.07 000.22 000.44 000.58 000.44 000.22 000.07 000.00
000.00 000.09 000.28 000.58 001.00 000.58 000.28 000.09 000.00
000.00 000.07 000.22 000.44 000.58 000.44 000.22 000.07 000.00
...... 000.02 000.11 000.22 000.28 000.22 000.11 000.02 ......
...... 000.00 000.02 000.06 000.09 000.06 000.02 000.00 ......
...... ...... ...... 000.00 000.00 000.00 ...... ...... ......
When using a small search radius, cells must also be set to a small
value. Otherwise, there may not be enough cells with data within the
search radius to support interpolation.
NOTES
The straight-line metric used for converting distances in map units to
cell numbers is only adequate for planar coordinate systems. Using this
module with lat/lon input data will likely give inaccurate results, es-
pecially when interpolating over large geographical areas.
If the distance is set to a relatively large value, processing time
will quickly approach and eventually exceed that of point-based inter-
polation modules such as v.surf.rst.
This module can handle cells with different X and Y resolutions. How-
ever, note that the weight matrix will be skewed in such cases, with
higher weights occurring close to the center and along the axis with
the higher resolution. This is because weights on the lower resolution
axis are less accurately calculated. The skewing effect will be
stronger if the difference between the X and Y axis resolution is
greater and a larger "power" setting is chosen. This property of the
weights matrix directly reflects the higher information density along
the higher resolution axis.
Note on printing the weights matrix (using the -w flag): the matrix
cannot be printed if it is too large.
The memory estimate provided by the -u flag is a lower limit on the
amount of RAM that will be needed.
If the -s flag is set, floating point type output will be saved as a
"single precision" raster map, saving ~50% disk space compared to the
default "double precision" output.
EXAMPLES
Gap-filling of a dataset using spatially weighted mean (IDW)
Gap-fill a dataset using spatially weighted mean (IDW) and a maximum
search radius of 3.0 map units; also produce uncertainty estimation
map:
r.fill.stats input=measurements output=result dist=3.0 -m mode=wmean uncertainty=uncert_map
Run a fast low-pass filter (replacement all cells with mean value of
neighboring cells) on the input map:
r.fill.stats input=measurements output=result dist=10 mode=mean
Fill data gaps in a categorized raster map; preserve existing data:
r.fill.stats input=categories output=result dist=100 -m mode=mode -k
Lidar point cloud example
Inspect the point density and determine the extent of the point cloud
using the r.in.lidar module:
r.in.lidar -e input=points.las output=density method=n resolution=5 class_filter=2
Based on the result, set computational region extent and desired reso-
lution:
g.region -pa raster=density res=1
Import the point cloud as raster using binning:
r.in.lidar input=points.las output=ground_raw method=mean class_filter=2
Check that there are more non-NULL cells than NULL ("no data") cells:
r.univar map=ground_raw
total null and non-null cells: 2340900
total null cells: 639184
...
Fill in the NULL cells using the default 3-cell search radius:
r.fill.stats input=ground output=ground_filled uncertainty=uncertainty distance=3 mode=wmean power=2.0 cells=8
Binning of Lidar and resulting ground surface with filled gaps. Note
the remaining NULL cells (white) in the resulting ground surface.
These are areas with a lack of cells with values in close proximity.
Outlier removal and gap-filling of SRTM elevation data
In this example, the SRTM elevation map in the North Carolina sample
dataset location is filtered for outlier elevation values; missing pix-
els are then re-interpolated to obtain a complete elevation map:
g.region raster=elev_srtm_30m -p
d.mon wx0
d.histogram elev_srtm_30m
# remove SRTM outliers, i.e. SRTM below 50m (esp. lakes), leading to no data areas
r.mapcalc "elev_srtm_30m_filt = if(elev_srtm_30m < 50.0, null(), elev_srtm_30m)"
d.histogram elev_srtm_30m_filt
d.rast elev_srtm_30m_filt
# using the IDW method to fill these holes in DEM without low-pass filter
# increase distance to gap-fill larger holes
r.fill.stats -k input=elev_srtm_30m_filt output=elev_srtm_30m_idw distance=100
d.histogram elev_srtm_30m_idw
d.rast elev_srtm_30m_idw
r.mapcalc "diff_orig_idw = elev_srtm_30m - elev_srtm_30m_idw"
r.colors diff_orig_idw color=differences
r.univar -e diff_orig_idw
d.erase
d.rast diff_orig_idw
d.legend diff_orig_idw
SEE ALSO
r.fillnulls, r.neighbors, r.surf.idw, v.surf.idw, v.surf.rst
Inverse Distance Weighting in Wikipedia
AUTHOR
Benjamin Ducke
SOURCE CODE
Available at: r.fill.stats source code (history)
Accessed: unknown
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