NAME
r.smooth.seg - Generates a piece-wise smooth approximation of the input raster and a discontinuity map.
KEYWORDS
raster,
segmentation,
imagery,
edge detection,
smoothing
SYNOPSIS
r.smooth.seg
r.smooth.seg --help
r.smooth.seg [-k] in_g=name[,name,...] out_u=name out_z=name [lambda=float] [alpha=float] [mxi=integer] [tol=float] [kepsilon=float] [beta=float] [--overwrite] [--help] [--verbose] [--quiet] [--ui]
Flags:
- -k
- Activate MSK model (Mumford-Shah with curvature term)
- --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:
- in_g=name[,name,...] [required]
- Input raster map to segment
- out_u=name [required]
- Output segmented raster map
- out_z=name [required]
- Output raster map with detected discontinuities
- lambda=float
- Smoothness coefficient [>0]
- Default: 1.0
- alpha=float
- Discontinuity coefficient [>0]
- Default: 1.0
- mxi=integer
- Maximal number of numerical iterations
- Default: 100
- tol=float
- Convergence tolerance [>0]
- Default: 0.001
- kepsilon=float
- Discontinuity thickness [>0]
- Default: 1.0
- beta=float
- Curvature coefficient [>=0]
- Default: 0.0
r.smooth.seg generates a piece-wise smooth approximation of the
input raster map and a raster map of the discontinuities of the output
approximation.
The discontinuities of the output approximation are preserved from being
smoothed. The values of the discontinuity map are close to one where the
output approximation is "homogeneous", where the output approximation
has discontinuities (edges) the values are close to zero.
The module makes use of the
varseg library which implements
the Mumford-Shah [1] variational model for image segmentation. The
Mumford-Shah variational model with curvature term [2] is also implemented
in the library. The curvature term prevents the discontinuities from being
shortened too much when the parameter alpha is set to very high values,
(this happens very rarely).
An overview of the underlying theory with some applications can be found in
[3].
Other examples of use of the module can be found
here
and in
this presentation [FOSS4G 2009 - pdf].
For details on the numerical implementation see [4].
Remove any MASK before the execution of the module.
Replace any NULL data (using
r.null) with the map average value (calculate
it with
r.univar).
The segmentation depends on the parameters alpha and lambda:
- alpha controls how many discontinuities are allowed to exist.
- lambda controls the smoothness of the solution.
- It is not possible to select the values of the parameters in an
automatic way. Test some different values to understand their
influence on the results.
Try the following procedure:
- run the module with both alpha and lambda set to 1.0
- run the module with alpha set to 1.0 and different values for lambda
e.g., 0.01, 0.1, 1, 10, 100
- run the module with lambda set to 1.0 and different values for alpha
e.g., 0.01, 0.1, 1, 10, 100
- see how the segmentations change and select the values that
produce the result that best fits your requirements.
The module computes the segmentation by means of an iterative
procedure.
The module stops either when the number of iterations reaches the maximum
number of iterations [mxi] or when the maximum difference between the solutions
of two successive iterations is less than the convergence tolerance [tol].
To stop the iteration procedure, it is easier to act on the maximum number of
iterations parameter [mxi] than on the convergence tolerance parameter [tol].
The number of iterations needed to reach the convergence tolerance increases
for high values of the parameter lambda. The larger the total number of pixels
of the input raster map the larger the number of iterations will be.
The data type of the output raster maps is DOUBLE PRECISION.
The module works on one raster map at a time, imagery groups are not
supported.
To avoid to inappropriately re-sampled the input raster map, the settings
for the current region should be set so that:
- the resolution of the region matches the resolution of the input raster map;
- the boundaries of the region are lined up along the edges of the nearest
cells in the input raster map.
The discontinuity thickness should be changed for test purposes only.
The actual need to use the MSK model should be very rare, see [4].
Due to a different implementation of the MSK model with respect to MS
one, the values of the parameters lambda and alpha in MSK have to be
set independently from the values used in MS.
This example is based on the
North Carolina GRASS sample data set:
# set the region to match the ortho_2001_t792_1m raster map:
g.region raster=ortho_2001_t792_1m -p
# select a smaller region:
g.region n=221725 s=220225 w=638350 e=639550 -p
# run r.smooth.seg:
r.smooth.seg in_g=ortho_2001_t792_1m out_u=u_OF out_z=z_OF lambda=10 alpha=200 mxi=250
# for a better visualization of the output raster map u_OF, set its color table to:
r.colors u_OF raster=ortho_2001_t792_1m
# compute the difference between the input raster map and the output raster map u_OF:
r.mapcalc "diff = abs(ortho_2001_t792_1m@PERMANENT - u_OF)"
# for a better visualization of the differences, compute the natural logarithm of the diff map:
r.mapcalc "log_diff = log(1 + diff)"
# and set its color table to the "differences" style:
r.colors log_diff color=differences
# for a better visualization of the output raster map u_OF, set its color table to:
r.colors z_OF color=bgyr
# run r.smooth.seg with different parameter values:
r.smooth.seg in_g=ortho_2001_t792_1m out_u=u1_OF out_z=z1_OF lambda=10 alpha=65 mxi=250
r.smooth.seg in_g=ortho_2001_t792_1m out_u=u2_OF out_z=z2_OF lambda=10 alpha=600 mxi=250
r.smooth.seg in_g=ortho_2001_t792_1m out_u=u3_OF out_z=z3_OF lambda=0.1 alpha=200 mxi=250
r.smooth.seg in_g=ortho_2001_t792_1m out_u=u4_OF out_z=z4_OF lambda=1 alpha=200 mxi=250
# visualize and compare the different results
- [1] D. Mumford and J. Shah. Optimal Approximation by
Piecewise Smooth Functions and Associated Variational Problems.
Communications on Pure Applied Mathematics, 42(5):577-685, 1989.
DOI: 10.1002/cpa.3160420503
- [2] R. March and M. Dozio. A variational method for the
recovery of smooth boundaries.
Image and Vision Computing,
15(9):705-712, 1997.
DOI: 10.1016/S0262-8856(97)00002-4
- [3] A. Vitti. The Mumford-Shah variational model
for image segmentation: An overview of the theory, implementation and use.
ISPRS Journal of Photogrammetry and Remote Sensing, 69:50-64, 2012.
DOI: 10.1016/j.isprsjprs.2012.02.005
- [4] A. Vitti. Free discontinuity
problems in image and signal segmentatiion.
Ph.D. Thesis - University of Trento (Italy), 2008.
http://www.ing.unitn.it/~vittia/misc/vitti_phd.pdf
i.smap,
i.zc,
r.clump,
r.mfilter
Alfonso Vitti
Dept. Civil, Environmental and Mechanical Engineering
University of Trento - Italy
alfonso.vitti [at] unitn.it
SOURCE CODE
Available at: r.smooth.seg source code (history)
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GRASS Development Team,
GRASS GIS 7.8.3dev Reference Manual