grdhisteq

grdhisteq - Perform histogram equalization for a grid

Synopsis

grdhisteq in_grdfile [ -Gout_grdfile ] [ -Cn_cells ] [ -D[file] ] [ -N[norm] ] [ -Q ] -Rregion -V[level]

Note: No space is allowed between the option flag and the associated arguments.

Description

grdhisteq allows the user to find the data values which divide a given grid file into patches of equal area. One common use of grdhisteq is in a kind of histogram equalization of an image. In this application, the user might have a grid of flat topography with a mountain in the middle. Ordinary gray shading of this file (using grdimage or grdview) with a linear mapping from topography to graytone will result in most of the image being very dark gray, with the mountain being almost white. One could use grdhisteq to write to stdout or file an ASCII list of those data values which divide the range of the data into n_cells segments, each of which has an equal area in the image. Using awk or makecpt one can take this output and build a CPT; using the CPT with grdimage will result in an image with all levels of gray occurring equally. Alternatively, see grd2cpt.

The second common use of grdhisteq is in writing a grid with statistics based on some kind of cumulative distribution function. In this application, the output has relative highs and lows in the same (x,y) locations as the input file, but the values are changed to reflect their place in some cumulative distribution. One example would be to find the lowest 10% of the data: Take a grid, run grdhisteq and make a grid using n_cells = 10, and then contour the result to trace the 1 contour. This will enclose the lowest 10% of the data, regardless of their original values. Another example is in equalizing the output of grdgradient. For shading purposes it is desired that the data have a smooth distribution, such as a Gaussian. If you run grdhisteq on output from grdgradient and make a grid file output with the Gaussian option, you will have a grid whose values are distributed according to a Gaussian distribution with zero mean and unit variance. The locations of these values will correspond to the locations of the input; that is, the most negative output value will be in the (x,y) location of the most negative input value, and so on.

Required Arguments

in_grdfile
2-D grid file to be equalized. (See GRID FILE FORMATS below).

Optional Arguments

-Cn_cells
Sets how many cells (or divisions) of data range to make [16].
-D
Dump level information to file, or standard output if no file is provided.
-Gout_grdfile
Name of output 2-D grid file. Used with -N only. (See GRID FILE FORMATS below).
-N[norm]
Gaussian output. Use with -G to make an output grid with standard normal scores. Append norm to force the scores to fall in the <-1,+1> range [Default is standard normal scores].
-Q
Quadratic output. Selects quadratic histogram equalization. [Default is linear].
-Rxmin/xmax/ymin/ymax[+r][+uunit] (more ...)
Specify the region of interest. Using the -R option will select a subsection of in_grdfile grid. If this subsection exceeds the boundaries of the grid, only the common region will be extracted.
-V[level] (more ...)
Select verbosity level [c].
-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explanation of any module-specific option (but not the GMT common options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.

Grid File Formats

By default GMT writes out grid as single precision floats in a COARDS-complaint netCDF file format. However, GMT is able to produce grid files in many other commonly used grid file formats and also facilitates so called "packing" of grids, writing out floating point data as 1- or 2-byte integers. (more ...)

Examples

To find the height intervals that divide the file heights.nc into 16 divisions of equal area:

gmt grdhisteq heights.nc -C16 -D > levels.d

To make the poorly distributed intensities in the file raw_intens.nc suitable for use with grdimage or grdview, run

gmt grdhisteq raw_intens.nc -Gsmooth_intens.nc -N -V

Notes

  1. For geographical grids we do a weighted histogram equalization since the area of each node varies with latitude.
  2. If you use grdhisteq to make a Gaussian output for gradient shading in grdimage or grdview, you should be aware of the following: the output will be in the range [-x, x], where x is based on the number of data in the input grid (nx * ny) and the cumulative Gaussian distribution function F(x). That is, let N = nx * ny. Then x will be adjusted so that F(x) = (N - 1 + 0.5)/N. Since about 68% of the values from a standard normal distribution fall within +/- 1, this will be true of the output grid. But if N is very large, it is possible for x to be greater than 4. Therefore, with the grdview program clipping gradients to the range [-1, 1], you will get correct shading of 68% of your data, while 16% of them will be clipped to -1 and 16% of them clipped to +1. If this makes too much of the image too light or too dark, you should take the output of grdhisteq and rescale it using grdmath and multiplying by something less than 1.0, to shrink the range of the values, thus bringing more than 68% of the image into the range [-1, 1]. Alternatively, supply a normalization factor with -N.