Performing grid histogram equalization

The pygmt.grdhisteq.equalize_grid function creates a grid using statistics based on a cumulative distribution function.

import pygmt

Load sample data

Load the sample Earth relief data for a region around Yosemite valley and use pygmt.grd2xyz to create a pandas.Series with the z values.

grid = pygmt.datasets.load_earth_relief(
    resolution="03s", region=[-119.825, -119.4, 37.6, 37.825]
)
grid_dist = pygmt.grd2xyz(grid=grid, output_type="pandas")["elevation"]

Plot the original digital elevation model and data distribution

For comparison, we will create a map of the original digital elevation model and a histogram showing the distribution of elevation data values.

# Create an instance of the Figure class
fig = pygmt.Figure()
# Define figure configuration
pygmt.config(FORMAT_GEO_MAP="ddd.x", MAP_FRAME_TYPE="plain")
# Define the colormap for the figure
pygmt.makecpt(series=[500, 3540], cmap="turku")
# Setup subplots with two panels
with fig.subplot(
    nrows=1, ncols=2, figsize=("13.5c", "4c"), title="Digital Elevation Model"
):
    # Plot the original digital elevation model in the first panel
    with fig.set_panel(panel=0):
        fig.grdimage(grid=grid, projection="M?", frame="WSne", cmap=True)
    # Plot a histogram showing the z-value distribution in the original digital
    # elevation model
    with fig.set_panel(panel=1):
        fig.histogram(
            data=grid_dist,
            projection="X?",
            region=[500, 3600, 0, 20],
            series=[500, 3600, 100],
            frame=["wnSE", "xaf+lElevation (m)", "yaf+lCounts"],
            cmap=True,
            histtype=1,
            pen="1p,black",
        )
        fig.colorbar(position="JMR+o1.5c/0c+w3c/0.3c", frame=True)
fig.show()
grid equalization

Out:

<IPython.core.display.Image object>

Equalize grid based on a linear distribution

The pygmt.grdhisteq.equalize_grid method creates a new grid with the z-values representing the position of the original z-values in a given cumulative distribution. By default, it computes the position in a linear distribution. Here, we equalize the grid into nine divisions based on a linear distribution and produce a pandas.Series with the z-values for the new grid.

Calculate the bins used for data transformation

The pygmt.grdhisteq.compute_bins method reports statistics about the grid equalization. Here, we report the bins that would linearly divide the original data into 9 divisions with equal area. In our new grid produced by pygmt.grdhisteq.equalize_grid, all the grid cells with values between start and stop of bin_id=0 are assigned the value 0, all grid cells with values between start and stop of bin_id=1 are assigned the value 1, and so on.

start stop
bin_id
0 508.0 1352.0
1 1352.0 1719.0
2 1719.0 1972.0
3 1972.0 2156.0
4 2156.0 2270.0
5 2270.0 2391.0
6 2391.0 2520.0
7 2520.0 2739.0
8 2739.0 3533.0


Plot the equally distributed data

Here we create a map showing the grid that has been transformed to have a linear distribution with nine divisions and a histogram of the data values.

# Create an instance of the Figure class
fig = pygmt.Figure()
# Define figure configuration
pygmt.config(FORMAT_GEO_MAP="ddd.x", MAP_FRAME_TYPE="plain")
# Define the colormap for the figure
pygmt.makecpt(series=[0, divisions, 1], cmap="lajolla")
# Setup subplots with two panels
with fig.subplot(
    nrows=1, ncols=2, figsize=("13.5c", "4c"), title="Linear distribution"
):
    # Plot the grid with a linear distribution in the first panel
    with fig.set_panel(panel=0):
        fig.grdimage(grid=linear, projection="M?", frame="WSne", cmap=True)
    # Plot a histogram showing the linear z-value distribution
    with fig.set_panel(panel=1):
        fig.histogram(
            data=linear_dist,
            projection="X?",
            region=[0, divisions, 0, 40],
            series=[0, divisions, 1],
            frame=["wnSE", "xaf+lElevation (m)", "yaf+lCounts"],
            cmap=True,
            histtype=1,
            pen="1p,black",
        )
        fig.colorbar(position="JMR+o1.5c/0c+w3c/0.3c", frame=True)
fig.show()
grid equalization

Out:

<IPython.core.display.Image object>

Transform grid based on a normal distribution

The gaussian parameter of pygmt.grdhisteq.equalize_grid can be used to transform the z-values relative to their position in a normal distribution rather than a linear distribution. In this case, the output data are continuous rather than discrete.

normal = pygmt.grdhisteq.equalize_grid(grid=grid, gaussian=True)
normal_dist = pygmt.grd2xyz(grid=normal, output_type="pandas")["z"]

Plot the normally distributed data

Here we create a map showing the grid that has been transformed to have a normal distribution and a histogram of the data values.

# Create an instance of the Figure class
fig = pygmt.Figure()
# Define figure configuration
pygmt.config(FORMAT_GEO_MAP="ddd.x", MAP_FRAME_TYPE="plain")
# Define the colormap for the figure
pygmt.makecpt(series=[-4.5, 4.5], cmap="vik")
# Setup subplots with two panels
with fig.subplot(
    nrows=1, ncols=2, figsize=("13.5c", "4c"), title="Normal distribution"
):
    # Plot the grid with a normal distribution in the first panel
    with fig.set_panel(panel=0):
        fig.grdimage(grid=normal, projection="M?", frame="WSne", cmap=True)
    # Plot a histogram showing the normal z-value distribution
    with fig.set_panel(panel=1):
        fig.histogram(
            data=normal_dist,
            projection="X?",
            region=[-4.5, 4.5, 0, 20],
            series=[-4.5, 4.5, 0.2],
            frame=["wnSE", "xaf+lElevation (m)", "yaf+lCounts"],
            cmap=True,
            histtype=1,
            pen="1p,black",
        )
        fig.colorbar(position="JMR+o1.5c/0c+w3c/0.3c", frame=True)
fig.show()
grid equalization

Out:

<IPython.core.display.Image object>

Equalize grid based on a quadratic distribution

The quadratic parameter of pygmt.grdhisteq.equalize_grid can be used to transform the z-values relative to their position in a quadratic distribution rather than a linear distribution. Here, we equalize the grid into nine divisions based on a quadratic distribution and produce a pandas.Series with the z-values for the new grid.

Calculate the bins used for data transformation

We can also use the quadratic parameter of pygmt.grdhisteq.compute_bins to report the bins used for dividing the grid into 9 divisions based on their position in a quadratic distribution.

start stop
bin_id
0 508.0 1155.0
1 1155.0 1375.0
2 1375.0 1605.0
3 1605.0 1821.0
4 1821.0 1972.0
5 1972.0 2131.0
6 2131.0 2245.0
7 2245.0 2391.0
8 2391.0 3533.0


Plot the quadratic distribution of data

Here we create a map showing the grid that has been transformed to have a quadratic distribution and a histogram of the data values.

# Create an instance of the Figure class
fig = pygmt.Figure()
# Define figure configuration
pygmt.config(FORMAT_GEO_MAP="ddd.x", MAP_FRAME_TYPE="plain")
# Define the colormap for the figure
pygmt.makecpt(series=[0, divisions, 1], cmap="lajolla")
# Setup subplots with two panels
with fig.subplot(
    nrows=1, ncols=2, figsize=("13.5c", "4c"), title="Quadratic distribution"
):
    # Plot the grid with a quadratic distribution in the first panel
    with fig.set_panel(panel=0):
        fig.grdimage(grid=quadratic, projection="M?", frame="WSne", cmap=True)
    # Plot a histogram showing the quadratic z-value distribution
    with fig.set_panel(panel=1):
        fig.histogram(
            data=quadratic_dist,
            projection="X?",
            region=[0, divisions, 0, 40],
            series=[0, divisions, 1],
            frame=["wnSE", "xaf+lElevation (m)", "yaf+lCounts"],
            cmap=True,
            histtype=1,
            pen="1p,black",
        )
        fig.colorbar(position="JMR+o1.5c/0c+w3c/0.3c", frame=True)
fig.show()
grid equalization

Out:

<IPython.core.display.Image object>

Total running time of the script: ( 0 minutes 8.656 seconds)

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