Density maps using GDAL/OGR python

Having a cloud of points is quite common. This tutorial shows how to calculate the density of points in a set of polygons.
As always, you can download all the data and scripts.

The data

Seeking some data for the tutorial, I found  the  position of all the tornado touchdowns in the period 1950-2004. Calculating the "tornado density" in the US seemed interesting enough.

You can find the data at the data.gov site.

The density can be calculated in a regular grid or a set of polygons. We will do both things, using the US counties as the polygons, which I found at wingis.org

So the downloaded data looks like that when opened in QGIS:

It's easy to see that most of the tornadoes occur in the east half of the USA, but it's still difficult to see actual density differences.

Tornado density in every US county 

First, a script to assign to every county a "tornado touchdown density" value. What the script will do is basically:

1. Open the input datasets: The tornado points file, and the counties file
2. Create the output file, and the fields we will use (name and state name, plus the density field)
3. For each county, we use the method Within for all the points representing the tornadoes. 
4. We calculate the density. Since the file is in latlon projection, the GetArea method would be in square degrees, which is incorrect when comparing, because the actual area would be much smaller in northern regions.
   So we re project the county geometry to the EPSG:900913 projection, which is in meters. I think that is actually incorrect, that the UTM would be better, but the zone changes too much and it's out of the scope of the entry.
   The density is simply the number of tornadoes divided by the county area.
5. We write the output file.

So the code looks like:

from osgeo import ogr
from osgeo import osr
import sys


def density(pointsFile,polygonsFile,outFile):
    #Opening the input files
    dsPolygons = ogr.Open(polygonsFile)
    if dsPolygons is None:
       raise Exception('Could not open ' + pointsFile)
    dsPoints = ogr.Open(pointsFile)
    if dsPoints is None:
       raise Exception('Could not open ' + pointsFile)
    
    polygonsLayer = dsPolygons.GetLayer()
    pointsLayer = dsPoints.GetLayer()


    #Creating the output file

    driverName = "ESRI Shapefile"
    drv = ogr.GetDriverByName( driverName )
    dsOut = drv.CreateDataSource( outFile )  
    outLayer = dsOut.CreateLayer('DENSITY', None, ogr.wkbPolygon)  
    field = ogr.FieldDefn( "Density", ogr.OFTReal )
    outLayer.CreateField ( field )
    field = ogr.FieldDefn( "Name", ogr.OFTString )
    outLayer.CreateField ( field )
    field = ogr.FieldDefn( "State_name", ogr.OFTString )
    outLayer.CreateField ( field )
    
    #Preparing the coordinate transformation
    srsQuery = osr.SpatialReference()
    srsQuery.ImportFromEPSG(4326)    
    srsArea = osr.SpatialReference()
    srsArea.ImportFromEPSG(900913)  

    transf = osr.CoordinateTransformation(srsQuery,srsArea)

    #Iterating all the polygons
    polygonFeature = polygonsLayer.GetNextFeature()
    k=0
    while polygonFeature:
        k = k + 1
        print  "processing " + polygonFeature.GetField("NAME") + " ("+polygonFeature.GetField("STATE_NAME")+") - " + str(k) + " of " + str(polygonsLayer.GetFeatureCount())
         
        geometry = polygonFeature.GetGeometryRef()
        numCounts = 0.0
        pointsLayer.ResetReading()
        pointFeature = pointsLayer.GetNextFeature()
        #Iterating all the points
        while pointFeature:
            if pointFeature.GetGeometryRef().Within(geometry):
                numCounts = numCounts + 1
            pointFeature = pointsLayer.GetNextFeature()
        
        #Calculating the actual area
        geometryArea = geometry.Clone()
        geometryArea.Transform(transf)
        polygonArea = geometryArea.GetArea()/(1000000.0)
        density = numCounts/polygonArea

        #Writting the fields in the output layer
        feature = ogr.Feature( outLayer.GetLayerDefn())
        feature.SetField( "Density", density )
        feature.SetField( "Name", polygonFeature.GetField("NAME") )
        feature.SetField( "State_name", polygonFeature.GetField("STATE_NAME") )

        feature.SetGeometry(geometry)
        outLayer.CreateFeature(feature)        

        polygonFeature = polygonsLayer.GetNextFeature()

    dsOut = None
    dsPolygons = None
    dsPoints = None


if __name__ == "__main__":
    points = sys.argv[1]
    polygons = sys.argv[2]
    outfile = sys.argv[3]

    density(points,polygons,outfile)

To run the script, just type:

python density.py "data/tornadx020.shp" "data/UScounties.shp" "out.shp"

Note that the script isn't for any general case. Different input projections should be handled, and the input fields should be different according to the file. Besides, no geometry checks are done.


The result, opening and colouring the file with QGIS looks like that:

 Now is easy to see that the central USA and Florida have the highest tornado density.

Tornado density in a grid

Sometimes we don't have a particular set of polygons of interest, but a raster where every pixel has the density value is an interesting data.
In this case, the output is created using GDAL instead of OGR, and is a regular grid defined by the user. But the steps are very similar.
As in the example before, the areas in each pixel are in square degrees, and this must be changed to square kilometers.
The code is:

from osgeo import ogr
from osgeo import osr
from osgeo import gdal
from struct import pack
import sys

def density(pointsFile,outFile,x0,y0,x1,y1,samples,lines):
    
    deltax = (x1 - x0) / samples  
    deltay = (y1 - y0) / lines

    dsPoints = ogr.Open(pointsFile)
    if dsPoints is None:
       raise Exception('Could not open ' + pointsFile)
    
    pointsLayer = dsPoints.GetLayer()

    #Creating the output file

    driverName = "ESRI Shapefile"
    drv = ogr.GetDriverByName( driverName )
    
    srsQuery = osr.SpatialReference()
    srsQuery.ImportFromEPSG(4326)    
    srsArea = osr.SpatialReference()
    srsArea.ImportFromEPSG(900913)  

    transf = osr.CoordinateTransformation(srsQuery,srsArea)

    driverName = gdal.GetDriverByName( 'GTiff' )
    dsOut = driverName.Create( outFile, samples, lines, 1, gdal.GDT_Float32)
    dsOut.SetProjection(srsPeticio.ExportToWkt())
    dsOut.SetGeoTransform([x0,deltax,0,y0,0,deltay])
    

    #Iterating all the pixels to write the raster values
    dataString = ''
    for j in range(0,lines):
      for i in range(0,samples):
 print "sample " + str(i) + " line " + str(j)
        px = x0 + deltax * i
        py = y0 + deltay * j
        #The pixel geometry must be created to execute the within method, and to calculate the actual area
        wkt = "POLYGON(("+str(px)+" "+str(py)+","+str(px + deltax)+" "+str(py)+","+str(px + deltax)+" "+str(py+deltay)+","+str(px)+" "+str(py+deltay)+","+str(px)+" "+str(py)+"))"
        
        geometry = ogr.CreateGeometryFromWkt(wkt)
        
        numCounts = 0.0
        pointsLayer.ResetReading()
        pointFeature = pointsLayer.GetNextFeature()
        
        #Iterating all the points
        while pointFeature:
            if pointFeature.GetGeometryRef().Within(geometry):
                numCounts = numCounts + 1
            pointFeature = pointsLayer.GetNextFeature()
        
        geometryArea = geometry.Clone()
        geometryArea.Transform(transf)
        polygonArea = geometryArea.GetArea()/(1000000.0)
        density = numCounts/polygonArea
        dataString = dataString + pack('f',density)
    
    #Writting the raster
    dsOut.GetRasterBand(1).WriteRaster( 0, 0, samples, lines, dataString ) 

    dsOut = None
    dsPoints = None
if __name__ == "__main__":
    points = sys.argv[1]
    outfile = sys.argv[2]
    x0=float(sys.argv[3])
    y0=float(sys.argv[4])
    x1=float(sys.argv[5])
    y1=float(sys.argv[6])
    samples=int(sys.argv[7])
    lines=int(sys.argv[8])

  
    density(points,outfile,x0,y0,x1,y1,samples,lines)

To run the script, type:

python density_raster.py "data/tornadx020.shp" "grid.tiff" -127.0 51.0 -65.0 24.0 50 50

Where the numbers are the coordinates and the size of the output raster as explained in the code.

Again, the script lasts quite a lot to run.

The result seen with QGIS looks like that:

Is similar to the counties map, because both pixels and counties have similar sizes. The result may be easier to handle in this way.

Final thoughts

In the example data, executing the script takes a long time, since 53000 points are given, and there are about 3500 counties. Using PostGIS or so would be faster, but the example doesn't require more installations than GDAL and python.

It would be nice improve the code, creating all the functionalities in a class, checking the input values, accepting different projections, etc.

Remember that all the example is available in a zip file.

Creating a grid from scattered data using inverse of the distance with python (gdal_grid approach)

OK, I have to admit that I was so happy when I found the  scipy rbf function that I went too fast writing the entry about inverse of the distance.
I swear that the images are real (you can check it yourself), but when you change a few parameters or the point position, the result is really strange, definitely not the inverse of the distance algorithm I was thinking about.
Looking a little more around the gdal documentation, I found this explanation, which is very easy and clear:
http://www.gdal.org/grid_tutorial.html
The problem is that, at least in my python gdal version, is not possible to call the function directly, so I've been coding a little to get it.
All the example code and files can be downloaded in a zip file.

First version: the algorithm

Putting all the code directly makes things difficult to understand, so first,  I'll reproduce the same program I wanted to show in the entrance, using matplotlib to show the results:

from math import pow
from math import sqrt
import numpy as np
import matplotlib.pyplot as plt

def pointValue(x,y,power,smoothing,xv,yv,values):
    nominator=0
    denominator=0
    for i in range(0,len(values)):
        dist = sqrt((x-xv[i])*(x-xv[i])+(y-yv[i])*(y-yv[i])+smoothing*smoothing);
        #If the point is really close to one of the data points, return the data point value to avoid singularities
        if(dist<0.0000000001):
            return values[i]
        nominator=nominator+(values[i]/pow(dist,power))
        denominator=denominator+(1/pow(dist,power))
    #Return NODATA if the denominator is zero
    if denominator > 0:
        value = nominator/denominator
    else:
        value = -9999
    return value

def invDist(xv,yv,values,xsize=100,ysize=100,power=2,smoothing=0):
    valuesGrid = np.zeros((ysize,xsize))
    for x in range(0,xsize):
        for y in range(0,ysize):
            valuesGrid[y][x] = pointValue(x,y,power,smoothing,xv,yv,values)
    return valuesGrid
    

if __name__ == "__main__":
    power=1
    smoothing=20

    #Creating some data, with each coodinate and the values stored in separated lists
    xv = [10,60,40,70,10,50,20,70,30,60]
    yv = [10,20,30,30,40,50,60,70,80,90]
    values = [1,2,2,3,4,6,7,7,8,10]
    
    #Creating the output grid (100x100, in the example)
    ti = np.linspace(0, 100, 100)
    XI, YI = np.meshgrid(ti, ti)

    #Creating the interpolation function and populating the output matrix value
    ZI = invDist(xv,yv,values,100,100,power,smoothing)


    # Plotting the result
    n = plt.normalize(0.0, 100.0)
    plt.subplot(1, 1, 1)
    plt.pcolor(XI, YI, ZI)
    plt.scatter(xv, yv, 100, values)
    plt.title('Inv dist interpolation - power: ' + str(power) + ' smoothing: ' + str(smoothing))
    plt.xlim(0, 100)
    plt.ylim(0, 100)
    plt.colorbar()

    plt.show()
    

Let's explain it step by step:

1. The main method defines some sample data, calls the interpolation function and draws it using matplotlib. Just copy&paste, since it's long to explain.
2. invDist function: For each point in the coordinates matrix, a value needs to be calculated. First, a xSize*ySize zeroes values is calculated. Then for each point coordinate (the pixel position, in this simple case), a function that calculates the value is called.
3. This is the important part: We apply the formula: $V=\frac{\sum\limits_{i=1}^n \frac{v_{i}}{d_{i}^{p}}}{\sum\limits_{i=1}^n \frac{1}{d_{i}^{p}}}$ for each pixel.
   
   • V is the interpolated value. 
   • n is the number of points
   • d is the distance from the point to the pixel
   • v is the value of the point
   • p is the power we want to apply to the distance o weight it.
   The distance is the Cartesian one, plus the smoothing factor (it gives more distance than the actual one, lowering the influence around the points). If the distance is close to the precision of the float numbers, we give the data value instead of the interpolated one, to avoid strange results.

And that's all. Here, the results (you can compare them with the ones in the other entry) which are consistent to the inverse of the distance method:

 If the smoothing is zero and the power is high, the interpolation changes a lot around the points to give them their exact value.

If the smoothing is high and the power is one, the result is much smoother, but the values at the points are not maintained.

Adding the GIS stuff:

The example above doesn't write to a GIS file. The function invDist must be changed so it creates the file using a gdal driver:

def invDist(xv,yv,values,geotransform,proj,xSize,ySize,power,smoothing,driverName,outFile):
    #Transform geographic coordinates to pixels
    for i in range(0,len(xv)):
         xv[i] = (xv[i]-geotransform[0])/geotransform[1]
    for i in range(0,len(yv)):
         yv[i] = (yv[i]-geotransform[3])/geotransform[5]
    #Creating the file
    driver = gdal.GetDriverByName( driverName )
    ds = driver.Create( outFile, xSize, ySize, 1, gdal.GDT_Float32)
    if proj is not None:
        ds.SetProjection(proj.ExportToWkt())
    ds.SetGeoTransform(geotransform)
    valuesGrid = np.zeros((ySize,xSize))
    #Getting the interpolated values
    for x in range(0,xSize):
        for y in range(0,ySize):
            valuesGrid[y][x] = pointValue(x,y,power,smoothing,xv,yv,values)
    
    ds.GetRasterBand(1).WriteArray(valuesGrid)
    ds = None
    return valuesGrid

1. Note that the function will  need the geographic parameters geotransform and proj, as well as the output file name and driver.
2. First, the point positions must be changed to pixel locations in order to calculate distances
3. Then, the output file is created with the size and projection asked by the user
4. The values are calculated in the same way as in the other example
5. The file is written

The data in the first example was set into three lists, but the correct way to do it would be read it from a geometry file with the OGR library. Another function is defined to do that:

def readPoints(dataFile,Zfield='Z'):
    data = {}
    xv=[]
    yv=[]
    values=[]
    ds = ogr.Open(dataFile)
    if ds is None:
       raise Exception('Could not open ' + dataFile)
    
    layer = ds.GetLayer()
    proj = layer.GetSpatialRef()
    extent = layer.GetExtent()

    feature = layer.GetNextFeature()
    if feature.GetFieldIndex(zField) == -1:
         raise Exception('zField is not valid: ' + zField)

    while feature:
        geometry = feature.GetGeometryRef()
        xv.append(geometry.GetX())
        yv.append(geometry.GetY())
        values.append(feature.GetField(zField))

        feature = layer.GetNextFeature()
    data['extent'] = extent 
    data['xv']=xv
    data['yv']=yv
    data['values']=values
    data['proj'] = proj
    ds = None
    return data

1. The function reads the point position and values from the given file and field name.
2. A dictionary is returned, to help retrieving all the values we may need to create the output raster. If no projection or geotransform is passed by the user, the input file extents and projection are used.
3. In the example files, a file called points.shp has some sample points to test the functions.

Finally, the main method must get the  parameters from the user, and call the other two methods to create the raster. I have copied some of the input options from the gdal_grid program, so it's easier to test the results. Of course, not all the options are implemented, but it shouldn't be difficult to do it.

if __name__ == "__main__":
    #Setting the default values
    power=2
    smoothing=0
    
    zField='Z'
    dataFile=None
    outFile=None
    driverName='GTiff'
    proj=None

    geotransform = None
    xMin=None
    xMax=None
    yMin=None
    yMax=None
    xSize=100
    ySize=100

    #Parsing the command line
    argv = gdal.GeneralCmdLineProcessor( sys.argv )
    
    i = 1
    while i < len(argv):
        arg = argv[i]
        if arg == '-out_format':
         driverName = argv[i+1]
         driverName = driverName.replace("'","")
         driverName = driverName.replace('"','')
         i = i + 1
        elif arg == '-zfield':
         zField = argv[i+1]
         zField = zField.replace("'","")
         zField = zField.replace('"','')
         i = i + 1
        elif arg == '-a_srs':
         proj = argv[i+1]
         proj = proj.replace("'","")
         proj = proj.replace('"','')
         i = i + 1
        elif arg == '-outsize':
         xSize = argv[i+1]
         xSize = xSize.replace("'","")
         xSize = int(xSize.replace('"',''))
         ySize = argv[i+2]
         ySize = ySize.replace("'","")
         ySize = int(ySize.replace('"',''))
         i = i + 2
        elif arg == '-txe':
         xMin = argv[i+1]
         xMin = xMin.replace("'","")
         xMin = float(xMin.replace('"',''))
         xMax = argv[i+2]
         xMax = xMax.replace("'","")
         xMax = float(xMax.replace('"',''))
         i = i + 2
        elif arg == '-tye':
         yMin = argv[i+1]
         yMin = yMin.replace("'","")
         yMin = float(yMin.replace('"',''))
         yMax = argv[i+2]
         yMax = yMax.replace("'","")
         yMax = float(yMax.replace('"',''))
         i = i + 2
        elif dataFile is None:
         dataFile = arg
         dataFile = dataFile.replace("'","")
         dataFile = dataFile.replace('"','')
        elif outFile is None:
         outFile = arg
         outFile = outFile.replace("'","")
         outFile = outFile.replace('"','')
        i = i + 1



    if dataFile is None or outFile is None:
        usage()
    try:
        data = readPoints(dataFile,zField)
    except Exception,ex:
        print ex
        sys.exit(0)
    if xMin is None:
        xMin=data['extent'][0]
        xMax=data['extent'][1]
    if yMin is None:
        yMin=data['extent'][2]
        yMax=data['extent'][3]

    geotransform=[]
    geotransform.append(xMin)
    geotransform.append((xMax-xMin)/xSize)
    geotransform.append(0)
    geotransform.append(yMax)
    geotransform.append(0)
    geotransform.append((yMin-yMax)/ySize)

    if proj is None:
        proj = data['proj'] 
    else:
        try:
            proj = osr.SpatialReference()
            proj.SetFromUserInput(str(proj))  
        except Exception,ex:
            print ex 
            sys.exit(0)
    #Creating the interpolation function and populating the output matrix value
    try:
        ZI = invDist(data['xv'],data['yv'],data['values'],geotransform,proj,xSize,ySize,power,smoothing,driverName,outFile)
    except Exception,ex:
        print ex
        sys.exit(0)

1. First, the default parameter values are set. Some of them are None, since they are mandatory.
2. Then, the input arguments are read.
3. After having the input arguments, all the parameters that can be set, are set.
4. The function that reads the input file is run, and with it's result, the raster is created. Note that the geotransform is defined from the input file if no one is set by the user.

And the result is something like this when opened with QGis or any GIS:

The points are not coloured, but are the ones in the original file.
The whole code comes in the example file, with all the data you need to run the example.
To generate the picture above, the command is:
 python invdistgis.py -zfield value points.shp out.tiff

What's next

The original gdal_grid implements more interpolation methods (nearest value, and average). Doing the same in the script is as easy as adding other functions to use instead of pointValue.

Also, in the original program, an ellipse can be set to search only in some area around each pixel. This would be a little more difficult do implement, but is easy to find it in the gdal source code in a file called gdalgrid.cpp. I've put it in the example data.

As you can see, implementing this kind of stuff in python is not as difficult as it may seem at the beginning.

Running GDAL Java

The GDAL Java bindings work very well, but the documentation is very very limited.
The API documentation is much better that the one in python, but it's quite difficult to find how to run a simple example.

Installation (Ubuntu)

In the Ubuntu distribution, there is a GDAL package, but the java bindings are not included. So it's necessary to compile the libraries to have it. 

If you have the gdal libraries already installed from the packages, is not necessary to remove them, since you can use just the compiled jar with the old libraries.

Before compiling, make sure that swig, libgeos-dev and proj4 packages are installed.

The, just run:

./configure --with-java --with-static-proj4=[path_to_libproj.la]
make

Go to  the /path_to_gdal/swig/java directory and edit the file java.opt to set the correct JAVA_HOME variable, which is set to a Windows installation by default.
Then type make.
The gdal.jar file will be in the /path_to_gdal/swig/java directory.
The official docs to install the GDAL Java bindings are here: http://trac.osgeo.org/gdal/wiki/GdalOgrInJavaBuildInstructionsUnix

Running the classes

GDAL java bindings use the native GDAL installation, so they make use of JNI. The Java Virtual Machine must find the GDAL binaries. To do so, an environment variable must be set. Froma the command line in linux, the order would be:

 export LD_LIBRARY_PATH=/path_to/gdal-1.9.0/swig/java

where the path is the one you have compiled.

If any coordinate transformation is used in the code, GDAL must find a file named gcs.csv. To find where is this file, just run:

gdal-config --datadir

Then, set the environment variable:

export GDAL_DATA= /path_to_gdal_data

or, even better, execute directly:

export GDAL_DATA=`gdal-config --datadir`

Don't forget to include the file gdal.jar in the classpath, and the class will run properly.

Anyway, is much easier to use an IDE to code in JAVA. Next two sections explain how.

 Running in Eclipse

Using the Eclipse IDE, is possible to configure the environment variables from the configuration window. To do it, click the small arrow next to the play button, and choose Run Configurations...

Once there, choose the Environment tab and add both GDAL_DATA and LD_LIBRARY_PATH using the new button.

Running in Netbeans

I haven't found a graphical solution for configuring both LD_LIBRARY_PATH and GDAL_DATA with Netbeans.

To set these environment variables, locate and open the file netbeans.conf. In my case (ubuntu 12.04), it was located at the path: /usr/local/netbeans-7.0.1/etc/

Add at the end of the file, the lines

export GDAL_DATA=/path_to/gdal/1.9
export LD_LIBRARY_PATH=/path_to/gdal-1.9.0/swig/java

Running in Apache Tomcat

If you are using Apache Tomcat to serve web pages, reading GIS files with GDAL can be a good idea. As in the other cases,  the environment variables must be set.

Edit /path_to_tomcat/bin/catalina.sh (the path may change depending of your installation), and, as in NetBeans, add the lines:

export GDAL_DATA=/path_to/gdal/1.9
export LD_LIBRARY_PATH=/path_to/gdal-1.9.0/swig/java

The libraries must be installed as shared libraries, or the loading will crash if two instances are generated (a java.lang.UnsatisfiedLinkError will be launched).   So:

• Create the directory: $CATALINA_HOME/shared/lib
• Put into this directory the contents of  gdal_home/swig/java, which includes the gdal.jar file
• Edit catalina.properties (in my case was the one under the conf directory) and change the shared.loader variable as:
  shared.loader=${catalina.home}/shared/lib/gdal.jar

Using Maven

gdal.jar is not in the maven repositories (as far as I know), so it must be added manually. Besides, if gdal has to be used in Tomcat in a specific directory, different from the one in maven.

So the pom.xml file has to be edited in the gdal section like this:

<properties>
   <path.shared.gdal>/path/to/apache-tomcat/shared/lib</path.shared.gdal>
</properties>
     
<dependency>
    <groupid>com.osgeo</groupid>
    <artifactid>gdal</artifactid>
    <version>1.9.0</version>
    <scope>system</scope>
    <systempath>${path.shared.gdal}/gdal.jar</systempath>
</dependency>

  Example class

If you want to check how to run a GDAL java class, you can use this example. The class prints the number of bands of the GIS file passed as a parameter:

import org.gdal.gdal.Dataset;
import org.gdal.gdal.gdal;
import org.gdal.gdalconst.gdalconstConstants;

/**
 * Test class for GDAL java bindings 
 */
public class Test {
 Dataset hDataset;
 int numBands;
 public Test(String filename){
  gdal.AllRegister();
  hDataset = gdal.Open(filename, gdalconstConstants.GA_ReadOnly);
  this.numBands = hDataset.getRasterCount();
 }
 /**
  * @param args
  */
 public static void main(String[] args) {
  if(args.length == 0){
   System.out.println("You must pass the file name as an argument");
  } else {
  Test instance = new Test(args[0]);
  System.out.println(instance.numBands);
  }
 }
}

Creating a grid from scattered data using inverse of the distance with python

Attention: I've found some problems in this post. Please read the new one about the same topic.


A usual problem is drawing a map from some scattered data. So it's necessary to set a value for each point in the map from the data in the points already known.
There are different methods used for this purpose, such as kriging or inverse of the distance. The second one is the one used in the example.
The python library scipy has a function called RBF that does that. The code:

import numpy as np
from scipy.interpolate import Rbf

import matplotlib.pyplot as plt

#Creating some data, with each coordinate and the values stored in separated lists
x = [10,60,40,70,10,50,20,70,30,60]
y = [10,20,30,30,40,50,60,70,80,90]
values = [1,2,2,3,4,6,7,7,8,10]

#Creating the output grid (100x100, in the example)
ti = np.linspace(0, 100.0, 100)
XI, YI = np.meshgrid(ti, ti)

#Creating the interpolation function and populating the output matrix value
rbf = Rbf(x, y, values, function='inverse')
ZI = rbf(XI, YI)

# Plotting the result
n = plt.normalize(0.0, 100.0)
plt.subplot(1, 1, 1)
plt.pcolor(XI, YI, ZI)
plt.scatter(x, y, 100, values)
plt.title('RBF interpolation')
plt.xlim(0, 100)
plt.ylim(0, 100)
plt.colorbar()

plt.show() 

When executing the script, the output is an image like this:

 

The Rbf function  takes as arguments the x and y axes, and a list of the values in the points.  A function to use has to be set as well. In our example, inverse of the distance is used, but there are other options, and even a custom function can be used.

Then an output matrix has to be defined. To do it, the new x and y axes must be defined. In our example, a 100x100 pixel matrix has been defined with the meshgrid function.

Finally, the output matrix is created with the function that was th output of the Rbf function. This ZI matrix is what we can use to draw a map.

In this example, there is only a simple plot, but in the next post a real case will be shown.

Colorize raster with GDAL python

As I was telling in my last post, what we usually want is to take a raster file, classify it, and output a png in a color scale.
The easiest way to do it, is using gdaldem with the color-relief option.
But is not in python.
So, if you want to integrate it in a script, or modify it's behavior easily, here you have a solution.
All the example data, including the whole script, dataset, etc, can be downloaded here.

The script:


The first thing to do is reading the color file. As in the gdaldem application, the file is plain text with four columns, value, red value, green value, blue value, and, optionally, the alpha value. We will consider alpha value to be 255 if is not set. The comments are indicated with the hash. This format is the one used in the GRASS r.colors utility
So a function is defined:

def readColorTable(color_file):
    color_table = {}
    if exists(color_file) is False:
        raise Exception("Color file " + color_file + " does not exist")
    
    fp = open(color_file, "r")
    for line in fp:
        if line.find('#') == -1 and line.find('/') == -1:
            entry = line.split()
            if len(entry) == 5:
                alpha = int(entry[4])
            else:
                alpha=0
            color_table[eval(entry[0])]=[int(entry[1]),int(entry[2]),int(entry[3]),alpha]
    fp.close()
    
    return color_table

Once the table is read, is necessary to read the band in the raster file:

from os.path import exists
from osgeo import gdal
from osgeo.gdalconst import GA_ReadOnly
from struct import unpack

data_types ={'Byte':'B','UInt16':'H','Int16':'h','UInt32':'I','Int32':'i','Float32':'f','Float64':'d'}
if exists(raster_file) is False:
    raise Exception('[Errno 2] No such file or directory: \'' + raster_file + '\'')    
    
dataset = gdal.Open(raster_file, GA_ReadOnly )
if dataset == None:
    raise Exception("Unable to read the data file")
band = dataset.GetRasterBand(raster_band)
values = band.ReadRaster( 0, 0, band.XSize, band.YSize, band.XSize, band.YSize, band.DataType )
values = unpack(data_types[gdal.GetDataTypeName(band.DataType)]*band.XSize*band.YSize,values)

Notice that the data types in the struct command and in the GDAL library haven't got the same names, so a dict has to be created to translate them. (Maybe there's a better way to do it, but this one works) A band has to be set. If the file has got only one band (as in our example), the value must be one. Then, two images must be created, one for the colors, an the other for the alpha channel:

import Image
import ImageDraw
base = Image.new( 'RGBA', (band.XSize,band.YSize) )
base_draw = ImageDraw.Draw(base)
alpha_mask = Image.new('L', (band.XSize,band.YSize), 255)
alpha_draw = ImageDraw.Draw(alpha_mask)

Now, the classification is done. There are two modes, the one that gives the exact color defined in the color file, and the one that calculates the color according to the value, and the two nearest colors in the palette. Here, to make more readable, only the exact color is shown:

import Image
color_table = readColorTable(color_file)
classification_values = color_table.keys()
classification_values.sort()
for pos in range(len(values)):
        y = pos/band.XSize
        x = pos - y * band.XSize
        for index in range(len(classification_values)):

            if values[pos] <= classification_values[index] or index == len(classification_values)-1:
                if index == 0:
                        index = 1
                    elif index == len(classification_values)-1 and values[pos] >= classification_values[index]:
                        index = index + 1
                    color = color_table[classification_values[index-1]]
                    base_draw.point((x,y), (color[0],color[1],color[2]))
                    alpha_draw.point((x,y),color[3])
                                    
                    base_draw.point((x,y), (int(r),int(g),int(b)))
                    alpha_draw.point((x,y),int(a))
                    
            break

The first thing to do is getting the values of the color table. Then, for each pixel, the pixel position is calculated. To know the color value to be used, is necessary to iterate all the values in the color table to see which one is just over the pixel value. There is a special case if the pixel value is under the minimum value of the scale. Then, the pixel is set in the color image and the alpha channel. See the break statement to exit the loop.
Once the image and the alpha channel are calculated, the alpha channel has to be blend with the color channel before saving the result:

color_layer = Image.new('RGBA', base.size, (255, 255, 255, 0))
base = Image.composite(color_layer, base, alpha_mask)
base.save(out_file_name)

And that's all.
In the example, everything is packed in a function, and is possible to call it from the command line.
To calculate the color in the -nearest_color_entry mode, the code would be like this for each channel:

r = color_table[classification_values[index-1]][0] + (values[pos] - classification_values[index-1])*(color_table[classification_values[index]][0] - color_table[classification_values[index-1]][0])/(classification_values[index]-classification_values[index-1])

Of course, there is also the special case when the pixel value is lower than the lowest value in the scale or higher than the higher one. The solution is in the script.

Running the code:

We will use the same data of the last post (elevation data from the USGS).
All the sample data and the script is here.
A color file example could be this one (for our elevation data)

1600 166 122 59
1900 180 165 98
2200 188 189 123
2500 74 156 74
2800 123 189 83
3100 165 205 132
3300 255 255 255

To create the file, just type:

python colorize.py -exact_color_entry w001001.adf colorfile.clr out.png

or

python colorize.py -nearest_color_entry w001001.adf colorfile.clr out.png

Sample output with the -exact_color_entry option

Sample output with the default behaviour

It is possible to call the function from another python script just by typing

from colorize import raster2png
try:
    raster2png(file_name,colorfile_name,out_file_name,band,discrete)
except Exception, ex:
    print "Error: " + str(ex) 

If discrete is True, the output is with the exact color in the palette. If is False, with the continuous mode.