Image processing with Python and SciPy
Given that NumPy provides multidimensional arrays, and that there is core support through the Python Imaging Library and Matplotlib to display images and manipulate images in the Python environment, it's easy to take the next step and combine these for scientific image processing. As part of our short course on Python for Physics and Astronomy we begin by exploring how Python handle image input and output
Python Imaging Library - PIL
Before we get into the broad area of image processing in Python, there is a caveat for users PIL in Python 3. The essential Python Imaging Library (PIL) is not yet completely compatible with new version of Python. Consequently the FITS tools we will need for astronomical image processing are also currently only supported in the mature versions of Python 2. The comments that follow are based on Python 2.7.
PIL provides functions to manipulate images, including reading, modifying and saving in various standard image formats. Its functions are documented in an on-line manual with a tutorial, and in this handy pdf guide.
As a simple starting example, suppose you have an image that was taken with the camera turned so that "up" is to the side when the image is displayed. Here's how you would rotate an image 90 degrees.
import Image as pil
parser= argparse.ArgumentParser(description = 'Rotate a png image 90 degrees')
if len(sys.argv) == 1: sys.exit("Usage: png_image_rotate file.png ") exit() elif len(sys.argv) == 2: infilename = sys.argv else: sys.exit("Usage: png_image_rotate file.png ") exit()
myimage = pil.open(infilename) mirror = myimage.transpose(pil.ROTATE_90) outfilename = os.path.splitext(os.path.basename(infilename))+'_r90.png' mirror.save(outfilename)
The first part of this is standard form to get the image name on the command line and make it available to the program. The PIL is imported with Image, and appears in the code as "pil". This is an amazingly short program, because in opening the image the library handles all the conversions in formatting and stores the image internally so that you refer to it only by the name assigned when it is loaded. We operate on the image with the transpose function, which has an argument that controls what it does. Here we rotate the image 90 degrees, and then save it to a file with a new name. The saving operation converts the internal data back to the file format set by the extension used in the file name.
You can transpose an image left-right with
mirror = myimage.transpose(pil.FLIP_LEFT_RIGHT)
or do both in one step with
mirror = myimage.transpose(Image.FLIP_LEFT_RIGHT).transpose(pil.ROTATE_90)
Processing is not limited to "PNG" files, though that file type is preferred because it is not a lossy storage option. Python reads and writes "jpg" files too. While PIL provides some essential functionality, for more practical uses in astronomy we need to read Flexible Image Transport or "FITS" files, and to enable numerical work on images in SciPy.
Images with NumPy and SciPy
import numpy as np import matplotlib.pyplot as plt from scipy.misc import imread, imsave
image_data = imread('test.jpg').astype(np.float32) print 'Size: ', image_data.size print 'Shape: ', image_data.shape scaled_image_data = image_data / 255.
# Save the modified image if you want to # imsave('test_out.png', scaled_image_data)
For our 512x512 color test image, this returns
Size: 786432 Shape: (512, 512, 3)
We can display images with matplotlib.pyplot using imshow() --
imshow(X, cmap=None, norm=None, aspect=None, interpolation=None, alpha=None, vmin=None, vmax=None, origin=None, extent=None, **kwargs)
where "X" is the image array. If X is 3-dimensional, imshow will display a color image. Matplotlib has a tutorial on how to manage images. Here, we linearly scale the image data because for floating point imshow requires values between 0. and 1., and we know beforehand that the image is 8-bits with maximum values of 255.
Here's what a single test image displayed from this program looks like in Python.
We can slice the image data to see each color plane by creating new arrays indexed from the original one.
import numpy as np from scipy.misc import imread, imsave import pylab as plt
image_data = imread('test.jpg').astype(np.float32) scaled_image_data = image_data / 255.
print 'Size: ', image_data.size print 'Shape: ', image_data.shape image_slice_red = scaled_image_data[:,:,0] image_slice_green = scaled_image_data[:,:,1] image_slice_blue = scaled_image_data[:,:,2]
print 'Size: ', image_slice_0.size print 'Shape: ', image_slice_0.shape
plt.subplot(221) plt.imshow(image_slice_red, cmap=plt.cm.Reds_r)
plt.subplot(222) plt.imshow(image_slice_green, cmap=plt.cm.Greens_r')
plt.subplot(223) plt.imshow(image_slice_blue, cmap=plt.cm.Blues_r)
For a colorful image you will see the differences between each slice --
This approach offers a template for displaying multidimensional computed or experimental data as an image created with Python. Consider this short program that creates and displays an image with Gaussian noise:
# Import the packages you need import numpy as np import matplotlib.pyplot as plt from scipy.misc import imsave
# Create the image data image_data = np.zeros(512*512, dtype=np.float32).reshape(512,512) random_data = np.random.randn(512,512) image_data = image_data + 100.*random_data print 'Size: ', image_data.size print 'Shape: ', image_data.shape scaled_image_data = image_data / 255.
# Save and display the image imsave('noise.png', scaled_image_data) plt.imshow(scaled_image_data, cmap='gray') plt.show()
Instead of random noise, you could create any functional data you wanted to display. For images with color, the NumPy array would have red, green, and blue planes.
Astronomical FITS files with PyFITS
PyFITS is available from the Space Telescope Science Institute, and can be added easily to a Python installation that already has NumPy and SciPy. As of January 2013, the current version 3.1.1 of PyFITS supports all the functions needed to manage image and table data in the standard Flexibile Image Transport System (FITS) files of astronomy.
Once a FITS file has been read, the header is accessible for reading, and the image data are available in a NumPy array. With PyFITS and NumPY you can read, extract information, modify, display and save image data.
Displaying a FITS file in Python
There are many image display tools for astronomy, and perhaps the most widely used is ds9 which is available for Linux, MacOS, and Windows, as well as in source code. It is useful to have a version on your computer when you are working with FITS images. However, sometimes we want to view an image while we are processing it in Python, and for that we could use a routine such as this one.
import os import sys import argparse import numpy as np import pyfits import matplotlib import matplotlib.pyplot
Sometimes submodules are not loaded with the larger package, and we explictly ask for pyplot.
# Define a function for making a linear gray scale def lingray(x, a=None, b=None): """ Auxiliary function that specifies the linear gray scale. a and b are the cutoffs : if not specified, min and max are used """ if a == None: a = np.min(x) if b == None: b = np.max(x) return 255.0 * (x-float(a))/(b-a)
# Define a function for making a logarithmic gray scale def loggray(x, a=None, b=None): """ Auxiliary function that specifies the logarithmic gray scale. a and b are the cutoffs : if not specified, min and max are used """ if a == None: a = np.min(x) if b == None: b = np.max(x) linval = 10.0 + 990.0 * (x-float(a))/(b-a) return (np.log10(linval)-1.0)*0.5 * 255.0
These functions may be used to rescale the data for display. Scaling can be done with a colormap, or by modifying the data before displaying. Here, we modify the data and save it in a temporary buffer for display. In a more elaborate program with a full user interface, this scaling could be done interactively.
# Provide information to the argparse routine if we need it parser= argparse.ArgumentParser(description = 'Display a fits image')
The argparse function offers more flexibility than the system routines, though here we only include this for future additions.
# Test for command line arguments if len(sys.argv) == 1: sys.exit("Usage: display_fits infile.fits ") exit() elif len(sys.argv) == 2: infits = sys.argv else: sys.exit("Usage: display_fits infile.fits ") exit()
# Open the fits file and create an hdulist inhdulist = pyfits.open(infits)
# Assign the input header in case it is needed later inhdr = inhdulist.header
# Assign image data to a numpy array image_data = inhdulist.data
The header and data are now available. We'll look at header information later. For now, all we need are the values in the numpy data array. It will be indexed from [0,0] at the upper left of the data space, which would be the upper left of the displayed image.
# Print information about the image print 'Size: ', image_data.size print 'Shape: ', image_data.shape
For this example we use linear scaling.
# Show the image new_image_data = lingray(image_data) new_image_min = 0. new_image_max = np.max(new_image_data) matplotlib.pyplot.imshow(new_image_data, vmin = new_image_min, vmax = new_image_max, cmap ='gray') matplotlib.pyplot.show()
# Close the input image file and exit inhdulist.close() exit ()
It would be a straightforward exercise to add an interactive scale control and to read out the value of each pixel in this program. With that, it has the basic functionality of ds9.
Correcting and combining images
There are processing operations done on all "raw" astronomical images taken with charge coupled device cameras. Since the voltage that is digitized is proprotional to the number of photons that arrived at each pixel during the exposure, the data for that pixel should be proportional to the photon count, that is to the irradiance of photons/area-time times the area of the pixel times the exposure time. An absolute conversion to the flux from the sources that are imaged requires correcting for
- Signal at each pixel with no light present -- the "dark" image
- Signal at each pixel for the same irradiance/pixel -- the "flat" field
- Non-linear responses
- Absolute calibration to an energy or photon flux based on spectral response
We can do all of these in NumPy using its built-in array math. By taking an image with no light and subtracting it from an image, we have corrected for the dark response (as well as for electronic "bias"). Or, if needed, we can scale a dark image taken at a different exposure time from the image we are measuring, and then subtract that. We can divide an image by a reference flat to correct for pixel-to-pixel variations in response, for vignetting in an optical system (the non-linear fall-off of transmission across the field of view). We can scale images non-linearly to correct for non-linear amplifier responses and saturation or charge loss from each pixel.
For dark subtraction we take the difference of two images:
dark_corrected_image = raw_image - reference_dark_image
and for flat field correction we divide
final_image = dark_corrected_image / reference_flat_image
In NumPy there is no array indexing needed, and the operations are one-liners. Similarly, a non-linear second order correction or a scaling to physical units may be done on the entire array with
corrected_image = a * (final_image) + b * (final_image**2)
The reference dark and flat images must be obtained beforehand. For example, a reference dark image may be a median average of many images taken with the same exposure time as the science image, but with the shutter closed. To perform the median operation on the arrays rather than sequentially on the elements, we stack all of the original individual dark images to make a 3-d stack of 2-d arrays. Using numpy arrays we would have
dark_stack = np.array([dark_1, dark_2, dark_3])
where dark_1, dark_2, and dark_3 are the original dark images. We need at least 3, or any odd number in the dark stack. If the images are m rows of n columns, and if we have k images in the stack, the stack will have a shape (k,n,m): k images, each of n rows, each of m columns. A median on the first axis of this stack returns the median value for each pixel in the stack --
dark_median = np.median(dark_stack, axis=0)
and has a shape that is (n,m) with the elements that we wanted.
Median operations on a image stack remove random noise more effectively than averaging because one source of noise in CCD images is cosmic ray events that produce an occasional large signal at a pixel. If we mean-averaged with an outlier in one pixel the result would be too large because of the one singular event in the stack, but by median-averaging we discard that event without adversely affecting the new reference frame.
Fortunately, normalizing an image is very simple because
image_mean = np.mean(image_data)
returns the mean value of all elements in the array. Divide an image by its mean to create a normalized image with unity mean
normalized_image = image_data / image_mean
As long as the images have the same size you can sum them by simple addition
sum_image = image1 + image2 + image3 ...
We will open an image v1701_00146_i.fits in interactive Python and look at the header.
import numpy as np import pyfits infits='v1701_00146_i.fits' inhdulist = pyfits.open(infits) inhdr = inhdulist.header inhdr
SIMPLE = T / file does conform to FITS standard BITPIX = 16 / number of bits per data pixel NAXIS = 2 / number of data axes NAXIS1 = 4096 / length of data axis 1 NAXIS2 = 4096 / length of data axis 2 EXTEND = T / FITS dataset may contain extensions COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H BZERO = 32768 / offset data range to that of unsigned short BSCALE = 1 / default scaling factor EXPTIME = 100. / exposure time (seconds) DATE-OBS= '2013-01-19T04:18:09.140' / date of observation (UT) IMAGETYP= 'Light Frame' / image type TARGET = 'V1701 ' / target INSTRUME= 'griz ' / instrument CCD-TEMP= -9.921 / temperature (C) FILTER = ' (3) i (700-825)' / filter TELESCOP= 'CDK20N ' / telescope DATE = '2013-01-19T04:20:08' / file creation date (YYYY-MM-DDThh:mm:ss UT)
The header in PyFITS is a Python dictionary. If you want to know the exposure time, ask
and Python responds
When a new FITS image is written with PyFITS it contains only the bare necessities in the header -- the data type, some reference values for zero and scaling if needed, the size of the array. However you can copy items from the header of an image into images you create, and annotate the headers of your work to maintain a record of what has been done.
An output FITS image file is created in steps from a NumPy data array outimage with
outhdu = pyfits.PrimaryHDU(outimage)
which encapsulates an image in an "HDU" object. The line
outhdulist = pyfits.HDUList([outhdu])
creates a list that contains the primary HDU which will have a default header
outhdr = outhdulist.header
Now you can append to this header or modify it
history = 'This is what I did to the file.' outhdr.append(('HISTORY',history)) more_history = 'I did this today.' outhdr.append(('HISTORY',more_history))
since it is only a standard Python dictionary.
For astronomical images headers may also include information that maps the image to the sky, a World Coordinate System or WCS header within the FITS header. These keywords apply only if the spatial mapping of the image is unchanged, and in processing that shifts or distorts images the WCS header should not be copied. Setting the WCS header and intepreting it to obtain the celestial coordinates requires -- what else -- PyWCS from the Space Telescope Institute.
We have seen that there are many useful basic operations for image processing available simply through NumPy and PyFITS. SciPy adds several others in the ndimage package. The functions include image convolution, various averaging or filtering algorithms, Fourier processing, image interpolation, and image rotation.
Since images are stored as arrays, there are some simple one-line ways to modify them. Flipping an image top to bottom or left to right is done with
import numpy as np np.flipud(image_data) np.fliplr(image_data)
While we also have to add lines to read the file, update the header, and write it out again, the program to preform these operations is remarkably short. A template program is given in the examples below.
Rotating it by 90 degrees is also easy
Rotated and flipped images may be saved either as FITS image (using PyFITS) or as png or jpg images using
from scipy.misc import imsave imsave(filename,rotated_image_data)
Image rotation by other angles is somewhat more complex since it requires tranforming an image in a way that does not preserve its shape, or even the number of elements. We will consider this with the help of scipy.ndimage later.
For example, arbitrary image rotation requires interpolation and will change the shape of an array. There is a simple one-line command that does all this for you
from scipy.misc import imrotate angle = 22.5 new_image = imrotate(image_data, angle, interp='bilinear')
The angle is in degrees. The interp string determines how the interpolation will be done, with self-explanatory options
Finally, for spectroscopy the useful data in an image may be a sum over a region. In that case we could index through the array and explicitly create the sum if needed, but in the ideal case of a spectrum we may want only the sum along a column for each element of a row. For that, the function is
spectrum = np.sum(image, axis)
which returns a numpy array that is the sum along the specified axis. If there are regions in the image that should not be included in the sum, then the image could be masked before computing the sum. The result is a 1-d array in which each element is the signal at a different wavelength.
Sometimes the spectral lines are not along a column but are still straight (if curved, then we need other ways to mask the array), in which case scipy.misc.imrotate can be used before the sum to align the spectrum with a row or column.
We've mentioned that SciKits is a searchable index of tools that are built on SciPy and NumPy. There is an imaging package that includes a very useful tool for astronomy to find local maxima (stars!!) in an image. Look for
The package may be available for your computer system, or if not, the instructions on the website will work for Linux and MacOS. Routines in SciKits are usually not available pre-compiled, which can limit their use in Windows. On an OpenSUSE installation, with SciPy already installed, you will need to run as root
easy_install cython easy_install scikit-image
where the first one is a Python processor for C programs that may (or may not) already be on your system.
We will use this package to identify stars in an image, adapting a program given by Eli Bressert in his book SciPy and NumPy to handle an image from one of our telescopes. The complete program is given in the Examples section below.
It begins with the requisite imports including the ones from SciKit
import os import sys import argparse import matplotlib.pyplot as mpl import numpy as np import pyfits import skimage.morphology as morph import skimage.exposure as skie
It opens an FITS file and loads only part of the image
img = pyfits.getdata(infits)[1000:3000, 1000:3000]
to insure a square sample area and to limit the size of the search region. This is an alternative to reading a FITS image and also getting the header.
With this data the program creates a new image using an mapping arc sinh that captures the full dynamic range effectively. It locates lower and upper bounds that should include only stars. The parameters would probably have to be refined to optimize the extraction of stars from background.
limg = np.arcsinh(img) limg = limg / limg.max() low = np.percentile(limg, 0.25) high = np.percentile(limg, 99.5) opt_img = skie.exposure.rescale_intensity(limg, in_range=(low,high))
With the useful range determined, we create a new image that is scaled between the lower and upper limits that will be used for displaying the star map. We search the arcsinh-stretched original image for local maxima and catalog those brighter than a threshold that is adjusted based on the image.
lm = morph.is_local_maximum(limg) x1, y1 = np.where(lm.T == True) v = limg[(y1,x1)] lim = 0.7 x2, y2 = x1[v > lim], y1[v > lim]
The list x2,y2 has the stars the were found. The rest is image display code to draw circles around the stars and create an image that shows where they are.
When the program processes a 100 second image of the open cluster M34, shown above, it identifies the stars in the right panel below.
For examples of Python illustrating image processing, see the examples section.
For the assigned homework to use these ideas, see the assignments section.