Transform implements a general-purpose coordinate transformation framework for use with NumPy and other scientific analysis software. It defines an object (a Transform) that represents a function mapping R^N->R^M. These Transform objects can be inverted, composed, and manipulated in the same way as their mathematical counterparts. They can be used in two important ways: directly, to manipulate vectors and large arrays of vectors within the NumPy ndarray formalism; and indirectly, to resample discretized data sets such as images.
Subclasses of Transform implement parameterized families of mathematical operations; instances of each subclass represent particular operations from the family, specified at construction time.
The package includes the "transform" module, which defines the main Transform class and some useful general-purpose families of transformations including support for the World Coordinate System transformations that have been adopted into the FITS scientific data standard; and also, once they are released, the "transform.cartography" and "transform.color" modules which define more specific groups of transformations for specific applications
Many objects implement coordinate systems and reprojection between them. For example, astropy.nddata and sunpy.map and NDCube all support several well-known WCS coordinates. These treatments generally handle coordinate system transformation implicitly, requiring the object classes to store hidden knowledge about how the coordinate systems relate -- often through a simple resolver which may or may not allow new coordinate systems, and which may be inefficient in routing transformations through its implicit transformation graph.
By representing coordinate transformations directly and explicitly, Transform allows direct manipulation of transformation graphs, and also ad-hoc transformations (such as distortion correction in scientific images) that are not easily available within a framework that represents only coordinate systems directly.
To load the transform package including defining the Transform object and a collection of useful Transform subclasses, do this::
import transform as t
import numpy as npTransforms can be used on vector data to manipulate them. An example usage is::
a = t.Scale(3, dim=2)
b = np.array( [[1,2],[3,4],[5,6]] )
c = a.apply(b)
print(c)That snippet should output::
[[ 3 6]
[ 9 12]
[15 18]]as the transform "a" represents multiplication of all dimensions by 3.
Other transform instances can represent arbitrarily complex operations, both by composing and inverting many simple operations together and by subclassing transform to define particular mathematical operations.
Transforms can also be used on image data, to change the meaning of the intrinsic pixel coordinate system and/or resample the image to a new coordinate system. To aid scientific usage, Transform can also interpret and manipulate the World Coordinate System (WCS) tags present in many scientific image FITS headers. This interpretation is managed through the astropy.WCS formalism. It is useful, e.g., for aligning images of the same subject collected with different instruments, provided that they have WCS tags attached.
An example usage is::
a = astropy.io.fits.open('myfile.fits')
trans = t.Rotation(45,'deg')
b = trans.remap(a,method='lin')which loads 'myfile.fits' into a, and returns it rotated 45 degrees about its scientific origin, in b. The remap() method includes autoscaling and autoplacement to fit the remapped data onto a specified pixel grid (which defaults to the same size as the original image), so the example above yields a rotated image even if the scientific origin is outside the original pixel grid. The WCS information, if present, is unchanged, so the data are rotated within the scientific coordinate system with the same pixel representation as the original data.
The two methods used for image resampling this way are remap(), which includes WCS interpretation and autoscaling; and resample(), which uses only the intrinsic pixel coordinate system.
This package was ported and adapted from a Perl Data Language module (PDL::Transform) first written in 2001.
Craig DeForest - concept, architecture, development
Matt West - development & testing
Jake Wilson - initial prototype development