# Registration API Design

This contains design ideas for the end-user api when registering images in nipy.

We want to provide a simple api, but with enough flexibility to allow users to changes various components of the pipeline. We will also provide various Standard scripts that perform typical pipelines.

The pluggable script:

    func_img = load_image(filename)
    anat_img = load_image(filename)
    interpolator = SplineInterpolator(order=3)
    metric = NormalizedMutualInformation()
    optimizer = Powell()
    strategy = RegistrationStrategy(interpolator, metric, optimizer)
    w2w = strategy.apply(img_fixed, img_moving)

To apply the transform and resample the image:

    new_img = resample(img_moving, w2w, interp=interpolator)

Or:

    new_img = Image(img_moving, w2w*img_moving.coordmap)

## Transform Multiplication

The multiplication order is important and coordinate systems must make sense. The output coordinates of the mapping on the right-hand of the operator, must match the input coordinates of the mapping on the left-hand side of the operator.

For example, imageA has a mapping from voxels-to-world (v2w), imageB has a mapping from world-to-world (w2w). So the output of imageA, world, maps to the input of imageB, world. We would compose a new mapping (transform) from these mappings like this:

    new_coordmap = imageB.coordmap * imageA.coordmap

If one tried to compose a mapping in the other order, an error should be raised as the code would detect a mismatch of trying to map output coordinates from imageB, world to the input coordinates of imageA, voxels:

    new_coordmap = imageA.coordmap * imageB.coordmap
    raise ValueError!!!

Note: We should consider a meaningful error message to help people quickly correct this mistake.

One way to remember this ordering is to think of composing functions. If these were functions, the output of the first function to evaluate (imageA.coordmap) is passed as input to the second function (imageB.coordmap). And therefore they must match:

    new_coordmap = imageB.coordmap(imageA.coordmap())

## Matching Coordinate Systems

We need to make sure we can detect mismatched coordinate mappings. The CoordinateSystem class has a check for equality (__eq__ method) based on the axis and name attributes. Long-term this may not be robust enough, but it’s a starting place. We should write tests for failing cases of this, if they don’t already exists.

## CoordinateMap

Recall the CoordinateMap defines a mapping between two coordinate systems, an input coordinate system and an output coordinate system. One example of this would be a mapping from voxel space to scanner space. In a Nifti1 header we would have an affine transform to apply this mapping. The input coordinates would be voxel space, the output coordinates would be world space, and the affine transform provides the mapping between them.