A Python lib to estimate scale, rotation, and translation between two sets of 2D points. Applicable for example in cases where one wants to move objects by multiple fingers or where a large number of points from an eye tracker device are wanted to be corrected based on a few calibration points. In general, you can apply nudged in any situation where you want to move a number of points based on a few sample points.
Mathematically speaking, nudged is an optimal least squares estimator for affine transformation matrices with uniform scaling, rotation, and translation and without reflection or shearing. The estimation has time complexity of O(n) that consists of 6n+22 multiplications and 11n+19 additions, where n is the cardinality (size) of the point sets. In other words, nudged solves an affine 2D to 2D point set registration problem in linear time.
Install
$ pip install nudged
Usage
You have lists of points for the domain and range of the tranformation function to be estimated:
dom = [[0,0], [2,0], [ 1,2]] ran = [[1,1], [1,3], [-1,2]]
Compute optimal tranformation based on the points:
trans = nudged.estimate(dom, ran);
Apply the transformation to other points:
trans.transform([2,2]) # [-1,3]
To explore the estimated transformation, you can:
trans.get_matrix() # [[0,-1, 1], # [1, 0, 1], # [0, 0, 1]] trans.get_rotation() # 1.5707... = π / 2 (radians) trans.get_scale() # 1.0 trans.get_translation() # [1, 1]
API
nudged.estimate(dom, ran)
Parameters
dom: domain, list of [x,y] points
ran: range, list of [x,y] points
The dom and ran should have equal length. Different lengths are allowed but additional points in the longer list are ignored in the estimation.
Return a new nudged.Transform(…) instance.
nudged.version
Contains the module version string equal to the version in setup.py.
nudged.Transform(s, r, tx, ty)
An instance returned by the nudged.estimate(…).
In addition to the methods below, it has attributes s, r, tx, ty that define the augmented transformation matrix:
|s -r tx| |r s ty| |0 0 1|
nudged.Transform#transform(points)
Return an list of transformed points or single point if only a point was given. For example:
trans.transform([1,1]) # [2,2] trans.transform([[1,1]]) # [[2,2]] trans.transform([[1,1], [2,3]]) # [[2,2], [3,4]]
nudged.Transform#get_matrix()
Return an 3x3 augmented transformation matrix in the following list format:
[[s,-r, tx], [r, s, ty], [0, 0, 1]]
nudged.Transform#get_rotation()
Return rotation in radians.
nudged.Transform#get_scale()
Return scaling multiplier, e.g. 0.333 for a threefold shrink.
nudged.Transform#get_translation()
Return [tx, ty] where tx and ty denotes movement along x-axis and y-axis accordingly.
For developers
Follow instructions to install pyenv <http://sqa.stackexchange.com/a/15257/14918>`_ and then either run quick tests:
$ python2.7 setup.py test
or comprehensive tests for multiple Python versions in tox.ini:
$ eval "$(pyenv init -)" $ pyenv rehash $ tox
Versioning
License
1 maintainer
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