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Improve documentation of geometric transformations

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Johannes Schönberger
2016-06-21 22:39:54 +02:00
parent d440d1bf74
commit 034a4eb0cf
1 changed files with 7 additions and 16 deletions
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skimage/transform/_geometric.py
+7 -16
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@@ -144,7 +144,7 @@ def _umeyama(src, dst, estimate_scale):
class GeometricTransform(object): class GeometricTransform(object):
"""Perform geometric transformations on a set of coordinates. """Base class for geometric transformations.
""" """
def __call__(self, coords): def __call__(self, coords):
@@ -292,8 +292,7 @@ class ProjectiveTransform(GeometricTransform):
return self._apply_mat(coords, self._inv_matrix) return self._apply_mat(coords, self._inv_matrix)
def estimate(self, src, dst): def estimate(self, src, dst):
"""Set the transformation matrix with the explicit transformation """Estimate the transformation from a set of corresponding points.
parameters.
You can determine the over-, well- and under-determined parameters You can determine the over-, well- and under-determined parameters
with the total least-squares method. with the total least-squares method.
@@ -417,7 +416,6 @@ class ProjectiveTransform(GeometricTransform):
class AffineTransform(ProjectiveTransform): class AffineTransform(ProjectiveTransform):
"""2D affine transformation of the form: """2D affine transformation of the form:
X = a0*x + a1*y + a2 = X = a0*x + a1*y + a2 =
@@ -426,7 +424,7 @@ class AffineTransform(ProjectiveTransform):
Y = b0*x + b1*y + b2 = Y = b0*x + b1*y + b2 =
= sx*x*sin(rotation) + sy*y*cos(rotation + shear) + b2 = sx*x*sin(rotation) + sy*y*cos(rotation + shear) + b2
where ``sx`` and ``sy`` are zoom factors in the x and y directions, where ``sx`` and ``sy`` are scale factors in the x and y directions,
and the homogeneous transformation matrix is:: and the homogeneous transformation matrix is::
[[a0 a1 a2] [[a0 a1 a2]
@@ -509,7 +507,6 @@ class AffineTransform(ProjectiveTransform):
class PiecewiseAffineTransform(GeometricTransform): class PiecewiseAffineTransform(GeometricTransform):
"""2D piecewise affine transformation. """2D piecewise affine transformation.
Control points are used to define the mapping. The transform is based on Control points are used to define the mapping. The transform is based on
@@ -532,7 +529,7 @@ class PiecewiseAffineTransform(GeometricTransform):
self.inverse_affines = None self.inverse_affines = None
def estimate(self, src, dst): def estimate(self, src, dst):
"""Set the control points with which to perform the piecewise mapping. """Estimate the transformation from a set of corresponding points.
Number of source and destination coordinates must match. Number of source and destination coordinates must match.
@@ -652,7 +649,7 @@ class SimilarityTransform(ProjectiveTransform):
Y = b0 * x + a0 * y + b1 = Y = b0 * x + a0 * y + b1 =
= m * x * sin(rotation) + m * y * cos(rotation) + b1 = m * x * sin(rotation) + m * y * cos(rotation) + b1
where ``m`` is a zoom factor and the homogeneous transformation matrix is:: where ``m`` is a scale factor and the homogeneous transformation matrix is::
[[a0 b0 a1] [[a0 b0 a1]
[b0 a0 b1] [b0 a0 b1]
@@ -708,18 +705,13 @@ class SimilarityTransform(ProjectiveTransform):
self.params = np.eye(3) self.params = np.eye(3)
def estimate(self, src, dst): def estimate(self, src, dst):
"""Set the transformation matrix with the explicit parameters. """Estimate the transformation from a set of corresponding points.
You can determine the over-, well- and under-determined parameters You can determine the over-, well- and under-determined parameters
with the total least-squares method. with the total least-squares method.
Number of source and destination coordinates must match. Number of source and destination coordinates must match.
The transformation is defined as::
X = a0 * x - b0 * y + a1
Y = b0 * x + a0 * y + b1
Parameters Parameters
---------- ----------
src : (N, 2) array src : (N, 2) array
@@ -785,8 +777,7 @@ class PolynomialTransform(GeometricTransform):
self.params = params self.params = params
def estimate(self, src, dst, order=2): def estimate(self, src, dst, order=2):
"""Set the transformation matrix with the explicit transformation """Estimate the transformation from a set of corresponding points.
parameters.
You can determine the over-, well- and under-determined parameters You can determine the over-, well- and under-determined parameters
with the total least-squares method. with the total least-squares method.