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a |
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b/ants/contrib/sampling/affine2d.py |
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""" |
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Affine transforms |
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See http://www.cs.cornell.edu/courses/cs4620/2010fa/lectures/03transforms3D.pdf |
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""" |
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__all__ = [ |
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"Zoom2D", |
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"RandomZoom2D", |
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"Rotate2D", |
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"RandomRotate2D", |
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"Shear2D", |
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"RandomShear2D", |
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"Translate2D", |
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"RandomTranslate2D", |
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] |
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import random |
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import math |
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import numpy as np |
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from ...core import ants_transform as tio |
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class Translate2D(object): |
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""" |
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Create an ANTs Affine Transform with a specified translation. |
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""" |
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def __init__(self, translation, reference=None, lazy=False): |
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""" |
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Initialize a Translate2D object |
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Arguments |
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--------- |
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translation : list or tuple |
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translation values for each axis, in degrees. |
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Negative values can be used for translation in the |
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other direction |
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reference : ANTsImage (optional but recommended) |
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image providing the reference space for the transform. |
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this will also set the transform fixed parameters. |
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lazy : boolean (default = False) |
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if True, calling the `transform` method only returns |
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the randomly generated transform and does not actually |
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transform the image |
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""" |
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if (not isinstance(translation, (list, tuple))) or (len(translation) != 2): |
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raise ValueError("translation argument must be list/tuple with two values!") |
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self.translation = translation |
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self.lazy = lazy |
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self.reference = reference |
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self.tx = tio.ANTsTransform( |
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precision="float", dimension=2, transform_type="AffineTransform" |
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) |
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if self.reference is not None: |
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self.tx.set_fixed_parameters(self.reference.get_center_of_mass()) |
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def transform(self, X=None, y=None): |
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""" |
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Transform an image using an Affine transform with the given |
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translation parameters. Return the transform if X=None. |
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Arguments |
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--------- |
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X : ANTsImage |
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Image to transform |
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y : ANTsImage (optional) |
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Another image to transform |
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Returns |
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------- |
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ANTsImage if y is None, else a tuple of ANTsImage types |
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Examples |
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-------- |
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>>> import ants |
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>>> img = ants.image_read(ants.get_data('r16')) |
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>>> tx = ants.contrib.Translate2D(translation=(10,0)) |
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>>> img2_x = tx.transform(img) |
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>>> tx = ants.contrib.Translate2D(translation=(-10,0)) # other direction |
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>>> img2_x = tx.transform(img) |
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>>> tx = ants.contrib.Translate2D(translation=(0,10)) |
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>>> img2_z = tx.transform(img) |
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>>> tx = ants.contrib.Translate2D(translation=(10,10)) |
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>>> img2 = tx.transform(img) |
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""" |
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# convert to radians and unpack |
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translation_x, translation_y = self.translation |
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translation_matrix = np.array([[1, 0, translation_x], [0, 1, translation_y]]) |
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self.tx.set_parameters(translation_matrix) |
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if self.lazy or X is None: |
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return self.tx |
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else: |
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if y is None: |
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return self.tx.apply_to_image(X, reference=self.reference) |
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else: |
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return ( |
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self.tx.apply_to_image(X, reference=self.reference), |
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self.tx.apply_to_image(y, reference=self.reference), |
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) |
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class RandomTranslate2D(object): |
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""" |
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Apply a Translate2D transform to an image, but with the |
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parameters randomly generated from a user-specified range. |
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The range is determined by a mean (first parameter) and standard deviation |
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(second parameter) via calls to random.gauss. |
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""" |
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def __init__(self, translation_range, reference=None, lazy=False): |
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""" |
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Initialize a RandomTranslate2D object |
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Arguments |
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--------- |
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translation_range : list or tuple |
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Lower and Upper bounds on rotation parameter, in degrees. |
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e.g. translation_range = (-10,10) will result in a random |
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draw of the rotation parameters between -10 and 10 degrees |
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reference : ANTsImage (optional but recommended) |
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image providing the reference space for the transform. |
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this will also set the transform fixed parameters. |
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lazy : boolean (default = False) |
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if True, calling the `transform` method only returns |
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the randomly generated transform and does not actually |
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transform the image |
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""" |
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if (not isinstance(translation_range, (list, tuple))) or ( |
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len(translation_range) != 2 |
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): |
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raise ValueError("shear_range argument must be list/tuple with two values!") |
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self.translation_range = translation_range |
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self.reference = reference |
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self.lazy = lazy |
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def transform(self, X=None, y=None): |
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""" |
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Transform an image using an Affine transform with |
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translation parameters randomly generated from the user-specified |
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range. Return the transform if X=None. |
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Arguments |
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--------- |
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X : ANTsImage |
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Image to transform |
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y : ANTsImage (optional) |
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Another image to transform |
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Returns |
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------- |
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ANTsImage if y is None, else a tuple of ANTsImage types |
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Examples |
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-------- |
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>>> import ants |
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>>> img = ants.image_read(ants.get_data('r16')) |
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>>> tx = ants.contrib.RandomShear2D(translation_range=(-10,10)) |
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>>> img2 = tx.transform(img) |
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""" |
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# random draw in translation range |
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translation_x = random.gauss( |
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self.translation_range[0], self.translation_range[1] |
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) |
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translation_y = random.gauss( |
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self.translation_range[0], self.translation_range[1] |
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) |
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self.params = (translation_x, translation_y) |
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tx = Translate2D( |
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(translation_x, translation_y), reference=self.reference, lazy=self.lazy |
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) |
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return tx.transform(X, y) |
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class Shear2D(object): |
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""" |
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Create an ANTs Affine Transform with a specified shear. |
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""" |
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def __init__(self, shear, reference=None, lazy=False): |
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""" |
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Initialize a Shear2D object |
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Arguments |
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--------- |
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shear : list or tuple |
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shear values for each axis, in degrees. |
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Negative values can be used for shear in the |
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other direction |
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reference : ANTsImage (optional but recommended) |
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image providing the reference space for the transform. |
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this will also set the transform fixed parameters. |
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lazy : boolean (default = False) |
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if True, calling the `transform` method only returns |
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the randomly generated transform and does not actually |
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transform the image |
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""" |
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if (not isinstance(shear, (list, tuple))) or (len(shear) != 2): |
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raise ValueError("shear argument must be list/tuple with two values!") |
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self.shear = shear |
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self.lazy = lazy |
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self.reference = reference |
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self.tx = tio.ANTsTransform( |
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precision="float", dimension=2, transform_type="AffineTransform" |
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) |
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if self.reference is not None: |
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self.tx.set_fixed_parameters(self.reference.get_center_of_mass()) |
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def transform(self, X=None, y=None): |
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""" |
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Transform an image using an Affine transform with the given |
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shear parameters. Return the transform if X=None. |
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Arguments |
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--------- |
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X : ANTsImage |
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Image to transform |
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y : ANTsImage (optional) |
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Another image to transform |
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Returns |
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------- |
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ANTsImage if y is None, else a tuple of ANTsImage types |
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Examples |
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-------- |
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>>> import ants |
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>>> img = ants.image_read(ants.get_data('r16')) |
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>>> tx = ants.contrib.Shear2D(shear=(10,0,0)) |
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>>> img2_x = tx.transform(img)# x axis stays same |
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>>> tx = ants.contrib.Shear2D(shear=(-10,0,0)) # other direction |
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>>> img2_x = tx.transform(img)# x axis stays same |
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>>> tx = ants.contrib.Shear2D(shear=(0,10,0)) |
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>>> img2_y = tx.transform(img) # y axis stays same |
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>>> tx = ants.contrib.Shear2D(shear=(0,0,10)) |
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>>> img2_z = tx.transform(img) # z axis stays same |
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>>> tx = ants.contrib.Shear2D(shear=(10,10,10)) |
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>>> img2 = tx.transform(img) |
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""" |
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# convert to radians and unpack |
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shear = [math.pi / 180 * s for s in self.shear] |
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shear_x, shear_y = shear |
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shear_matrix = np.array([[1, shear_x, 0], [shear_y, 1, 0]]) |
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self.tx.set_parameters(shear_matrix) |
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if self.lazy or X is None: |
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return self.tx |
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else: |
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if y is None: |
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return self.tx.apply_to_image(X, reference=self.reference) |
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else: |
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return ( |
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self.tx.apply_to_image(X, reference=self.reference), |
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self.tx.apply_to_image(y, reference=self.reference), |
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) |
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274 |
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275 |
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class RandomShear2D(object): |
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""" |
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Apply a Shear2D transform to an image, but with the shear |
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parameters randomly generated from a user-specified range. |
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280 |
The range is determined by a mean (first parameter) and standard deviation |
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281 |
(second parameter) via calls to random.gauss. |
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282 |
""" |
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283 |
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def __init__(self, shear_range, reference=None, lazy=False): |
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""" |
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286 |
Initialize a RandomShear2D object |
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287 |
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Arguments |
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--------- |
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shear_range : list or tuple |
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291 |
Lower and Upper bounds on rotation parameter, in degrees. |
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292 |
e.g. shear_range = (-10,10) will result in a random |
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293 |
draw of the rotation parameters between -10 and 10 degrees |
|
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294 |
|
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295 |
reference : ANTsImage (optional but recommended) |
|
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296 |
image providing the reference space for the transform. |
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297 |
this will also set the transform fixed parameters. |
|
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298 |
|
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299 |
lazy : boolean (default = False) |
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300 |
if True, calling the `transform` method only returns |
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301 |
the randomly generated transform and does not actually |
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302 |
transform the image |
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303 |
""" |
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304 |
if (not isinstance(shear_range, (list, tuple))) or (len(shear_range) != 2): |
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305 |
raise ValueError("shear_range argument must be list/tuple with two values!") |
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306 |
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self.shear_range = shear_range |
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self.reference = reference |
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309 |
self.lazy = lazy |
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310 |
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311 |
def transform(self, X=None, y=None): |
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312 |
""" |
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313 |
Transform an image using an Affine transform with |
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314 |
shear parameters randomly generated from the user-specified |
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315 |
range. Return the transform if X=None. |
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316 |
|
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317 |
Arguments |
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318 |
--------- |
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X : ANTsImage |
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320 |
Image to transform |
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321 |
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y : ANTsImage (optional) |
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323 |
Another image to transform |
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324 |
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325 |
Returns |
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326 |
------- |
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327 |
ANTsImage if y is None, else a tuple of ANTsImage types |
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328 |
|
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329 |
Examples |
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330 |
-------- |
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331 |
>>> import ants |
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332 |
>>> img = ants.image_read(ants.get_data('r16')) |
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333 |
>>> tx = ants.contrib.RandomShear2D(shear_range=(-10,10)) |
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334 |
>>> img2 = tx.transform(img) |
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335 |
""" |
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336 |
# random draw in shear range |
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337 |
shear_x = random.gauss(self.shear_range[0], self.shear_range[1]) |
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338 |
shear_y = random.gauss(self.shear_range[0], self.shear_range[1]) |
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339 |
self.params = (shear_x, shear_y) |
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340 |
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341 |
tx = Shear2D((shear_x, shear_y), reference=self.reference, lazy=self.lazy) |
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342 |
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343 |
return tx.transform(X, y) |
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344 |
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345 |
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346 |
class Rotate2D(object): |
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347 |
""" |
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348 |
Create an ANTs Affine Transform with a specified level |
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349 |
of rotation. |
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350 |
""" |
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351 |
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352 |
def __init__(self, rotation, reference=None, lazy=False): |
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353 |
""" |
|
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354 |
Initialize a Rotate2D object |
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355 |
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356 |
Arguments |
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357 |
--------- |
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358 |
rotation : scalar |
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359 |
rotation value in degrees. |
|
|
360 |
Negative values can be used for rotation in the |
|
|
361 |
other direction |
|
|
362 |
|
|
|
363 |
reference : ANTsImage (optional but recommended) |
|
|
364 |
image providing the reference space for the transform. |
|
|
365 |
this will also set the transform fixed parameters. |
|
|
366 |
|
|
|
367 |
lazy : boolean (default = False) |
|
|
368 |
if True, calling the `transform` method only returns |
|
|
369 |
the randomly generated transform and does not actually |
|
|
370 |
transform the image |
|
|
371 |
""" |
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372 |
self.rotation = rotation |
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373 |
self.lazy = lazy |
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374 |
self.reference = reference |
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375 |
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376 |
self.tx = tio.ANTsTransform( |
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377 |
precision="float", dimension=2, transform_type="AffineTransform" |
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378 |
) |
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379 |
if self.reference is not None: |
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380 |
self.tx.set_fixed_parameters(self.reference.get_center_of_mass()) |
|
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381 |
|
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382 |
def transform(self, X=None, y=None): |
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|
383 |
""" |
|
|
384 |
Transform an image using an Affine transform with the given |
|
|
385 |
rotation parameters. Return the transform if X=None. |
|
|
386 |
|
|
|
387 |
Arguments |
|
|
388 |
--------- |
|
|
389 |
X : ANTsImage |
|
|
390 |
Image to transform |
|
|
391 |
|
|
|
392 |
y : ANTsImage (optional) |
|
|
393 |
Another image to transform |
|
|
394 |
|
|
|
395 |
Returns |
|
|
396 |
------- |
|
|
397 |
ANTsImage if y is None, else a tuple of ANTsImage types |
|
|
398 |
|
|
|
399 |
Examples |
|
|
400 |
-------- |
|
|
401 |
>>> import ants |
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|
402 |
>>> img = ants.image_read(ants.get_data('r16')) |
|
|
403 |
>>> tx = ants.contrib.Rotate2D(rotation=(10,-5,12)) |
|
|
404 |
>>> img2 = tx.transform(img) |
|
|
405 |
""" |
|
|
406 |
# unpack zoom range |
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407 |
rotation = self.rotation |
|
|
408 |
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|
409 |
# Rotation about X axis |
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|
410 |
theta = math.pi / 180 * rotation |
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|
411 |
rotation_matrix = np.array( |
|
|
412 |
[[np.cos(theta), -np.sin(theta), 0], [np.sin(theta), np.cos(theta), 0]] |
|
|
413 |
) |
|
|
414 |
|
|
|
415 |
self.tx.set_parameters(rotation_matrix) |
|
|
416 |
if self.lazy or X is None: |
|
|
417 |
return self.tx |
|
|
418 |
else: |
|
|
419 |
if y is None: |
|
|
420 |
return self.tx.apply_to_image(X, reference=self.reference) |
|
|
421 |
else: |
|
|
422 |
return ( |
|
|
423 |
self.tx.apply_to_image(X, reference=self.reference), |
|
|
424 |
self.tx.apply_to_image(y, reference=self.reference), |
|
|
425 |
) |
|
|
426 |
|
|
|
427 |
|
|
|
428 |
class RandomRotate2D(object): |
|
|
429 |
""" |
|
|
430 |
Apply a Rotated2D transform to an image, but with the zoom |
|
|
431 |
parameters randomly generated from a user-specified range. |
|
|
432 |
The range is determined by a mean (first parameter) and standard deviation |
|
|
433 |
(second parameter) via calls to random.gauss. |
|
|
434 |
""" |
|
|
435 |
|
|
|
436 |
def __init__(self, rotation_range, reference=None, lazy=False): |
|
|
437 |
""" |
|
|
438 |
Initialize a RandomRotate2D object |
|
|
439 |
|
|
|
440 |
Arguments |
|
|
441 |
--------- |
|
|
442 |
rotation_range : list or tuple |
|
|
443 |
Lower and Upper bounds on rotation parameter, in degrees. |
|
|
444 |
e.g. rotation_range = (-10,10) will result in a random |
|
|
445 |
draw of the rotation parameters between -10 and 10 degrees |
|
|
446 |
|
|
|
447 |
reference : ANTsImage (optional but recommended) |
|
|
448 |
image providing the reference space for the transform. |
|
|
449 |
this will also set the transform fixed parameters. |
|
|
450 |
|
|
|
451 |
lazy : boolean (default = False) |
|
|
452 |
if True, calling the `transform` method only returns |
|
|
453 |
the randomly generated transform and does not actually |
|
|
454 |
transform the image |
|
|
455 |
""" |
|
|
456 |
if (not isinstance(rotation_range, (list, tuple))) or ( |
|
|
457 |
len(rotation_range) != 2 |
|
|
458 |
): |
|
|
459 |
raise ValueError( |
|
|
460 |
"rotation_range argument must be list/tuple with two values!" |
|
|
461 |
) |
|
|
462 |
|
|
|
463 |
self.rotation_range = rotation_range |
|
|
464 |
self.reference = reference |
|
|
465 |
self.lazy = lazy |
|
|
466 |
|
|
|
467 |
def transform(self, X=None, y=None): |
|
|
468 |
""" |
|
|
469 |
Transform an image using an Affine transform with |
|
|
470 |
rotation parameters randomly generated from the user-specified |
|
|
471 |
range. Return the transform if X=None. |
|
|
472 |
|
|
|
473 |
Arguments |
|
|
474 |
--------- |
|
|
475 |
X : ANTsImage |
|
|
476 |
Image to transform |
|
|
477 |
|
|
|
478 |
y : ANTsImage (optional) |
|
|
479 |
Another image to transform |
|
|
480 |
|
|
|
481 |
Returns |
|
|
482 |
------- |
|
|
483 |
ANTsImage if y is None, else a tuple of ANTsImage types |
|
|
484 |
|
|
|
485 |
Examples |
|
|
486 |
-------- |
|
|
487 |
>>> import ants |
|
|
488 |
>>> img = ants.image_read(ants.get_data('r16')) |
|
|
489 |
>>> tx = ants.contrib.RandomRotate2D(rotation_range=(-10,10)) |
|
|
490 |
>>> img2 = tx.transform(img) |
|
|
491 |
""" |
|
|
492 |
# random draw in rotation range |
|
|
493 |
rotation = random.gauss(self.rotation_range[0], self.rotation_range[1]) |
|
|
494 |
self.params = rotation |
|
|
495 |
|
|
|
496 |
tx = Rotate2D(rotation, reference=self.reference, lazy=self.lazy) |
|
|
497 |
|
|
|
498 |
return tx.transform(X, y) |
|
|
499 |
|
|
|
500 |
|
|
|
501 |
class Zoom2D(object): |
|
|
502 |
""" |
|
|
503 |
Create an ANTs Affine Transform with a specified level |
|
|
504 |
of zoom. Any value greater than 1 implies a "zoom-out" and anything |
|
|
505 |
less than 1 implies a "zoom-in". |
|
|
506 |
""" |
|
|
507 |
|
|
|
508 |
def __init__(self, zoom, reference=None, lazy=False): |
|
|
509 |
""" |
|
|
510 |
Initialize a Zoom2D object |
|
|
511 |
|
|
|
512 |
Arguments |
|
|
513 |
--------- |
|
|
514 |
zoom_range : list or tuple |
|
|
515 |
Lower and Upper bounds on zoom parameter. |
|
|
516 |
e.g. zoom_range = (0.7,0.9) will result in a random |
|
|
517 |
draw of the zoom parameters between 0.7 and 0.9 |
|
|
518 |
|
|
|
519 |
reference : ANTsImage (optional but recommended) |
|
|
520 |
image providing the reference space for the transform. |
|
|
521 |
this will also set the transform fixed parameters. |
|
|
522 |
|
|
|
523 |
lazy : boolean (default = False) |
|
|
524 |
if True, calling the `transform` method only returns |
|
|
525 |
the randomly generated transform and does not actually |
|
|
526 |
transform the image |
|
|
527 |
""" |
|
|
528 |
if (not isinstance(zoom, (list, tuple))) or (len(zoom) != 2): |
|
|
529 |
raise ValueError("zoom_range argument must be list/tuple with two values!") |
|
|
530 |
|
|
|
531 |
self.zoom = zoom |
|
|
532 |
self.lazy = lazy |
|
|
533 |
self.reference = reference |
|
|
534 |
|
|
|
535 |
self.tx = tio.ANTsTransform( |
|
|
536 |
precision="float", dimension=2, transform_type="AffineTransform" |
|
|
537 |
) |
|
|
538 |
if self.reference is not None: |
|
|
539 |
self.tx.set_fixed_parameters(self.reference.get_center_of_mass()) |
|
|
540 |
|
|
|
541 |
def transform(self, X=None, y=None): |
|
|
542 |
""" |
|
|
543 |
Transform an image using an Affine transform with the given |
|
|
544 |
zoom parameters. Return the transform if X=None. |
|
|
545 |
|
|
|
546 |
Arguments |
|
|
547 |
--------- |
|
|
548 |
X : ANTsImage |
|
|
549 |
Image to transform |
|
|
550 |
|
|
|
551 |
y : ANTsImage (optional) |
|
|
552 |
Another image to transform |
|
|
553 |
|
|
|
554 |
Returns |
|
|
555 |
------- |
|
|
556 |
ANTsImage if y is None, else a tuple of ANTsImage types |
|
|
557 |
|
|
|
558 |
Examples |
|
|
559 |
-------- |
|
|
560 |
>>> import ants |
|
|
561 |
>>> img = ants.image_read(ants.get_data('r16')) |
|
|
562 |
>>> tx = ants.contrib.Zoom2D(zoom=(0.8,0.8,0.8)) |
|
|
563 |
>>> img2 = tx.transform(img) |
|
|
564 |
""" |
|
|
565 |
# unpack zoom range |
|
|
566 |
zoom_x, zoom_y = self.zoom |
|
|
567 |
|
|
|
568 |
self.params = (zoom_x, zoom_y) |
|
|
569 |
zoom_matrix = np.array([[zoom_x, 0, 0], [0, zoom_y, 0]]) |
|
|
570 |
self.tx.set_parameters(zoom_matrix) |
|
|
571 |
if self.lazy or X is None: |
|
|
572 |
return self.tx |
|
|
573 |
else: |
|
|
574 |
if y is None: |
|
|
575 |
return self.tx.apply_to_image(X, reference=self.reference) |
|
|
576 |
else: |
|
|
577 |
return ( |
|
|
578 |
self.tx.apply_to_image(X, reference=self.reference), |
|
|
579 |
self.tx.apply_to_image(y, reference=self.reference), |
|
|
580 |
) |
|
|
581 |
|
|
|
582 |
|
|
|
583 |
class RandomZoom2D(object): |
|
|
584 |
""" |
|
|
585 |
Apply a Zoom2D transform to an image, but with the zoom |
|
|
586 |
parameters randomly generated from a user-specified range. |
|
|
587 |
The range is determined by a mean (first parameter) and standard deviation |
|
|
588 |
(second parameter) via calls to random.gauss. |
|
|
589 |
""" |
|
|
590 |
|
|
|
591 |
def __init__(self, zoom_range, reference=None, lazy=False): |
|
|
592 |
""" |
|
|
593 |
Initialize a RandomZoom2D object |
|
|
594 |
|
|
|
595 |
Arguments |
|
|
596 |
--------- |
|
|
597 |
zoom_range : list or tuple |
|
|
598 |
Lower and Upper bounds on zoom parameter. |
|
|
599 |
e.g. zoom_range = (0.7,0.9) will result in a random |
|
|
600 |
draw of the zoom parameters between 0.7 and 0.9 |
|
|
601 |
|
|
|
602 |
reference : ANTsImage (optional but recommended) |
|
|
603 |
image providing the reference space for the transform. |
|
|
604 |
this will also set the transform fixed parameters. |
|
|
605 |
|
|
|
606 |
lazy : boolean (default = False) |
|
|
607 |
if True, calling the `transform` method only returns |
|
|
608 |
the randomly generated transform and does not actually |
|
|
609 |
transform the image |
|
|
610 |
""" |
|
|
611 |
if (not isinstance(zoom_range, (list, tuple))) or (len(zoom_range) != 2): |
|
|
612 |
raise ValueError("zoom_range argument must be list/tuple with two values!") |
|
|
613 |
|
|
|
614 |
self.zoom_range = zoom_range |
|
|
615 |
self.reference = reference |
|
|
616 |
self.lazy = lazy |
|
|
617 |
|
|
|
618 |
def transform(self, X=None, y=None): |
|
|
619 |
""" |
|
|
620 |
Transform an image using an Affine transform with |
|
|
621 |
zoom parameters randomly generated from the user-specified |
|
|
622 |
range. Return the transform if X=None. |
|
|
623 |
|
|
|
624 |
Arguments |
|
|
625 |
--------- |
|
|
626 |
X : ANTsImage |
|
|
627 |
Image to transform |
|
|
628 |
|
|
|
629 |
y : ANTsImage (optional) |
|
|
630 |
Another image to transform |
|
|
631 |
|
|
|
632 |
Returns |
|
|
633 |
------- |
|
|
634 |
ANTsImage if y is None, else a tuple of ANTsImage types |
|
|
635 |
|
|
|
636 |
Examples |
|
|
637 |
-------- |
|
|
638 |
>>> import ants |
|
|
639 |
>>> img = ants.image_read(ants.get_data('r16')) |
|
|
640 |
>>> tx = ants.contrib.RandomZoom2D(zoom_range=(0.8,0.9)) |
|
|
641 |
>>> img2 = tx.transform(img) |
|
|
642 |
""" |
|
|
643 |
# random draw in zoom range |
|
|
644 |
zoom_x = np.exp( |
|
|
645 |
random.gauss(np.log(self.zoom_range[0]), np.log(self.zoom_range[1])) |
|
|
646 |
) |
|
|
647 |
zoom_y = np.exp( |
|
|
648 |
random.gauss(np.log(self.zoom_range[0]), np.log(self.zoom_range[1])) |
|
|
649 |
) |
|
|
650 |
self.params = (zoom_x, zoom_y) |
|
|
651 |
|
|
|
652 |
tx = Zoom2D((zoom_x, zoom_y), reference=self.reference, lazy=self.lazy) |
|
|
653 |
|
|
|
654 |
return tx.transform(X, y) |