mirror of
https://github.com/wassname/scikit-image.git
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Johannes Schönberger
189 lines
6.0 KiB
Python
189 lines
6.0 KiB
Python
# coding: utf-8
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import numpy as np
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from . import _moments_cy
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def moments(image, order=3):
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"""Calculate all raw image moments up to a certain order.
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The following properties can be calculated from raw image moments:
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* Area as: ``m[0, 0]``.
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* Centroid as: {``m[0, 1] / m[0, 0]``, ``m[1, 0] / m[0, 0]``}.
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Note that raw moments are neither translation, scale nor rotation
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invariant.
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Parameters
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----------
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image : 2D double or uint8 array
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Rasterized shape as image.
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order : int, optional
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Maximum order of moments. Default is 3.
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Returns
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-------
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m : (``order + 1``, ``order + 1``) array
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Raw image moments.
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References
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----------
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.. [1] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing:
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Core Algorithms. Springer-Verlag, London, 2009.
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.. [2] B. Jähne. Digital Image Processing. Springer-Verlag,
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Berlin-Heidelberg, 6. edition, 2005.
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.. [3] T. H. Reiss. Recognizing Planar Objects Using Invariant Image
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Features, from Lecture notes in computer science, p. 676. Springer,
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Berlin, 1993.
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.. [4] http://en.wikipedia.org/wiki/Image_moment
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Examples
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--------
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>>> image = np.zeros((20, 20), dtype=np.double)
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>>> image[13:17, 13:17] = 1
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>>> m = moments(image)
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>>> cr = m[0, 1] / m[0, 0]
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>>> cc = m[1, 0] / m[0, 0]
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>>> cr, cc
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(14.5, 14.5)
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"""
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return _moments_cy.moments_central(image, 0, 0, order)
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def moments_central(image, cr, cc, order=3):
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"""Calculate all central image moments up to a certain order.
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The center coordinates (cr, cc) can be calculated from the raw moments as:
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{``m[0, 1] / m[0, 0]``, ``m[1, 0] / m[0, 0]``}.
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Note that central moments are translation invariant but not scale and
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rotation invariant.
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Parameters
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----------
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image : 2D double or uint8 array
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Rasterized shape as image.
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cr : double
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Center row coordinate.
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cc : double
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Center column coordinate.
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order : int, optional
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Maximum order of moments. Default is 3.
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Returns
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-------
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mu : (``order + 1``, ``order + 1``) array
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Central image moments.
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References
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----------
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.. [1] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing:
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Core Algorithms. Springer-Verlag, London, 2009.
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.. [2] B. Jähne. Digital Image Processing. Springer-Verlag,
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Berlin-Heidelberg, 6. edition, 2005.
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.. [3] T. H. Reiss. Recognizing Planar Objects Using Invariant Image
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Features, from Lecture notes in computer science, p. 676. Springer,
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Berlin, 1993.
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.. [4] http://en.wikipedia.org/wiki/Image_moment
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Examples
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--------
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>>> image = np.zeros((20, 20), dtype=np.double)
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>>> image[13:17, 13:17] = 1
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>>> m = moments(image)
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>>> cr = m[0, 1] / m[0, 0]
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>>> cc = m[1, 0] / m[0, 0]
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>>> moments_central(image, cr, cc)
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array([[ 16., 0., 20., 0.],
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[ 0., 0., 0., 0.],
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[ 20., 0., 25., 0.],
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[ 0., 0., 0., 0.]])
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"""
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return _moments_cy.moments_central(image, cr, cc, order)
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def moments_normalized(mu, order=3):
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"""Calculate all normalized central image moments up to a certain order.
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Note that normalized central moments are translation and scale invariant
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but not rotation invariant.
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Parameters
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----------
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mu : (M, M) array
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Central image moments, where M must be > ``order``.
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order : int, optional
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Maximum order of moments. Default is 3.
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Returns
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-------
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nu : (``order + 1``, ``order + 1``) array
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Normalized central image moments.
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References
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----------
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.. [1] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing:
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Core Algorithms. Springer-Verlag, London, 2009.
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.. [2] B. Jähne. Digital Image Processing. Springer-Verlag,
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Berlin-Heidelberg, 6. edition, 2005.
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.. [3] T. H. Reiss. Recognizing Planar Objects Using Invariant Image
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Features, from Lecture notes in computer science, p. 676. Springer,
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Berlin, 1993.
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.. [4] http://en.wikipedia.org/wiki/Image_moment
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Examples
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--------
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>>> image = np.zeros((20, 20), dtype=np.double)
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>>> image[13:17, 13:17] = 1
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>>> m = moments(image)
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>>> cr = m[0, 1] / m[0, 0]
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>>> cc = m[1, 0] / m[0, 0]
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>>> mu = moments_central(image, cr, cc)
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>>> moments_normalized(mu)
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array([[ nan, nan, 0.078125 , 0. ],
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[ nan, 0. , 0. , 0. ],
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[ 0.078125 , 0. , 0.00610352, 0. ],
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[ 0. , 0. , 0. , 0. ]])
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"""
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if mu.ndim != 2:
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raise TypeError("Image moments must be 2-dimension")
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if mu.shape[0] <= order or mu.shape[1] <= order:
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raise TypeError("Shape of image moments must be >= `order`")
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return _moments_cy.moments_normalized(mu.astype(np.double), order)
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def moments_hu(nu):
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"""Calculate Hu's set of image moments.
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Note that this set of moments is proofed to be translation, scale and
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rotation invariant.
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Parameters
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----------
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nu : (M, M) array
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Normalized central image moments, where M must be > 4.
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Returns
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-------
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nu : (7, 1) array
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Hu's set of image moments.
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References
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----------
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.. [1] M. K. Hu, "Visual Pattern Recognition by Moment Invariants",
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IRE Trans. Info. Theory, vol. IT-8, pp. 179-187, 1962
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.. [2] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing:
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Core Algorithms. Springer-Verlag, London, 2009.
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.. [3] B. Jähne. Digital Image Processing. Springer-Verlag,
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Berlin-Heidelberg, 6. edition, 2005.
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.. [4] T. H. Reiss. Recognizing Planar Objects Using Invariant Image
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Features, from Lecture notes in computer science, p. 676. Springer,
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Berlin, 1993.
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.. [5] http://en.wikipedia.org/wiki/Image_moment
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"""
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return _moments_cy.moments_hu(nu.astype(np.double))
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