ó  ‰\c@ sÎddlmZddlZddlmZddlmZddlZddl m Z dd „Z ddd „Z dd „Zdddd „Zdd „Zd„Zd„Zdd„Zddd„ZdS(i˙˙˙˙(tdivisionNi(t assert_nDi(t _moments_cy(twarnicC st|dd|ƒS(sžCalculate all raw image moments up to a certain order. The following properties can be calculated from raw image moments: * Area as: ``M[0, 0]``. * Centroid as: {``M[1, 0] / M[0, 0]``, ``M[0, 1] / M[0, 0]``}. Note that raw moments are neither translation, scale nor rotation invariant. Parameters ---------- coords : (N, D) double or uint8 array Array of N points that describe an image of D dimensionality in Cartesian space. order : int, optional Maximum order of moments. Default is 3. Returns ------- M : (``order + 1``, ``order + 1``, ...) array Raw image moments. (D dimensions) References ---------- .. [1] Johannes Kilian. Simple Image Analysis By Moments. Durham University, version 0.2, Durham, 2001. Examples -------- >>> coords = np.array([[row, col] ... for row in range(13, 17) ... for col in range(14, 18)], dtype=np.double) >>> M = moments_coords(coords) >>> centroid_row = M[1, 0] / M[0, 0] >>> centroid_col = M[0, 1] / M[0, 0] >>> centroid_row, centroid_col (14.5, 15.5) itorder(tmoments_coords_central(tcoordsR((s7lib/python2.7/site-packages/skimage/measure/_moments.pytmoments_coords s'cC s#t|tƒr!tj|ƒ}nt|dƒ|jd}|dkr_tj|ddƒ}n|jt ƒ|}|dtj ftj |dƒ}|j |jd|dƒ}d}xMt |ƒD]?}|dd…|f}tj|dd|ƒ}||}qÇWtj|ddƒ}|S(s•Calculate all central image moments up to a certain order. The following properties can be calculated from raw image moments: * Area as: ``M[0, 0]``. * Centroid as: {``M[1, 0] / M[0, 0]``, ``M[0, 1] / M[0, 0]``}. Note that raw moments are neither translation, scale nor rotation invariant. Parameters ---------- coords : (N, D) double or uint8 array Array of N points that describe an image of D dimensionality in Cartesian space. A tuple of coordinates as returned by ``np.nonzero`` is also accepted as input. center : tuple of float, optional Coordinates of the image centroid. This will be computed if it is not provided. order : int, optional Maximum order of moments. Default is 3. Returns ------- Mc : (``order + 1``, ``order + 1``, ...) array Central image moments. (D dimensions) References ---------- .. [1] Johannes Kilian. Simple Image Analysis By Moments. Durham University, version 0.2, Durham, 2001. Examples -------- >>> coords = np.array([[row, col] ... for row in range(13, 17) ... for col in range(14, 18)]) >>> moments_coords_central(coords) array([[ 16., 0., 20., 0.], [ 0., 0., 0., 0.], [ 20., 0., 25., 0.], [ 0., 0., 0., 0.]]) As seen above, for symmetric objects, odd-order moments (columns 1 and 3, rows 1 and 3) are zero when centered on the centroid, or center of mass, of the object (the default). If we break the symmetry by adding a new point, this no longer holds: >>> coords2 = np.concatenate((coords, [[17, 17]]), axis=0) >>> np.round(moments_coords_central(coords2), 2) array([[ 17. , 0. , 22.12, -2.49], [ 0. , 3.53, 1.73, 7.4 ], [ 25.88, 6.02, 36.63, 8.83], [ 4.15, 19.17, 14.8 , 39.6 ]]) Image moments and central image moments are equivalent (by definition) when the center is (0, 0): >>> np.allclose(moments_coords(coords), ... moments_coords_central(coords, (0, 0))) True iitaxisi.N(i(t isinstancettupletnpt transposeRtshapetNonetmeantastypetfloattnewaxistarangetreshapetrangetmoveaxistsum(RtcenterRtndimtcalcRt isolated_axistMc((s7lib/python2.7/site-packages/skimage/measure/_moments.pyR4s >   $cC st|d|jd|ƒS(s4Calculate all raw image moments up to a certain order. The following properties can be calculated from raw image moments: * Area as: ``M[0, 0]``. * Centroid as: {``M[1, 0] / M[0, 0]``, ``M[0, 1] / M[0, 0]``}. Note that raw moments are neither translation, scale nor rotation invariant. Parameters ---------- image : nD double or uint8 array Rasterized shape as image. order : int, optional Maximum order of moments. Default is 3. Returns ------- m : (``order + 1``, ``order + 1``) array Raw image moments. References ---------- .. [1] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009. .. [2] B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005. .. [3] T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993. .. [4] http://en.wikipedia.org/wiki/Image_moment Examples -------- >>> image = np.zeros((20, 20), dtype=np.double) >>> image[13:17, 13:17] = 1 >>> M = moments(image) >>> cr = M[1, 0] / M[0, 0] >>> cc = M[0, 1] / M[0, 0] >>> cr, cc (14.5, 14.5) iR(i(tmoments_centralR(timageR((s7lib/python2.7/site-packages/skimage/measure/_moments.pytmoments˜s+c K s@|dk rld}t|ƒd|krG|dkrG|d|f}n ||f}t|d|d|ƒjS|dkr‡t|ƒ}n|jtƒ}xŁt|jƒD]’\}}t j |dtƒ||} | dd…t j ft j |dƒ} t j |||j ƒ}t j|| ƒ}t j |d|ƒ}qŚW|S( sCalculate all central image moments up to a certain order. The center coordinates (cr, cc) can be calculated from the raw moments as: {``M[1, 0] / M[0, 0]``, ``M[0, 1] / M[0, 0]``}. Note that central moments are translation invariant but not scale and rotation invariant. Parameters ---------- image : nD double or uint8 array Rasterized shape as image. center : tuple of float, optional Coordinates of the image centroid. This will be computed if it is not provided. order : int, optional The maximum order of moments computed. Other Parameters ---------------- cr : double DEPRECATED: Center row coordinate for 2D image. cc : double DEPRECATED: Center column coordinate for 2D image. Returns ------- mu : (``order + 1``, ``order + 1``) array Central image moments. References ---------- .. [1] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009. .. [2] B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005. .. [3] T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993. .. [4] http://en.wikipedia.org/wiki/Image_moment Examples -------- >>> image = np.zeros((20, 20), dtype=np.double) >>> image[13:17, 13:17] = 1 >>> M = moments(image) >>> cr = M[1, 0] / M[0, 0] >>> cc = M[0, 1] / M[0, 0] >>> moments_central(image, (cr, cc)) array([[ 16., 0., 20., 0.], [ 0., 0., 0., 0.], [ 20., 0., 25., 0.], [ 0., 0., 0., 0.]]) s°Using deprecated 2D-only, xy-coordinate interface to moments_central. This interface will be removed in scikit-image 0.16. Use moments_central(image, center=(cr, cc), order=3).tcrRRtdtypeNii˙˙˙˙(RRRtTtcentroidRRt enumerateR R RRtrollaxisRtdot( RRtccRtkwargstmessageRtdimt dim_lengthtdeltatpowers_of_delta((s7lib/python2.7/site-packages/skimage/measure/_moments.pyRĆs"7    *cC sÉtjtj|jƒ|kƒr0tdƒ‚ntj|ƒ}|jƒd}xstjt |dƒd|j ƒD]O}t |ƒdkrštj ||>> image = np.zeros((20, 20), dtype=np.double) >>> image[13:17, 13:17] = 1 >>> m = moments(image) >>> cr = m[0, 1] / m[0, 0] >>> cc = m[1, 0] / m[0, 0] >>> mu = moments_central(image, cr, cc) >>> moments_normalized(mu) array([[ nan, nan, 0.078125 , 0. ], [ nan, 0. , 0. , 0. ], [ 0.078125 , 0. , 0.00610352, 0. ], [ 0. , 0. , 0. , 0. ]]) s)Shape of image moments must be >= `order`iitrepeati( R tanytarrayR t ValueErrort zeros_liketravelt itertoolstproductRRRtnan(tmuRtnutmu0tpowers((s7lib/python2.7/site-packages/skimage/measure/_moments.pytmoments_normalizeds-!)+cC stj|jtjƒƒS(sĺCalculate Hu's set of image moments (2D-only). Note that this set of moments is proofed to be translation, scale and rotation invariant. Parameters ---------- nu : (M, M) array Normalized central image moments, where M must be > 4. Returns ------- nu : (7,) array Hu's set of image moments. References ---------- .. [1] M. K. Hu, "Visual Pattern Recognition by Moment Invariants", IRE Trans. Info. Theory, vol. IT-8, pp. 179-187, 1962 .. [2] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009. .. [3] B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005. .. [4] T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993. .. [5] http://en.wikipedia.org/wiki/Image_moment (Rt moments_huRR tdouble(R8((s7lib/python2.7/site-packages/skimage/measure/_moments.pyR<MscC sTt|dd|jddƒ}|ttj|jdtƒƒ|d|j}|S(sReturn the (weighted) centroid of an image. Parameters ---------- image : array The input image. Returns ------- center : tuple of float, length ``image.ndim`` The centroid of the (nonzero) pixels in ``image``. RiRiR!(i(i(RRR R teyetint(RtMR((s7lib/python2.7/site-packages/skimage/measure/_moments.pyR#os cC s1|dkr!t|ddƒ}n|d|j}tj|j|jfƒ}tdtj|jdtƒƒ}tj|ƒ}t |j _ tj ||ƒ||||(x€t jt|jƒdƒD]c}tj|jdtƒ}d|t|ƒ<|t|ƒ |||<|t|ƒ ||j|R?tdiagtTruetflagst writeableRR4t combinationsRtlistR"(RR7R9tresulttcorners2tdtdimstmu_index((s7lib/python2.7/site-packages/skimage/measure/_moments.pytinertia_tensorƒs "  " cC s@|dkrt||ƒ}ntjj|ƒ}t|dtƒS(sCompute the eigenvalues of the inertia tensor of the image. The inertia tensor measures covariance of the image intensity along the image axes. (See `inertia_tensor`.) The relative magnitude of the eigenvalues of the tensor is thus a measure of the elongation of a (bright) object in the image. Parameters ---------- image : array The input image. mu : array, optional The pre-computed central moments of ``image``. T : array, shape ``(image.ndim, image.ndim)`` The pre-computed inertia tensor. If ``T`` is given, ``mu`` and ``image`` are ignored. Returns ------- eigvals : list of float, length ``image.ndim`` The eigenvalues of the inertia tensor of ``image``, in descending order. Notes ----- Computing the eigenvalues requires the inertia tensor of the input image. This is much faster if the central moments (``mu``) are provided, or, alternatively, one can provide the inertia tensor (``T``) directly. treverseN(RRMR tlinalgteigvalshtsortedRC(RR7R"teigvals((s7lib/python2.7/site-packages/skimage/measure/_moments.pytinertia_tensor_eigvalsˇs (t __future__RtnumpyR t _shared.utilsRtRR4twarningsRRRRRRR;R<R#RMRS(((s7lib/python2.7/site-packages/skimage/measure/_moments.pyts   *d .N 9 "  4