0-PhEddlZddlZddlmZmZddlmZddlm Z ddZ dd Z ddd d Z ddd d Z dd ZdZdd dZddd dZddd dZdS)N)_supported_float_typecheck_nD) _moments_cy)moments_raw_to_centralc&t|d|S)avCalculate 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.float64) >>> M = moments_coords(coords) >>> centroid = (M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]) >>> centroid (14.5, 15.5) r)order)moments_coords_central)coordsr s X/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/skimage/measure/_moments.pymoments_coordsr sL "&!5 9 9 99cttrtjdt djd}t j}|tjdt} |d |z tjfd t|dzDd jd |dz zzd}t|D],}dd|f}tj |dd|z}||z}-tj|d}|S) aCalculate 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), ... decimals=2) # doctest: +NORMALIZE_WHITESPACE 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 )axisrrNr)rdtypeFcopycg|]}|zSr).0cr s r z*moments_coords_central..s;;;Qvqy;;;r)r) isinstancetuplenpstackrshaperrmeanfloatastyperangereshapemoveaxissum) r centerr ndim float_typecalcr isolated_axisMcs ` rr r 3sV~&%  +&r*** VQ <?D&v|44J ~au555]]:E] 2 2V ;FX;;;;% *:*:;;;" E E EF^^FL44!8+<< = =F Dd $$qqq$w  M1a$h?? m# 1   B Irspacingc8t|d|jz||S)uCalculate 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 : (N[, ...]) double or uint8 array Rasterized shape as image. order : int, optional Maximum order of moments. Default is 3. spacing: tuple of float, shape (ndim,) The pixel spacing along each axis of the image. 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] https://en.wikipedia.org/wiki/Image_moment Examples -------- >>> image = np.zeros((20, 20), dtype=np.float64) >>> image[13:17, 13:17] = 1 >>> M = moments(image) >>> centroid = (M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]) >>> centroid (14.5, 14.5) rr r/)moments_centralr))imager r/s rmomentsr5s#X 5$"35' R R RRrc L|!t|||}t|St|j}|t j|j|}||d}t|j D]\}} t j | |||z||z } | ddtj ft j |dz|z} t j |||j}t j || }t j |d|}|S)uCalculate all central image moments up to a certain order. The center coordinates (cr, cc) can be calculated from the raw moments as: {``M[1, 0] / M[0, 0]``, ``M[0, 1] / M[0, 0]``}. Note that central moments are translation invariant but not scale and rotation invariant. Parameters ---------- image : (N[, ...]) double or uint8 array Rasterized shape as image. center : tuple of float, optional Coordinates of the image centroid. This will be computed if it is not provided. order : int, optional The maximum order of moments computed. spacing: tuple of float, shape (ndim,) The pixel spacing along each axis of the image. Returns ------- mu : (``order + 1``, ``order + 1``) array Central image moments. References ---------- .. [1] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing: Core Algorithms. Springer-Verlag, London, 2009. .. [2] B. Jähne. Digital Image Processing. Springer-Verlag, Berlin-Heidelberg, 6. edition, 2005. .. [3] T. H. Reiss. Recognizing Planar Objects Using Invariant Image Features, from Lecture notes in computer science, p. 676. Springer, Berlin, 1993. .. [4] https://en.wikipedia.org/wiki/Image_moment Examples -------- >>> image = np.zeros((20, 20), dtype=np.float64) >>> image[13:17, 13:17] = 1 >>> M = moments(image) >>> centroid = (M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]) >>> moments_central(image, centroid) array([[16., 0., 20., 0.], [ 0., 0., 0., 0.], [20., 0., 25., 0.], [ 0., 0., 0., 0.]]) Nr2rFrrr)r5rrrronesr)r# enumerater arangenewaxisrollaxisdot) r4r(r r/kwargs moments_raw float_dtyper+dim dim_lengthdeltapowers_of_deltas rr3r3s(b~e5'BBB %k222' 44K'%*K888 << %< 0 0D$U[11**Z *K88873<G&QT+U2: .") AI[3 3 3  {4ej11vdO,,{4S)) KrcLtjtj|j|krt d|tj|j}tj|}|d}t|}tj t|dz|jD]a}t|dkrtj||<%|||t|zz |t||jz dzzz ||<b|S)u|Calculate all normalized central image moments up to a certain order. Note that normalized central moments are translation and scale invariant but not rotation invariant. Parameters ---------- mu : (M[, ...], M) array Central image moments, where M must be greater than or equal to ``order``. order : int, optional Maximum order of moments. Default is 3. spacing: tuple of float, shape (ndim,) The pixel spacing along each axis of the image. Returns ------- nu : (``order + 1``[, ...], ``order + 1``) array Normalized 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] https://en.wikipedia.org/wiki/Image_moment Examples -------- >>> image = np.zeros((20, 20), dtype=np.float64) >>> image[13:17, 13:17] = 1 >>> m = moments(image) >>> centroid = (m[0, 1] / m[0, 0], m[1, 0] / m[0, 0]) >>> mu = moments_central(image, centroid) >>> moments_normalized(mu) array([[ nan, nan, 0.078125 , 0. ], [ nan, 0. , 0. , 0. ], [0.078125 , 0. , 0.00610352, 0. ], [0. , 0. , 0. , 0. ]]) z)Shape of image moments must be >= `order`Nrr)repeatr)ranyarrayr ValueErrorr8r) zeros_likeravelmin itertoolsproductr$r'nan)mur r/numu0scalepowerss rmoments_normalizedrUsZ vbhrx  E)**FDEEE'"'"" r  B ((**Q-C LLE#E%!)$4$4RWEEE v;;??BvJJV*uF ';;F bg-12BvJJ Irc|jdkr tjn tj}t j||dS)u@Calculate Hu's set of image moments (2D-only). Note that this set of moments is proved 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] https://en.wikipedia.org/wiki/Image_moment Examples -------- >>> image = np.zeros((20, 20), dtype=np.float64) >>> image[13:17, 13:17] = 0.5 >>> image[10:12, 10:12] = 1 >>> mu = moments_central(image) >>> nu = moments_normalized(mu) >>> moments_hu(nu) array([0.74537037, 0.35116598, 0.10404918, 0.04064421, 0.00264312, 0.02408546, 0. ]) float32Fr)rrrWfloat64r moments_hur#)rQrs rrYrYLs?P(i//BJJRZE  !"))E)">"> ? ??rct|d|jzd|}|ttj|jt |d|jzz }|S)a4Return the (weighted) centroid of an image. Parameters ---------- image : array The input image. spacing: tuple of float, shape (ndim,) The pixel spacing along each axis of the image. Returns ------- center : tuple of float, length ``image.ndim`` The centroid of the (nonzero) pixels in ``image``. Examples -------- >>> image = np.zeros((20, 20), dtype=np.float64) >>> image[13:17, 13:17] = 0.5 >>> image[10:12, 10:12] = 1 >>> centroid(image) array([13.16666667, 13.16666667]) r1r)r(r r/r7)r3r)rreyeint)r4r/Mr(s rcentroidr^xsb. dUZ&7q'RRRA %uz--- . ./ D5:    Mrc|t|d|}|d|jz}tj|j|jf|j}t dtj|jtz}tj|}d|j _ tj ||||z |z |dd<tj t|jdD]q}tj|jt}d|t|<|t | |z ||<|t | |z |j|<r|S)uTCompute the inertia tensor of the input image. Parameters ---------- image : array The input image. mu : array, optional The pre-computed central moments of ``image``. The inertia tensor computation requires the central moments of the image. If an application requires both the central moments and the inertia tensor (for example, `skimage.measure.regionprops`), then it is more efficient to pre-compute them and pass them to the inertia tensor call. spacing: tuple of float, shape (ndim,) The pixel spacing along each axis of the image. Returns ------- T : array, shape ``(image.ndim, image.ndim)`` The inertia tensor of the input image. :math:`T_{i, j}` contains the covariance of image intensity along axes :math:`i` and :math:`j`. References ---------- .. [1] https://en.wikipedia.org/wiki/Moment_of_inertia#Inertia_tensor .. [2] Bernd Jähne. Spatio-Temporal Image Processing: Theory and Scientific Applications. (Chapter 8: Tensor Methods) Springer, 1993. Nrr2r1r7Tr)r3r)rzerosrrr[r\diagflags writeabler'rM combinationsr$listT) r4rPr/rRresultcorners2ddimsmu_indexs rinertia_tensorrlsJ: z  G    TEJ  C Xuz5:.bh ? ? ?FQ #666677H AAG F2h< 2h< /3 6AaaaD&uUZ'8'8!<<448EJc222 d5??++c1t U8__--3 Mrc|t|||}tj|}tj|dd|}t |dS)akCompute 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. spacing: tuple of float, shape (ndim,) The pixel spacing along each axis of the image. 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. Nr.r)outT)reverse)rlrlinalgeigvalshclipsorted)r4rPrfr/eigvalss rinertia_tensor_eigvalsrus`@ y 5"g 6 6 6i  ##G ggq$G444G '4 ( ( ((r)r )Nr )r N)N)NN)rMnumpyr _shared.utilsrrr_moments_analyticalrrr r5r3rUrYr^rlrurrrrzsg;;;;;;;;777777&:&:&:&:RddddN,St,S,S,S,S,S^BDBBBBBJ;;;;|)@)@)@X $@5d55555p()d()()()()()()()r