U ?hIE@sddlZddlZddlmZmZddlmZddlm Z ddd Z dd d Z ddd d dZ ddd ddZ dddZddZdd ddZd dd ddZd!dd ddZdS)"N)_supported_float_typecheck_nD) _moments_cy)moments_raw_to_centralcCst|d|dS)auCalculate 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 r J/var/www/html/venv/lib/python3.8/site-packages/skimage/measure/_moments.pymoments_coords s&rc sttrtjddtdjd}tj}|dkrNtjdt d}j |dd |tjfd d t |dDdd jd |dd}t |D].}dd|f}t |dd|}||}qtj|dd}|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)rdtypeFcopycsg|] }|qSr r ).0cr r r sz*moments_coords_central..)r) isinstancetuplenpstackrshaperrZmeanfloatastyperangeZreshapeZmoveaxissum) r centerr ndimZ float_typecalcrZ isolated_axisZMcr rr r 3s"?    $  r spacingcCst|d|j||dS)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 : nD 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%r r r momentss,r*c Ks|dkrt|||d}t|S|dkr2t|j}t|j}|j|dd}t|j D]t\}} tj | |d||||} | ddtj ftj |d|d} t |||j}t || }t |d|}qT|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 : 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. 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.]]) Nr'Frrrr)r*rronesr"rrr enumeraterZarangeZnewaxisZrollaxisdot) r)r!r r%kwargsZ moments_rawZ float_dtyper#dimZ dim_lengthdeltaZpowers_of_deltar r r r(s 1  " r(cCstt|j|krtd|dkr2t|j}t|}|d}t |}t j t |d|jdD]J}t |dkrtj||<qh|||t ||t ||jd||<qh|S)uCalculate 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. 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 ValueErrorr,r"Z zeros_likeZravelmin itertoolsproductrr nan)mur r%numu0scaleZpowersr r r moments_normalizeds+     0r>cCs*|jdkrtjntj}t|j|ddS)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)rrr?Zfloat64r moments_hur)r;rr r r r@Js(r@cCs@t|d|jd|d}|ttj|jtd|d|j}|S)a5Return 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]) r&r)r!r r%r+)r(r"rreyeint)r)r%Mr!r r r centroidvs  rDc Cs|dkrt|d|d}|d|j}tj|j|jf|jd}tdtj|jtd}t|}d|j _ t ||||||dd<t t|jdD]N}tj|jtd}d|t|<|t| |||<|t| ||j|<q|S)uUCompute 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. Nrr'r&r+Tr)r(r"rZzerosrrrArBZdiagflagsZ writeabler r7 combinationsrlistT) r)r:r%r<resultZcorners2dZdimsZmu_indexr r r inertia_tensors " rKcCs@|dkrt|||d}tj|}tj|dd|d}t|ddS)alCompute 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)rKrZlinalgZeigvalshZclipsorted)r)r:rHr%Zeigvalsr r r inertia_tensor_eigvalss  rO)r)Nr)r)Nr)rN)N)NN)r7numpyrZ _shared.utilsrrrZ_moments_analyticalrrr r*r(r>r@rDrKrOr r r r s   ) g/G :,6