9iu> SSKJr SSKJr SSKrSSKJr \R"/SQ/SQ/SQ/\RS9r \R"S\RS9r /S Qr/S Qr\R"/S Q5rSS jrSS jrSSjrSrg))sqrt)RealN)ndimage)rr)rrrdtype)r )rrrrrrrrrrrrrrr)rrrrrrr rrrrrrrr r(rrrrrrr rr rr rr r rrrr r r r r r r r r r rr rr rr r r r r r r r r r rr r rr r rr r rr r rr r rrrrrr r r rr r r r r r rr r r r rr r r r rrr r rrrr r rrr r r rr rrrr rr rr rr r r r r r rrrr rrrrrrrr r r r r r rrr r r r r r r r r r rr rrr r rrrrrr rrr r r r rrrr rrr r rr rr r r r rrr rr rr rrrrrrr r rr r rrr rr rrr r rr r rrr r r rr rrrr rrrr rr rr rrrr r r rr rrrrr r rr rrrr rrrrrrrcUS:R[5n[R"USSS9nUc URnURS:Xa5[R "/SQ/SQ/S Q/5nUS:Xa[ nO[nS nO`US:Xa [S 5e[R "/SQ/SQ/SQ//SQ/SQ/S Q//SQ/S Q/S Q//5nUS:Xa [SSS2nO[nSn[R"XSSS9n[R"UR5US9nURS:XaX6-$[SU-U-5$)uY Calculate the Euler characteristic in binary image. For 2D objects, the Euler number is the number of objects minus the number of holes. For 3D objects, the Euler number is obtained as the number of objects plus the number of holes, minus the number of tunnels, or loops. Parameters ---------- image: (M, N[, P]) ndarray Input image. If image is not binary, all values greater than zero are considered as the object. connectivity : int, optional Maximum number of orthogonal hops to consider a pixel/voxel as a neighbor. Accepted values are ranging from 1 to input.ndim. If ``None``, a full connectivity of ``input.ndim`` is used. 4 or 8 neighborhoods are defined for 2D images (connectivity 1 and 2, respectively). 6 or 26 neighborhoods are defined for 3D images, (connectivity 1 and 3, respectively). Connectivity 2 is not defined. Returns ------- euler_number : int Euler characteristic of the set of all objects in the image. Notes ----- The Euler characteristic is an integer number that describes the topology of the set of all objects in the input image. If object is 4-connected, then background is 8-connected, and conversely. The computation of the Euler characteristic is based on an integral geometry formula in discretized space. In practice, a neighborhood configuration is constructed, and a LUT is applied for each configuration. The coefficients used are the ones of Ohser et al. It can be useful to compute the Euler characteristic for several connectivities. A large relative difference between results for different connectivities suggests that the image resolution (with respect to the size of objects and holes) is too low. References ---------- .. [1] S. Rivollier. Analyse d’image geometrique et morphometrique par diagrammes de forme et voisinages adaptatifs generaux. PhD thesis, 2010. Ecole Nationale Superieure des Mines de Saint-Etienne. https://tel.archives-ouvertes.fr/tel-00560838 .. [2] Ohser J., Nagel W., Schladitz K. (2002) The Euler Number of Discretized Sets - On the Choice of Adjacency in Homogeneous Lattices. In: Mecke K., Stoyan D. (eds) Morphology of Condensed Matter. Lecture Notes in Physics, vol 600. Springer, Berlin, Heidelberg. Examples -------- >>> import numpy as np >>> SAMPLE = np.zeros((100,100,100)); >>> SAMPLE[40:60, 40:60, 40:60]=1 >>> euler_number(SAMPLE) # doctest: +ELLIPSIS 1... >>> SAMPLE[45:55,45:55,45:55] = 0; >>> euler_number(SAMPLE) # doctest: +ELLIPSIS 2... >>> SAMPLE = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0], ... [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], ... [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], ... [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], ... [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], ... [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], ... [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], ... [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0], ... [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1], ... [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]]) >>> euler_number(SAMPLE) # doctest: 0 >>> euler_number(SAMPLE, connectivity=1) # doctest: 2 rrconstant pad_widthmodeNrrrrrrrrrzJFor 3D images, Euler number is implemented for connectivities 1 and 3 only)rr@)r r rcval minlengthg?)astypeintnppadndimarrayEULER_COEFS2D_4EULER_COEFS2D_8NotImplementedErrorEULER_COEFS3D_26ndiconvolvebincountravel)image connectivityconfigcoefsbinsXFhs b/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/skimage/measure/_regionprops_utils.py euler_numberr8s5dQY  s #E FF5AJ 7Ezz  zzQ9i;< 1 #E#E 1 %2  Iy1Iy1K6   1 $TrT*E$E e*1 =B BHHJ$/A zzQy55=1$%%c (URS:wa [S5eUS:Xa[nO[nUR [ R 5n[R"XSS9nX- n[ R"S[ RS9nSU/S Q'[S5US S /'S[S5-S- US S /'[R"U[ R"/SQ/SQ/SQ/5SSS9n[ R"UR5SS9nXu-nU$)aCalculate total perimeter of all objects in binary image. Parameters ---------- image : (M, N) ndarray Binary input image. neighborhood : 4 or 8, optional Neighborhood connectivity for border pixel determination. It is used to compute the contour. A higher neighborhood widens the border on which the perimeter is computed. Returns ------- perimeter : float Total perimeter of all objects in binary image. References ---------- .. [1] K. Benkrid, D. Crookes. Design and FPGA Implementation of a Perimeter Estimator. The Queen's University of Belfast. http://www.cs.qub.ac.uk/~d.crookes/webpubs/papers/perimeter.doc Examples -------- >>> from skimage import data, util >>> from skimage.measure import label >>> # coins image (binary) >>> img_coins = data.coins() > 110 >>> # total perimeter of all objects in the image >>> perimeter(img_coins, neighborhood=4) # doctest: +ELLIPSIS 7796.867... >>> perimeter(img_coins, neighborhood=8) # doctest: +ELLIPSIS 8806.268... rz#`perimeter` supports 2D images onlyrr) border_value2rr)! ) rrG)rrrrrr )r&r*STREL_4STREL_8r"r$uint8r,binary_erosionzerosfloat64rr-r'r.r/) r0 neighborhoodstrel eroded_image border_imageperimeter_weightsperimeter_imageperimeter_histogramtotal_perimeters r7 perimeterrVsH zzQ!"GHHq LL "E%%eCL'L2::601,-"&q'r2h#$tAw;!"3r2hll +y+67   O++o&;&;&=L)=O r9cJURS:wa [S5eUS:R[R5n[R "USSS9n[ R"U[R"/SQ/SQ/S Q/5SSS 9n[R"UR5S S 9nUS:XatS[RS- SSS[RS- SS[RS- [RSS[RS- [RSS/nGOzS[RS - SS[R"S5- --[RS [R"S5-- [RS[R"S5-- S[RS - SS[R"S5- --S[RS [R"S5-- [RS - [RS- [RS [R"S5-- [RS [R"S5-- [RS - [RS- SS/nXC-nU$)uCalculate total Crofton perimeter of all objects in binary image. Parameters ---------- image : (M, N) ndarray Input image. If image is not binary, all values greater than zero are considered as the object. directions : 2 or 4, optional Number of directions used to approximate the Crofton perimeter. By default, 4 is used: it should be more accurate than 2. Computation time is the same in both cases. Returns ------- perimeter : float Total perimeter of all objects in binary image. Notes ----- This measure is based on Crofton formula [1], which is a measure from integral geometry. It is defined for general curve length evaluation via a double integral along all directions. In a discrete space, 2 or 4 directions give a quite good approximation, 4 being more accurate than 2 for more complex shapes. Similar to :func:`~.measure.perimeter`, this function returns an approximation of the perimeter in continuous space. References ---------- .. [1] https://en.wikipedia.org/wiki/Crofton_formula .. [2] S. Rivollier. Analyse d’image geometrique et morphometrique par diagrammes de forme et voisinages adaptatifs generaux. PhD thesis, 2010. Ecole Nationale Superieure des Mines de Saint-Etienne. https://tel.archives-ouvertes.fr/tel-00560838 Examples -------- >>> from skimage import data, util >>> from skimage.measure import label >>> # coins image (binary) >>> img_coins = data.coins() > 110 >>> # total perimeter of all objects in the image >>> perimeter_crofton(img_coins, directions=2) # doctest: +ELLIPSIS 8144.578... >>> perimeter_crofton(img_coins, directions=4) # doctest: +ELLIPSIS 7837.077... rz+`perimeter_crofton` supports 2D images onlyrrrrrrrrrr r) r&r*r"r$rJr%r,r-r'r.r/pir)r0 directionsr5r6r3rUs r7perimeter_croftonrZsd zzQ!"OPPQY  rxx (E FF5AJ 7E  rxxIy9:RS B BHHJ"-AQ EEAI EEAI EEAI EE EEAI EE ! (  EEAIQ"''!*-- . EEQ^ $ EEQ^ $ EEAIQ"''!*-- . 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