o :ήc@sddlZddlZddlZddlmZddlmZddlZddl m Z ddl m Z ddlmZmZmZddlmZdd lmZdd lmZmZdd lmZdd lmZd dlmZmZgdZ dGddZ!edddHddZ" dIddZ#dJddZ$dKdd!d"d#Z%dKdd!d$d%Z&dLdd!d&d'Z'e(e)d(d)d Z*e*fd*d+Z+dddd,d-d.Z,ed/d0id1d2d3dMdd!d5d6Z-d7d8Z.dNd9d:Z/d;d<Z0dOd?d@Z1dPdAdBZ2dCdDZ3dQdd!dEdFZ4dS)RN) OrderedDict)Iterable)ndimage)gaussian)_supported_float_typedeprecate_kwargwarn)require) histogram)_get_multiotsu_thresh_indices!_get_multiotsu_thresh_indices_lut)integral_image) dtype_limits)_correlate_sparse_validate_window_size) try_all_thresholdthreshold_otsu threshold_yenthreshold_isodata threshold_lithreshold_localthreshold_minimumthreshold_meanthreshold_niblackthreshold_sauvolathreshold_triangleapply_hysteresis_thresholdthreshold_multiotsuTc Cszddlm}d}t||dd}|pi}tt|d|}|j|||ddd\} } | } | dj||j j d | d d d } | D]b\} } t | }d |jvr[t|d ni}| |  | z| | j| |fi||j j d Wn'ty}z| | jdddt|jdd| | jdWYd}~nd}~ww| d 7} |rt| jqH| D]}|dq| | | fS)aReturns a figure comparing the outputs of different methods. Parameters ---------- image : (N, M) ndarray Input image. methods : dict, optional Names and associated functions. Functions must take and return an image. figsize : tuple, optional Figure size (in inches). num_cols : int, optional Number of columns. verbose : bool, optional Print function name for each method. Returns ------- fig, ax : tuple Matplotlib figure and axes. r)pyplotimage source_range?T)figsizesharexsharey)cmapOriginalrhistr+?z%scenter)hava transformNoff) matplotlibr r ravelmathceillensubplotsimshowcmgray set_titleitemsinspect signature parametersdict Exceptiontexttype__name__ transAxesprint __orifunc__axis tight_layout)r"methodsr&num_colsverbosepltnbinsr+num_rowsfigaxinamefuncsig_kwargsearZC/tmp/pip-target-vg8gfxp4/lib/python/skimage/filters/thresholding.py_try_all#s@    &   r\r3z>=3.0.3c CsLdd}t|t|t|t|t|t|t|td}t||||dS)aReturns a figure comparing the outputs of different thresholding methods. Parameters ---------- image : (N, M) ndarray Input image. figsize : tuple, optional Figure size (in inches). verbose : bool, optional Print function name for each method. Returns ------- fig, ax : tuple Matplotlib figure and axes. Notes ----- The following algorithms are used: * isodata * li * mean * minimum * otsu * triangle * yen Examples -------- >>> from skimage.data import text >>> fig, ax = try_all_threshold(text(), figsize=(10, 6), verbose=False) csBfdd}zj|_W|Sty jdj|_Y|Sw)zC A wrapper function to return a thresholded image. cs ||kS)NrZ)imrUrZr[wrappers z2try_all_threshold..thresh..wrapper.)rHAttributeError __module__rE)rUrbrZrar[threshs   z!try_all_threshold..thresh)IsodataLiMeanMinimumOtsuTriangleYen)r&rKrM) rrrrrrrrr\)r"r&rMrfrKrZrZr[ras# rrreflectc Cs6t|r |f|j}n t||jkrtdt|}tdd|Dr,td|dt|}|j|dd}tj |j |d}|d krRt j ||||||d ||S|d krs|d urdtd d|D} n|} t || |||d ||S|dkrt j|||||d ||S|dkrt j|||||d ||Std)aT Compute a threshold mask image based on local pixel neighborhood. Also known as adaptive or dynamic thresholding. The threshold value is the weighted mean for the local neighborhood of a pixel subtracted by a constant. Alternatively the threshold can be determined dynamically by a given function, using the 'generic' method. Parameters ---------- image : (N, M[, ..., P]) ndarray Grayscale input image. block_size : int or sequence of int Odd size of pixel neighborhood which is used to calculate the threshold value (e.g. 3, 5, 7, ..., 21, ...). method : {'generic', 'gaussian', 'mean', 'median'}, optional Method used to determine adaptive threshold for local neighbourhood in weighted mean image. * 'generic': use custom function (see ``param`` parameter) * 'gaussian': apply gaussian filter (see ``param`` parameter for custom sigma value) * 'mean': apply arithmetic mean filter * 'median': apply median rank filter By default the 'gaussian' method is used. offset : float, optional Constant subtracted from weighted mean of neighborhood to calculate the local threshold value. Default offset is 0. mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to 'constant'. Default is 'reflect'. param : {int, function}, optional Either specify sigma for 'gaussian' method or function object for 'generic' method. This functions takes the flat array of local neighbourhood as a single argument and returns the calculated threshold for the centre pixel. cval : float, optional Value to fill past edges of input if mode is 'constant'. Returns ------- threshold : (N, M[, ..., P]) ndarray Threshold image. All pixels in the input image higher than the corresponding pixel in the threshold image are considered foreground. References ---------- .. [1] Gonzalez, R. C. and Wood, R. E. "Digital Image Processing (2nd Edition)." Prentice-Hall Inc., 2002: 600--612. ISBN: 0-201-18075-8 Examples -------- >>> from skimage.data import camera >>> image = camera()[:50, :50] >>> binary_image1 = image > threshold_local(image, 15, 'mean') >>> func = lambda arr: arr.mean() >>> binary_image2 = image > threshold_local(image, 15, 'generic', ... param=func) z&len(block_size) must equal image.ndim.css|] }|ddkVqdS)rrNrZ.0brZrZr[ sz"threshold_local..z)block_size must be odd! Given block_size z contains even values.Fcopydtypegeneric)outputmodecvalrNcSsg|]}|ddqS)rg@rZrprZrZr[ sz#threshold_local..meanmedianzPInvalid method specified. Please use `generic`, `gaussian`, `mean`, or `median`.)npisscalarndimr7 ValueErrortupleanyrastypezerosshapendigeneric_filterruniform_filter median_filter) r" block_sizemethodoffsetrzparamr{ float_dtype thresh_imagesigmarZrZr[rsD A      rFc Cs|dur |dur td|durTt|ttfr|\}}n|}t|j}|ddks0|ddkrS|dk}t|}|jt|ddd}||||||}}n t| |d|d\}}| t |fS)aEnsure that either image or hist were given, return valid histogram. If hist is given, image is ignored. Parameters ---------- image : array or None Grayscale image. hist : array, 2-tuple of array, or None Histogram, either a 1D counts array, or an array of counts together with an array of bin centers. nbins : int, optional The number of bins with which to compute the histogram, if `hist` is None. normalize : bool If hist is not given, it will be computed by this function. This parameter determines whether the computed histogram is normalized (i.e. entries sum up to 1) or not. Returns ------- counts : 1D array of float Each element is the number of pixels falling in each intensity bin. bin_centers : 1D array Each element is the value corresponding to the center of each intensity bin. Raises ------ ValueError : if image and hist are both None Nz&Either image or hist must be provided.rr")r$ normalize) rB isinstancerlistrarangesizeargmaxr r4rfloat) r"r+rOrcounts bin_centerscondstartendrZrZr[_validate_image_histograms"      rr!r,c Cs|dur|jdkr|jddvrtd|jd|dur,|d}t||kr,|St|||\}}t|}t|dddddd}t|||}t||ddd|dddddd} |dd|dd|dd| ddd} t| } || } | S) azReturn threshold value based on Otsu's method. Either image or hist must be provided. If hist is provided, the actual histogram of the image is ignored. Parameters ---------- image : (N, M[, ..., P]) ndarray, optional Grayscale input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. hist : array, or 2-tuple of arrays, optional Histogram from which to determine the threshold, and optionally a corresponding array of bin center intensities. If no hist provided, this function will compute it from the image. Returns ------- threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground. References ---------- .. [1] Wikipedia, https://en.wikipedia.org/wiki/Otsu's_Method Examples -------- >>> from skimage.data import camera >>> image = camera() >>> thresh = threshold_otsu(image) >>> binary = image <= thresh Notes ----- The input image must be grayscale. NrrrnzTthreshold_otsu is expected to work correctly only for grayscale images; image shape ! looks like that of an RGB image.rr) rrr r4rallrcumsumr) r"rOr+ first_pixelrrweight1weight2mean1mean2 variance12idx thresholdrZrZr[r8s" (   04 rc Cst|||\}}|jdkr|dS|tj|}t|}t|d}t|ddddddd}t|dd|ddd|ddd|ddd} || S)a<Return threshold value based on Yen's method. Either image or hist must be provided. In case hist is given, the actual histogram of the image is ignored. Parameters ---------- image : (N, M[, ..., P]) ndarray Grayscale input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. hist : array, or 2-tuple of arrays, optional Histogram from which to determine the threshold, and optionally a corresponding array of bin center intensities. An alternative use of this function is to pass it only hist. Returns ------- threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground. References ---------- .. [1] Yen J.C., Chang F.J., and Chang S. (1995) "A New Criterion for Automatic Multilevel Thresholding" IEEE Trans. on Image Processing, 4(3): 370-378. :DOI:`10.1109/83.366472` .. [2] Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding Techniques and Quantitative Performance Evaluation" Journal of Electronic Imaging, 13(1): 146-165, :DOI:`10.1117/1.1631315` http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf .. [3] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold Examples -------- >>> from skimage.data import camera >>> image = camera() >>> thresh = threshold_yen(image) >>> binary = image <= thresh rrrNrr%) rrrrfloat32sumrlogr) r"rOr+rrpmfP1P1_sqP2_sqcritrZrZr[rs)  " rcCst|||\}}t|dkr|r|S|dS|tj}t|}|d|}||}t|} | dd|dd} | d| dd|dd} | | d} |d|d} | |dd}|dd|dk|| k@}|rt|S|dS)a Return threshold value(s) based on ISODATA method. Histogram-based threshold, known as Ridler-Calvard method or inter-means. Threshold values returned satisfy the following equality:: threshold = (image[image <= threshold].mean() + image[image > threshold].mean()) / 2.0 That is, returned thresholds are intensities that separate the image into two groups of pixels, where the threshold intensity is midway between the mean intensities of these groups. For integer images, the above equality holds to within one; for floating- point images, the equality holds to within the histogram bin-width. Either image or hist must be provided. In case hist is given, the actual histogram of the image is ignored. Parameters ---------- image : (N, M[, ..., P]) ndarray Grayscale input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. return_all : bool, optional If False (default), return only the lowest threshold that satisfies the above equality. If True, return all valid thresholds. hist : array, or 2-tuple of arrays, optional Histogram to determine the threshold from and a corresponding array of bin center intensities. Alternatively, only the histogram can be passed. Returns ------- threshold : float or int or array Threshold value(s). References ---------- .. [1] Ridler, TW & Calvard, S (1978), "Picture thresholding using an iterative selection method" IEEE Transactions on Systems, Man and Cybernetics 8: 630-632, :DOI:`10.1109/TSMC.1978.4310039` .. [2] Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding Techniques and Quantitative Performance Evaluation" Journal of Electronic Imaging, 13(1): 146-165, http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf :DOI:`10.1117/1.1631315` .. [3] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold Examples -------- >>> from skimage.data import coins >>> image = coins() >>> thresh = threshold_isodata(image) >>> binary = image > thresh rrrNg@)rr7rrrr)r"rO return_allr+rrcsumlcsumh intensity_sumcsum_intensitylowerhigherall_mean bin_width distances thresholdsrZrZr[rs&<       rggQo@cCstj||dd\}}tj|ddgdd}t||kd}t|d|}t||d}t|d||d|} t||d||d} | |} | |} | t| | t| } | S)aCompute cross-entropy between distributions above and below a threshold. Parameters ---------- image : array The input array of values. threshold : float The value dividing the foreground and background in ``image``. bins : int or array of float, optional The number of bins or the bin edges. (Any valid value to the ``bins`` argument of ``np.histogram`` will work here.) For an exact calculation, each unique value should have its own bin. The default value for bins ensures exact handling of uint8 images: ``bins=256`` results in aliasing problems due to bin width not being equal to 1. Returns ------- nu : float The cross-entropy target value as defined in [1]_. Notes ----- See Li and Lee, 1993 [1]_; this is the objective function ``threshold_li`` minimizes. This function can be improved but this implementation most closely matches equation 8 in [1]_ and equations 1-3 in [2]_. References ---------- .. [1] Li C.H. and Lee C.K. (1993) "Minimum Cross Entropy Thresholding" Pattern Recognition, 26(4): 617-625 :DOI:`10.1016/0031-3203(93)90115-D` .. [2] Li C.H. and Tam P.K.S. (1998) "An Iterative Algorithm for Minimum Cross Entropy Thresholding" Pattern Recognition Letters, 18(8): 771-776 :DOI:`10.1016/S0167-8655(98)00057-9` T)binsdensityr-validrzrN)rr convolve flatnonzerorr)r"rrr bin_edgesrtm0am0bm1am1bmuamubnurZrZr[_cross_entropy8s$r) tolerance initial_guess iter_callbackcCs|t|}|jdkrtjSt||jdkr|jdS|t|}|jdkr-dSt|}||8}|jj dvrA|p?d}n|pOtt t |d}|durZt |}n>> from skimage.data import camera >>> image = camera() >>> thresh = threshold_li(image) >>> binary = image > thresh rgiur-rNzNThe initial guess for threshold_li must be within the range of the image. Got z for image min z and max rczIncorrect type for `initial_guess`; should be a floating point value, or a function mapping an array to a floating point value.rr"r#)weights)risnanrnanrflatisfiniteminrwkinddiffuniquer}callablermaxr TypeErrorr reshaperrabsaverager)r"rrr image_mint_next image_maxmsgt_currr+r foreground background mean_fore mean_backrrZrZr[ris9                  rmax_iter max_num_iterz1.0z0.19)removed_versiondeprecated_version'c Csdd}t|||\}}|jtjdd}t|D]}t|d}||} t| dkr,nqt| dkr7td||dkrAtd t || d | dd} || d | S) a Return threshold value based on minimum method. The histogram of the input ``image`` is computed if not provided and smoothed until there are only two maxima. Then the minimum in between is the threshold value. Either image or hist must be provided. In case hist is given, the actual histogram of the image is ignored. Parameters ---------- image : (N, M[, ..., P]) ndarray, optional Grayscale input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. max_num_iter : int, optional Maximum number of iterations to smooth the histogram. hist : array, or 2-tuple of arrays, optional Histogram to determine the threshold from and a corresponding array of bin center intensities. Alternatively, only the histogram can be passed. Returns ------- threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground. Raises ------ RuntimeError If unable to find two local maxima in the histogram or if the smoothing takes more than 1e4 iterations. References ---------- .. [1] C. A. Glasbey, "An analysis of histogram-based thresholding algorithms," CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993. .. [2] Prewitt, JMS & Mendelsohn, ML (1966), "The analysis of cell images", Annals of the New York Academy of Sciences 128: 1035-1053 :DOI:`10.1111/j.1749-6632.1965.tb11715.x` Examples -------- >>> from skimage.data import camera >>> image = camera() >>> thresh = threshold_minimum(image) >>> binary = image > thresh cSsjt}d}t|jddD]$}|dkr&||d||kr%d}||q||d||kr2d}q|S)Nrrr)rrangerappend)r+ maximum_idxs directionrSrZrZr[find_local_maxima_idx5s z0threshold_minimum..find_local_maxima_idxFrtrnrz&Unable to find two maxima in histogramrz0Maximum iteration reached for histogramsmoothingr) rrrfloat64rruniform_filter1dr7 RuntimeErrorargmin) r"rOrr+rrr smooth_histcounterr threshold_idxrZrZr[rs7     rcCs t|S)aReturn threshold value based on the mean of grayscale values. Parameters ---------- image : (N, M[, ..., P]) ndarray Grayscale input image. Returns ------- threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground. References ---------- .. [1] C. A. Glasbey, "An analysis of histogram-based thresholding algorithms," CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993. :DOI:`10.1006/cgip.1993.1040` Examples -------- >>> from skimage.data import camera >>> image = camera() >>> thresh = threshold_mean(image) >>> binary = image > thresh )rr}r"rZrZr[r\s rcCst||dd\}}t|}t|}||}t|dkdddg\}}||||k}|rD|ddd}||d}||d}~||} t| } || |} t|d| d} || }| | } || | | } t| |}|r~||d}||S)aReturn threshold value based on the triangle algorithm. Parameters ---------- image : (N, M[, ..., P]) ndarray Grayscale input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. Returns ------- threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground. References ---------- .. [1] Zack, G. W., Rogers, W. E. and Latt, S. A., 1977, Automatic Measurement of Sister Chromatid Exchange Frequency, Journal of Histochemistry and Cytochemistry 25 (7), pp. 741-753 :DOI:`10.1177/25.7.70454` .. [2] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold Examples -------- >>> from skimage.data import camera >>> image = camera() >>> thresh = threshold_triangle(image) >>> binary = image > thresh r"r#rrNrr)r r4r7rrwherersqrt)r"rOr+rarg_peak_height peak_height arg_low_levelarg_high_levelflipwidthx1y1normlength arg_levelrZrZr[r{s,#      rcs.t|ts |fj}t|tj}tdd|D}tjj |dd|dd}t |tj d}||9}t |tj d}t t jtdd |D}fd d |D}t|} td d|D} t|| ||} | j |dd} | | } t|| ||} | j |dd} | | } tt| | | d d } | | fS)uHReturn local mean and standard deviation of each pixel using a neighborhood defined by a rectangular window size ``w``. The algorithm uses integral images to speedup computation. This is used by :func:`threshold_niblack` and :func:`threshold_sauvola`. Parameters ---------- image : (N, M[, ..., P]) ndarray Grayscale input image. w : int, or iterable of int Window size specified as a single odd integer (3, 5, 7, …), or an iterable of length ``image.ndim`` containing only odd integers (e.g. ``(1, 5, 5)``). Returns ------- m : ndarray of float, same shape as ``image`` Local mean of the image. s : ndarray of float, same shape as ``image`` Local standard deviation of the image. References ---------- .. [1] F. Shafait, D. Keysers, and T. M. Breuel, "Efficient implementation of local adaptive thresholding techniques using integral images." in Document Recognition and Retrieval XV, (San Jose, USA), Jan. 2008. :DOI:`10.1117/12.767755` css$|] }|dd|dfVqdS)rrNrZ)rqkrZrZr[rss"z_mean_std..FrtrorrvcSsg|]}d|fqS)rrZrq_wrZrZr[r|sz_mean_std..cs(g|]}djdt|dkqS)rr)rrr)rqindicesrrZr[r|s css|]}|dVqdS)rNrZrrZrZr[rssrN)rrrrrrwrrpadrrrr itertoolsproductprodrrclip)r"wr pad_widthpaddedintegral integral_sqkernel_indices kernel_valuestotal_window_size kernel_shapemg2srZrr[ _mean_stds:     r"皙?cCst||\}}|||S)uVApplies Niblack local threshold to an array. A threshold T is calculated for every pixel in the image using the following formula:: T = m(x,y) - k * s(x,y) where m(x,y) and s(x,y) are the mean and standard deviation of pixel (x,y) neighborhood defined by a rectangular window with size w times w centered around the pixel. k is a configurable parameter that weights the effect of standard deviation. Parameters ---------- image : (N, M[, ..., P]) ndarray Grayscale input image. window_size : int, or iterable of int, optional Window size specified as a single odd integer (3, 5, 7, …), or an iterable of length ``image.ndim`` containing only odd integers (e.g. ``(1, 5, 5)``). k : float, optional Value of parameter k in threshold formula. Returns ------- threshold : (N, M) ndarray Threshold mask. All pixels with an intensity higher than this value are assumed to be foreground. Notes ----- This algorithm is originally designed for text recognition. The Bradley threshold is a particular case of the Niblack one, being equivalent to >>> from skimage import data >>> image = data.page() >>> q = 1 >>> threshold_image = threshold_niblack(image, k=0) * q for some value ``q``. By default, Bradley and Roth use ``q=1``. References ---------- .. [1] W. Niblack, An introduction to Digital Image Processing, Prentice-Hall, 1986. .. [2] D. Bradley and G. Roth, "Adaptive thresholding using Integral Image", Journal of Graphics Tools 12(2), pp. 13-21, 2007. :DOI:`10.1080/2151237X.2007.10129236` Examples -------- >>> from skimage import data >>> image = data.page() >>> threshold_image = threshold_niblack(image, window_size=7, k=0.1) )r")r" window_sizer rr!rZrZr[r s; rcCsJ|durt|dd\}}d||}t||\}}|d|||dS)uApplies Sauvola local threshold to an array. Sauvola is a modification of Niblack technique. In the original method a threshold T is calculated for every pixel in the image using the following formula:: T = m(x,y) * (1 + k * ((s(x,y) / R) - 1)) where m(x,y) and s(x,y) are the mean and standard deviation of pixel (x,y) neighborhood defined by a rectangular window with size w times w centered around the pixel. k is a configurable parameter that weights the effect of standard deviation. R is the maximum standard deviation of a grayscale image. Parameters ---------- image : (N, M[, ..., P]) ndarray Grayscale input image. window_size : int, or iterable of int, optional Window size specified as a single odd integer (3, 5, 7, …), or an iterable of length ``image.ndim`` containing only odd integers (e.g. ``(1, 5, 5)``). k : float, optional Value of the positive parameter k. r : float, optional Value of R, the dynamic range of standard deviation. If None, set to the half of the image dtype range. Returns ------- threshold : (N, M) ndarray Threshold mask. All pixels with an intensity higher than this value are assumed to be foreground. Notes ----- This algorithm is originally designed for text recognition. References ---------- .. [1] J. Sauvola and M. Pietikainen, "Adaptive document image binarization," Pattern Recognition 33(2), pp. 225-236, 2000. :DOI:`10.1016/S0031-3203(99)00055-2` Examples -------- >>> from skimage import data >>> image = data.page() >>> t_sauvola = threshold_sauvola(image, window_size=15, k=0.2) >>> binary_image = image > t_sauvola NF) clip_negativer-r)rr")r"r%r riminimaxrr!rZrZr[rKs 5 rc CsZtj|d|d}||k}||k}t|\}}t||t|d}|dk}||} | S)akApply hysteresis thresholding to ``image``. This algorithm finds regions where ``image`` is greater than ``high`` OR ``image`` is greater than ``low`` *and* that region is connected to a region greater than ``high``. Parameters ---------- image : array, shape (M,[ N, ..., P]) Grayscale input image. low : float, or array of same shape as ``image`` Lower threshold. high : float, or array of same shape as ``image`` Higher threshold. Returns ------- thresholded : array of bool, same shape as ``image`` Array in which ``True`` indicates the locations where ``image`` was above the hysteresis threshold. Examples -------- >>> image = np.array([1, 2, 3, 2, 1, 2, 1, 3, 2]) >>> apply_hysteresis_threshold(image, 1.5, 2.5).astype(int) array([0, 1, 1, 1, 0, 0, 0, 1, 1]) References ---------- .. [1] J. Canny. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1986; vol. 8, pp.679-698. :DOI:`10.1109/TPAMI.1986.4767851` N)a_mina_maxrr)rrrlabelrr) r"lowhighmask_low mask_high labels_low num_labelssumsconnected_to_high thresholdedrZrZr[rs#rc Cs|dur|jdkr|jddvrtd|jdt|||dd\}}|d }t|}||kr>d |d |d }t|||krPt|d kd dd}nz t ||d}Wnt yit ||d}Ynw||} | S)a Generate `classes`-1 threshold values to divide gray levels in `image`, following Otsu's method for multiple classes. The threshold values are chosen to maximize the total sum of pairwise variances between the thresholded graylevel classes. See Notes and [1]_ for more details. Either image or hist must be provided. If hist is provided, the actual histogram of the image is ignored. Parameters ---------- image : (N, M[, ..., P]) ndarray, optional Grayscale input image. classes : int, optional Number of classes to be thresholded, i.e. the number of resulting regions. nbins : int, optional Number of bins used to calculate the histogram. This value is ignored for integer arrays. hist : array, or 2-tuple of arrays, optional Histogram from which to determine the threshold, and optionally a corresponding array of bin center intensities. If no hist provided, this function will compute it from the image (see notes). Returns ------- thresh : array Array containing the threshold values for the desired classes. Raises ------ ValueError If ``image`` contains less grayscale value then the desired number of classes. Notes ----- This implementation relies on a Cython function whose complexity is :math:`O\left(\frac{Ch^{C-1}}{(C-1)!}\right)`, where :math:`h` is the number of histogram bins and :math:`C` is the number of classes desired. If no hist is given, this function will make use of `skimage.exposure.histogram`, which behaves differently than `np.histogram`. While both allowed, use the former for consistent behaviour. The input image must be grayscale. References ---------- .. [1] Liao, P-S., Chen, T-S. and Chung, P-C., "A fast algorithm for multilevel thresholding", Journal of Information Science and Engineering 17 (5): 713-727, 2001. Available at: :DOI:`10.6688/JISE.2001.17.5.1` .. [2] Tosa, Y., "Multi-Otsu Threshold", a java plugin for ImageJ. Available at: Examples -------- >>> from skimage.color import label2rgb >>> from skimage import data >>> image = data.camera() >>> thresholds = threshold_multiotsu(image) >>> regions = np.digitize(image, bins=thresholds) >>> regions_colorized = label2rgb(regions) NrrrzYthreshold_multiotsu is expected to work correctly only for grayscale images; image shape rT)rrzThe input image has only z/ different values. It cannot be thresholded in z classes.rr) rrr rrr count_nonzerorrr MemoryErrorr ) r"classesrOr+probrnvaluesr thresh_idxrfrZrZr[rs. G    r)NNrT)r]T)rnrrroNr)NF)Nr!)Nr!F)Nr!r)r!)r#r$)r#r$N)Nrnr!)5r>rr5 collectionsrcollections.abcrnumpyrscipyrr_shared.filtersr _shared.utilsrrr _shared.version_requirementsr exposurer filters._multiotsur r r1rutilr_sparserr__all__r\rrrrrrrr_DEFAULT_ENTROPY_BINSrrrrrr"rrrrrZrZrZr[sV         > ; c8H=x 1  \ M D ?</