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https://github.com/wassname/scikit-image.git
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radioxoma
259 lines
9.5 KiB
Python
259 lines
9.5 KiB
Python
__all__ = ['threshold_adaptive',
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'threshold_otsu',
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'threshold_yen',
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'threshold_isodata']
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import numpy as np
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import scipy.ndimage
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from skimage.exposure import histogram
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def threshold_adaptive(image, block_size, method='gaussian', offset=0,
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mode='reflect', param=None):
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"""Applies an adaptive threshold to an array.
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Also known as local or dynamic thresholding where the threshold value is
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the weighted mean for the local neighborhood of a pixel subtracted by a
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constant. Alternatively the threshold can be determined dynamically by a a
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given function using the 'generic' method.
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Parameters
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----------
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image : (N, M) ndarray
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Input image.
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block_size : int
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Uneven size of pixel neighborhood which is used to calculate the
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threshold value (e.g. 3, 5, 7, ..., 21, ...).
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method : {'generic', 'gaussian', 'mean', 'median'}, optional
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Method used to determine adaptive threshold for local neighbourhood in
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weighted mean image.
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* 'generic': use custom function (see `param` parameter)
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* 'gaussian': apply gaussian filter (see `param` parameter for custom\
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sigma value)
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* 'mean': apply arithmetic mean filter
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* 'median': apply median rank filter
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By default the 'gaussian' method is used.
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offset : float, optional
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Constant subtracted from weighted mean of neighborhood to calculate
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the local threshold value. Default offset is 0.
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mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
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The mode parameter determines how the array borders are handled, where
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cval is the value when mode is equal to 'constant'.
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Default is 'reflect'.
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param : {int, function}, optional
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Either specify sigma for 'gaussian' method or function object for
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'generic' method. This functions takes the flat array of local
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neighbourhood as a single argument and returns the calculated
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threshold for the centre pixel.
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Returns
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-------
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threshold : (N, M) ndarray
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Thresholded binary image
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References
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----------
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.. [1] http://docs.opencv.org/modules/imgproc/doc/miscellaneous_transformations.html?highlight=threshold#adaptivethreshold
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Examples
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--------
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>>> from skimage.data import camera
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>>> image = camera()[:50, :50]
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>>> binary_image1 = threshold_adaptive(image, 15, 'mean')
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>>> func = lambda arr: arr.mean()
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>>> binary_image2 = threshold_adaptive(image, 15, 'generic', param=func)
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"""
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thresh_image = np.zeros(image.shape, 'double')
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if method == 'generic':
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scipy.ndimage.generic_filter(image, param, block_size,
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output=thresh_image, mode=mode)
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elif method == 'gaussian':
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if param is None:
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# automatically determine sigma which covers > 99% of distribution
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sigma = (block_size - 1) / 6.0
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else:
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sigma = param
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scipy.ndimage.gaussian_filter(image, sigma, output=thresh_image,
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mode=mode)
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elif method == 'mean':
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mask = 1. / block_size * np.ones((block_size,))
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# separation of filters to speedup convolution
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scipy.ndimage.convolve1d(image, mask, axis=0, output=thresh_image,
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mode=mode)
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scipy.ndimage.convolve1d(thresh_image, mask, axis=1,
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output=thresh_image, mode=mode)
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elif method == 'median':
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scipy.ndimage.median_filter(image, block_size, output=thresh_image,
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mode=mode)
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return image > (thresh_image - offset)
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def threshold_otsu(image, nbins=256):
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"""Return threshold value based on Otsu's method.
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Parameters
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----------
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image : array
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Input image.
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nbins : int, optional
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Number of bins used to calculate histogram. This value is ignored for
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integer arrays.
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Returns
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-------
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threshold : float
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Upper threshold value. All pixels intensities that less or equal of
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this value assumed as foreground.
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References
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----------
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.. [1] Wikipedia, http://en.wikipedia.org/wiki/Otsu's_Method
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Examples
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--------
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>>> from skimage.data import camera
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>>> image = camera()
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>>> thresh = threshold_otsu(image)
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>>> binary = image <= thresh
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"""
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hist, bin_centers = histogram(image, nbins)
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hist = hist.astype(float)
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# class probabilities for all possible thresholds
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weight1 = np.cumsum(hist)
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weight2 = np.cumsum(hist[::-1])[::-1]
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# class means for all possible thresholds
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mean1 = np.cumsum(hist * bin_centers) / weight1
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mean2 = (np.cumsum((hist * bin_centers)[::-1]) / weight2[::-1])[::-1]
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# Clip ends to align class 1 and class 2 variables:
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# The last value of `weight1`/`mean1` should pair with zero values in
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# `weight2`/`mean2`, which do not exist.
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variance12 = weight1[:-1] * weight2[1:] * (mean1[:-1] - mean2[1:]) ** 2
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idx = np.argmax(variance12)
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threshold = bin_centers[:-1][idx]
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return threshold
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def threshold_yen(image, nbins=256):
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"""Return threshold value based on Yen's method.
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Parameters
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----------
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image : array
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Input image.
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nbins : int, optional
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Number of bins used to calculate histogram. This value is ignored for
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integer arrays.
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Returns
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-------
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threshold : float
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Upper threshold value. All pixels intensities that less or equal of
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this value assumed as foreground.
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References
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----------
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.. [1] Yen J.C., Chang F.J., and Chang S. (1995) "A New Criterion
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for Automatic Multilevel Thresholding" IEEE Trans. on Image
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Processing, 4(3): 370-378
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.. [2] Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding
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Techniques and Quantitative Performance Evaluation" Journal of
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Electronic Imaging, 13(1): 146-165,
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http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf
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.. [3] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold
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Examples
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--------
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>>> from skimage.data import camera
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>>> image = camera()
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>>> thresh = threshold_yen(image)
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>>> binary = image <= thresh
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"""
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hist, bin_centers = histogram(image, nbins)
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# On blank images (e.g. filled with 0) with int dtype, `histogram()`
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# returns `bin_centers` containing only one value. Speed up with it.
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if bin_centers.size == 1:
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return bin_centers[0]
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# Calculate probability mass function
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pmf = hist.astype(np.float32) / hist.sum()
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P1 = np.cumsum(pmf) # Cumulative normalized histogram
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P1_sq = np.cumsum(pmf ** 2)
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# Get cumsum calculated from end of squared array:
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P2_sq = np.cumsum(pmf[::-1] ** 2)[::-1]
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# P2_sq indexes is shifted +1. I assume, with P1[:-1] it's help avoid '-inf'
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# in crit. ImageJ Yen implementation replaces those values by zero.
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crit = np.log(((P1_sq[:-1] * P2_sq[1:]) ** -1) *
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(P1[:-1] * (1.0 - P1[:-1])) ** 2)
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return bin_centers[crit.argmax()]
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def threshold_isodata(image, nbins=256):
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"""Return threshold value based on ISODATA method.
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Histogram-based threshold, known as Ridler-Calvard method or intermeans.
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Parameters
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----------
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image : array
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Input image.
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nbins : int, optional
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Number of bins used to calculate histogram. This value is ignored for
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integer arrays.
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Returns
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-------
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threshold : float or int, corresponding input array dtype.
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Upper threshold value. All pixels intensities that less or equal of
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this value assumed as background.
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References
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----------
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.. [1] Ridler, TW & Calvard, S (1978), "Picture thresholding using an
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iterative selection method"
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.. [2] IEEE Transactions on Systems, Man and Cybernetics 8: 630-632,
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http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4310039
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.. [3] Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding
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Techniques and Quantitative Performance Evaluation" Journal of
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Electronic Imaging, 13(1): 146-165,
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http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf
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.. [4] ImageJ AutoThresholder code,
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http://fiji.sc/wiki/index.php/Auto_Threshold
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Examples
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--------
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>>> from skimage.data import coins
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>>> image = coins()
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>>> thresh = threshold_isodata(image)
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>>> binary = image > thresh
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"""
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hist, bin_centers = histogram(image, nbins)
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# On blank images (e.g. filled with 0) with int dtype, `histogram()`
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# returns `bin_centers` containing only one value. Speed up with it.
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if bin_centers.size == 1:
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return bin_centers[0]
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# It is not necessary to calculate the probability mass function here,
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# because the l and h fractions already include the normalization.
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pmf = hist.astype(np.float32) # / hist.sum()
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cpmfl = np.cumsum(pmf, dtype=np.float32)
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cpmfh = np.cumsum(pmf[::-1], dtype=np.float32)[::-1]
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binnums = np.arange(pmf.size, dtype=np.uint8)
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# l and h contain average value of pixels in sum of bins, calculated
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# from lower to higher and from higher to lower respectively.
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l = np.ma.divide(np.cumsum(pmf * binnums, dtype=np.float32), cpmfl)
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h = np.ma.divide(
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np.cumsum((pmf[::-1] * binnums[::-1]), dtype=np.float32)[::-1],
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cpmfh)
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allmean = (l + h) / 2.0
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threshold = bin_centers[np.nonzero(allmean.round() == binnums)[0][0]]
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# This implementation returns threshold where
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# `background <= threshold < foreground`.
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return threshold
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