mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-30 08:46:14 +08:00
Steven Silvester
4680f30466
Add a function to set up a skimage test Switch to new test helper function Import local packages that raise warnings in test setup function More fixes to doctests Fix regionprops doc test Try and fix the test_rank failure. Remove no longer needed RectangleSelector shim Skip more doctests in _regionprops Try importing another scipy subpackage
303 lines
12 KiB
Python
303 lines
12 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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from skimage._shared.utils import assert_nD
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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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assert_nD(image, 2)
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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.ravel(), 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.ravel(), 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, return_all=False):
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"""Return threshold value(s) based on ISODATA method.
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Histogram-based threshold, known as Ridler-Calvard method or inter-means.
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Threshold values returned satisfy the following equality:
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threshold = (image[image <= threshold].mean() +
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image[image > threshold].mean()) / 2.0
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That is, returned thresholds are intensities that separate the image into
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two groups of pixels, where the threshold intensity is midway between the
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mean intensities of these groups.
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For integer images, the above equality holds to within one; for floating-
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point images, the equality holds to within the histogram bin-width.
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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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return_all: bool, optional
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If False (default), return only the lowest threshold that satisfies
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the above equality. If True, return all valid thresholds.
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Returns
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-------
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threshold : float or int or array
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Threshold value(s).
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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.ravel(), nbins)
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# image only contains one unique value
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if len(bin_centers) == 1:
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if return_all:
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return bin_centers
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else:
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return bin_centers[0]
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hist = hist.astype(np.float32)
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# csuml and csumh contain the count of pixels in that bin or lower, and
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# in all bins strictly higher than that bin, respectively
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csuml = np.cumsum(hist)
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csumh = np.cumsum(hist[::-1])[::-1] - hist
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# intensity_sum contains the total pixel intensity from each bin
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intensity_sum = hist * bin_centers
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# l and h contain average value of all pixels in that bin or lower, and
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# in all bins strictly higher than that bin, respectively.
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# Note that since exp.histogram does not include empty bins at the low or
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# high end of the range, csuml and csumh are strictly > 0, except in the
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# last bin of csumh, which is zero by construction.
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# So no worries about division by zero in the following lines, except
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# for the last bin, but we can ignore that because no valid threshold
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# can be in the top bin. So we just patch up csumh[-1] to not cause 0/0
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# errors.
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csumh[-1] = 1
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l = np.cumsum(intensity_sum) / csuml
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h = (np.cumsum(intensity_sum[::-1])[::-1] - intensity_sum) / csumh
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# isodata finds threshold values that meet the criterion t = (l + m)/2
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# where l is the mean of all pixels <= t and h is the mean of all pixels
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# > t, as calculated above. So we are looking for places where
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# (l + m) / 2 equals the intensity value for which those l and m figures
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# were calculated -- which is, of course, the histogram bin centers.
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# We only require this equality to be within the precision of the bin
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# width, of course.
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all_mean = (l + h) / 2.0
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bin_width = bin_centers[1] - bin_centers[0]
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# Look only at thresholds that are below the actual all_mean value,
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# for consistency with the threshold being included in the lower pixel
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# group. Otherwise can get thresholds that are not actually fixed-points
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# of the isodata algorithm. For float images, this matters less, since
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# there really can't be any guarantees anymore anyway.
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distances = all_mean - bin_centers
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thresholds = bin_centers[(distances >= 0) & (distances < bin_width)]
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if return_all:
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return thresholds
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else:
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return thresholds[0]
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