text: import numpy as np
  
  from ..color import rgb2gray
  from ..util.dtype import dtype_range, dtype_limits
  from .._shared.utils import warn
  
  
  __all__ = ['histogram', 'cumulative_distribution', 'equalize_hist',
             'rescale_intensity', 'adjust_gamma', 'adjust_log', 'adjust_sigmoid']
  
  
  DTYPE_RANGE = dtype_range.copy()
  DTYPE_RANGE.update((d.__name__, limits) for d, limits in dtype_range.items())
  DTYPE_RANGE.update({'uint10': (0, 2 ** 10 - 1),
                      'uint12': (0, 2 ** 12 - 1),
                      'uint14': (0, 2 ** 14 - 1),
                      'bool': dtype_range[np.bool_],
                      'float': dtype_range[np.float64]})
  
  
  def histogram(image, nbins=256):
      """Return histogram of image.
  
      Unlike `numpy.histogram`, this function returns the centers of bins and
      does not rebin integer arrays. For integer arrays, each integer value has
      its own bin, which improves speed and intensity-resolution.
  
      The histogram is computed on the flattened image: for color images, the
      function should be used separately on each channel to obtain a histogram
      for each color channel.
  
      Parameters
      ----------
      image : array
          Input image.
      nbins : int
          Number of bins used to calculate histogram. This value is ignored for
          integer arrays.
  
      Returns
      -------
      hist : array
          The values of the histogram.
      bin_centers : array
          The values at the center of the bins.
  
      See Also
      --------
      cumulative_distribution
  
      Examples
      --------
      >>> from skimage import data, exposure, img_as_float
      >>> image = img_as_float(data.camera())
      >>> np.histogram(image, bins=2)
      (array([107432, 154712]), array([ 0. ,  0.5,  1. ]))
      >>> exposure.histogram(image, nbins=2)
      (array([107432, 154712]), array([ 0.25,  0.75]))
      """
      sh = image.shape
      if len(sh) == 3 and sh[-1] < 4:
          warn("This might be a color image. The histogram will be "
               "computed on the flattened image. You can instead "
               "apply this function to each color channel.")
  
      # For integer types, histogramming with bincount is more efficient.
      if np.issubdtype(image.dtype, np.integer):
          offset = 0
          image_min = np.min(image)
          if image_min < 0:
              offset = image_min
              image_range = np.max(image).astype(np.int64) - image_min
              # get smallest dtype that can hold both minimum and offset maximum
              offset_dtype = np.promote_types(np.min_scalar_type(image_range),
                                              np.min_scalar_type(image_min))
              if image.dtype != offset_dtype:
                  # prevent overflow errors when offsetting
                  image = image.astype(offset_dtype)
              image = image - offset
          hist = np.bincount(image.ravel())
          bin_centers = np.arange(len(hist)) + offset
  
          # clip histogram to start with a non-zero bin
          idx = np.nonzero(hist)[0][0]
          return hist[idx:], bin_centers[idx:]
      else:
          hist, bin_edges = np.histogram(image.flat, bins=nbins)
          bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2.
          return hist, bin_centers
  
  
  def cumulative_distribution(image, nbins=256):
      """Return cumulative distribution function (cdf) for the given image.
  
      Parameters
      ----------
      image : array
          Image array.
      nbins : int
          Number of bins for image histogram.
  
      Returns
      -------
      img_cdf : array
          Values of cumulative distribution function.
      bin_centers : array
          Centers of bins.
  
      See Also
      --------
      histogram
  
      References
      ----------
      .. [1] https://en.wikipedia.org/wiki/Cumulative_distribution_function
  
      Examples
      --------
      >>> from skimage import data, exposure, img_as_float
      >>> image = img_as_float(data.camera())
      >>> hi = exposure.histogram(image)
      >>> cdf = exposure.cumulative_distribution(image)
      >>> np.alltrue(cdf[0] == np.cumsum(hi[0])/float(image.size))
      True
      """
      hist, bin_centers = histogram(image, nbins)
      img_cdf = hist.cumsum()
      img_cdf = img_cdf / float(img_cdf[-1])
      return img_cdf, bin_centers
  
  
  def equalize_hist(image, nbins=256, mask=None):
      """Return image after histogram equalization.
  
      Parameters
      ----------
      image : array
          Image array.
      nbins : int, optional
          Number of bins for image histogram. Note: this argument is
          ignored for integer images, for which each integer is its own
          bin.
      mask: ndarray of bools or 0s and 1s, optional
          Array of same shape as `image`. Only points at which mask == True
          are used for the equalization, which is applied to the whole image.
  
      Returns
      -------
      out : float array
          Image array after histogram equalization.
  
      Notes
      -----
      This function is adapted from [1]_ with the author's permission.
  
      References
      ----------
      .. [1] http://www.janeriksolem.net/histogram-equalization-with-python-and.html
      .. [2] https://en.wikipedia.org/wiki/Histogram_equalization
  
      """
      if mask is not None:
          mask = np.array(mask, dtype=bool)
          cdf, bin_centers = cumulative_distribution(image[mask], nbins)
      else:
          cdf, bin_centers = cumulative_distribution(image, nbins)
      out = np.interp(image.flat, bin_centers, cdf)
      return out.reshape(image.shape)
  
  
  def intensity_range(image, range_values='image', clip_negative=False):
      """Return image intensity range (min, max) based on desired value type.
  
      Parameters
      ----------
      image : array
          Input image.
      range_values : str or 2-tuple
          The image intensity range is configured by this parameter.
          The possible values for this parameter are enumerated below.
  
          'image'
              Return image min/max as the range.
          'dtype'
              Return min/max of the image's dtype as the range.
          dtype-name
              Return intensity range based on desired `dtype`. Must be valid key
              in `DTYPE_RANGE`. Note: `image` is ignored for this range type.
          2-tuple
              Return `range_values` as min/max intensities. Note that there's no
              reason to use this function if you just want to specify the
              intensity range explicitly. This option is included for functions
              that use `intensity_range` to support all desired range types.
  
      clip_negative : bool
          If True, clip the negative range (i.e. return 0 for min intensity)
          even if the image dtype allows negative values.
      """
      if range_values == 'dtype':
          range_values = image.dtype.type
  
      if range_values == 'image':
          i_min = np.min(image)
          i_max = np.max(image)
      elif range_values in DTYPE_RANGE:
          i_min, i_max = DTYPE_RANGE[range_values]
          if clip_negative:
              i_min = 0
      else:
          i_min, i_max = range_values
      return i_min, i_max
  
  
  def rescale_intensity(image, in_range='image', out_range='dtype'):
      """Return image after stretching or shrinking its intensity levels.
  
      The desired intensity range of the input and output, `in_range` and
      `out_range` respectively, are used to stretch or shrink the intensity range
      of the input image. See examples below.
  
      Parameters
      ----------
      image : array
          Image array.
      in_range, out_range : str or 2-tuple
          Min and max intensity values of input and output image.
          The possible values for this parameter are enumerated below.
  
          'image'
              Use image min/max as the intensity range.
          'dtype'
              Use min/max of the image's dtype as the intensity range.
          dtype-name
              Use intensity range based on desired `dtype`. Must be valid key
              in `DTYPE_RANGE`.
          2-tuple
              Use `range_values` as explicit min/max intensities.
  
      Returns
      -------
      out : array
          Image array after rescaling its intensity. This image is the same dtype
          as the input image.
  
      See Also
      --------
      equalize_hist
  
      Examples
      --------
      By default, the min/max intensities of the input image are stretched to
      the limits allowed by the image's dtype, since `in_range` defaults to
      'image' and `out_range` defaults to 'dtype':
  
      >>> image = np.array([51, 102, 153], dtype=np.uint8)
      >>> rescale_intensity(image)
      array([  0, 127, 255], dtype=uint8)
  
      It's easy to accidentally convert an image dtype from uint8 to float:
  
      >>> 1.0 * image
      array([  51.,  102.,  153.])
  
      Use `rescale_intensity` to rescale to the proper range for float dtypes:
  
      >>> image_float = 1.0 * image
      >>> rescale_intensity(image_float)
      array([ 0. ,  0.5,  1. ])
  
      To maintain the low contrast of the original, use the `in_range` parameter:
  
      >>> rescale_intensity(image_float, in_range=(0, 255))
      array([ 0.2,  0.4,  0.6])
  
      If the min/max value of `in_range` is more/less than the min/max image
      intensity, then the intensity levels are clipped:
  
      >>> rescale_intensity(image_float, in_range=(0, 102))
      array([ 0.5,  1. ,  1. ])
  
      If you have an image with signed integers but want to rescale the image to
      just the positive range, use the `out_range` parameter:
  
      >>> image = np.array([-10, 0, 10], dtype=np.int8)
      >>> rescale_intensity(image, out_range=(0, 127))
      array([  0,  63, 127], dtype=int8)
  
      """
      dtype = image.dtype.type
  
      imin, imax = intensity_range(image, in_range)
      omin, omax = intensity_range(image, out_range, clip_negative=(imin >= 0))
  
      image = np.clip(image, imin, imax)
  
      image = (image - imin) / float(imax - imin)
      return np.array(image * (omax - omin) + omin, dtype=dtype)
  
  
  def _assert_non_negative(image):
  
      if np.any(image < 0):
          raise ValueError('Image Correction methods work correctly only on '
                           'images with non-negative values. Use '
                           'skimage.exposure.rescale_intensity.')
  
  
  def adjust_gamma(image, gamma=1, gain=1):
      """Performs Gamma Correction on the input image.
  
      Also known as Power Law Transform.
      This function transforms the input image pixelwise according to the
      equation ``O = I**gamma`` after scaling each pixel to the range 0 to 1.
  
      Parameters
      ----------
      image : ndarray
          Input image.
      gamma : float
          Non negative real number. Default value is 1.
      gain : float
          The constant multiplier. Default value is 1.
  
      Returns
      -------
      out : ndarray
          Gamma corrected output image.
  
      See Also
      --------
      adjust_log
  
      Notes
      -----
      For gamma greater than 1, the histogram will shift towards left and
      the output image will be darker than the input image.
  
      For gamma less than 1, the histogram will shift towards right and
      the output image will be brighter than the input image.
  
      References
      ----------
      .. [1] https://en.wikipedia.org/wiki/Gamma_correction
  
      Examples
      --------
      >>> from skimage import data, exposure, img_as_float
      >>> image = img_as_float(data.moon())
      >>> gamma_corrected = exposure.adjust_gamma(image, 2)
      >>> # Output is darker for gamma > 1
      >>> image.mean() > gamma_corrected.mean()
      True
      """
      _assert_non_negative(image)
      dtype = image.dtype.type
  
      if gamma < 0:
          raise ValueError("Gamma should be a non-negative real number.")
  
      scale = float(dtype_limits(image, True)[1] - dtype_limits(image, True)[0])
  
      out = ((image / scale) ** gamma) * scale * gain
      return dtype(out)
  
  
  def adjust_log(image, gain=1, inv=False):
      """Performs Logarithmic correction on the input image.
  
      This function transforms the input image pixelwise according to the
      equation ``O = gain*log(1 + I)`` after scaling each pixel to the range 0 to 1.
      For inverse logarithmic correction, the equation is ``O = gain*(2**I - 1)``.
  
      Parameters
      ----------
      image : ndarray
          Input image.
      gain : float
          The constant multiplier. Default value is 1.
      inv : float
          If True, it performs inverse logarithmic correction,
          else correction will be logarithmic. Defaults to False.
  
      Returns
      -------
      out : ndarray
          Logarithm corrected output image.
  
      See Also
      --------
      adjust_gamma
  
      References
      ----------
      .. [1] http://www.ece.ucsb.edu/Faculty/Manjunath/courses/ece178W03/EnhancePart1.pdf
  
      """
      _assert_non_negative(image)
      dtype = image.dtype.type
      scale = float(dtype_limits(image, True)[1] - dtype_limits(image, True)[0])
  
      if inv:
          out = (2 ** (image / scale) - 1) * scale * gain
          return dtype(out)
  
      out = np.log2(1 + image / scale) * scale * gain
      return dtype(out)
  
  
  def adjust_sigmoid(image, cutoff=0.5, gain=10, inv=False):
      """Performs Sigmoid Correction on the input image.
  
      Also known as Contrast Adjustment.
      This function transforms the input image pixelwise according to the
      equation ``O = 1/(1 + exp*(gain*(cutoff - I)))`` after scaling each pixel
      to the range 0 to 1.
  
      Parameters
      ----------
      image : ndarray
          Input image.
      cutoff : float
          Cutoff of the sigmoid function that shifts the characteristic curve
          in horizontal direction. Default value is 0.5.
      gain : float
          The constant multiplier in exponential's power of sigmoid function.
          Default value is 10.
      inv : bool
          If True, returns the negative sigmoid correction. Defaults to False.
  
      Returns
      -------
      out : ndarray
          Sigmoid corrected output image.
  
      See Also
      --------
      adjust_gamma
  
      References
      ----------
      .. [1] Gustav J. Braun, "Image Lightness Rescaling Using Sigmoidal Contrast
             Enhancement Functions",
             http://www.cis.rit.edu/fairchild/PDFs/PAP07.pdf
  
      """
      _assert_non_negative(image)
      dtype = image.dtype.type
      scale = float(dtype_limits(image, True)[1] - dtype_limits(image, True)[0])
  
      if inv:
          out = (1 - 1 / (1 + np.exp(gain * (cutoff - image / scale)))) * scale
          return dtype(out)
  
      out = (1 / (1 + np.exp(gain * (cutoff - image / scale)))) * scale
      return dtype(out)
  
  
  def is_low_contrast(image, fraction_threshold=0.05, lower_percentile=1,
                      upper_percentile=99, method='linear'):
      """Determine if an image is low contrast.
  
      Parameters
      ----------
      image : array-like
          The image under test.
      fraction_threshold : float, optional
          The low contrast fraction threshold. An image is considered low-
          contrast when its range of brightness spans less than this
          fraction of its data type's full range. [1]_
      lower_percentile : float, optional
          Disregard values below this percentile when computing image contrast.
      upper_percentile : float, optional
          Disregard values above this percentile when computing image contrast.
      method : str, optional
          The contrast determination method.  Right now the only available
          option is "linear".
  
      Returns
      -------
      out : bool
          True when the image is determined to be low contrast.
  
      References
      ----------
      .. [1] https://scikit-image.org/docs/dev/user_guide/data_types.html
  
      Examples
      --------
      >>> image = np.linspace(0, 0.04, 100)
      >>> is_low_contrast(image)
      True
      >>> image[-1] = 1
      >>> is_low_contrast(image)
      True
      >>> is_low_contrast(image, upper_percentile=100)
      False
      """
      image = np.asanyarray(image)
      if image.ndim == 3 and image.shape[2] in [3, 4]:
          image = rgb2gray(image)
  
      dlimits = dtype_limits(image, clip_negative=False)
      limits = np.percentile(image, [lower_percentile, upper_percentile])
      ratio = (limits[1] - limits[0]) / (dlimits[1] - dlimits[0])
  
      return ratio < fraction_threshold
  