code: def hog(
      image,
      orientations=9,
      pixels_per_cell=(8, 8),
      cells_per_block=(3, 3),
      block_norm="L2-Hys",
      visualize=False,
      transform_sqrt=False,
      feature_vector=True,
      *,
      channel_axis=None,
  ):
      """Extract Histogram of Oriented Gradients (HOG) for a given image.
  
      Compute a Histogram of Oriented Gradients (HOG) by
  
          1. (optional) global image normalization
          2. computing the gradient image in `row` and `col`
          3. computing gradient histograms
          4. normalizing across blocks
          5. flattening into a feature vector
  
      Parameters
      ----------
      image : (M, N[, C]) ndarray
          Input image.
      orientations : int, optional
          Number of orientation bins.
      pixels_per_cell : 2-tuple (int, int), optional
          Size (in pixels) of a cell.
      cells_per_block : 2-tuple (int, int), optional
          Number of cells in each block.
      block_norm : str {'L1', 'L1-sqrt', 'L2', 'L2-Hys'}, optional
          Block normalization method:
  
          ``L1``
             Normalization using L1-norm.
          ``L1-sqrt``
             Normalization using L1-norm, followed by square root.
          ``L2``
             Normalization using L2-norm.
          ``L2-Hys``
             Normalization using L2-norm, followed by limiting the
             maximum values to 0.2 (`Hys` stands for `hysteresis`) and
             renormalization using L2-norm. (default)
             For details, see [3]_, [4]_.
  
      visualize : bool, optional
          Also return an image of the HOG.  For each cell and orientation bin,
          the image contains a line segment that is centered at the cell center,
          is perpendicular to the midpoint of the range of angles spanned by the
          orientation bin, and has intensity proportional to the corresponding
          histogram value.
      transform_sqrt : bool, optional
          Apply power law compression to normalize the image before
          processing. DO NOT use this if the image contains negative
          values. Also see `notes` section below.
      feature_vector : bool, optional
          Return the data as a feature vector by calling .ravel() on the result
          just before returning.
      channel_axis : int or None, optional
          If None, the image is assumed to be a grayscale (single channel) image.
          Otherwise, this parameter indicates which axis of the array corresponds
          to channels.
  
          .. versionadded:: 0.19
             `channel_axis` was added in 0.19.
  
      Returns
      -------
      out : (n_blocks_row, n_blocks_col, n_cells_row, n_cells_col, n_orient) ndarray
          HOG descriptor for the image. If `feature_vector` is True, a 1D
          (flattened) array is returned.
      hog_image : (M, N) ndarray, optional
          A visualisation of the HOG image. Only provided if `visualize` is True.
  
      Raises
      ------
      ValueError
          If the image is too small given the values of pixels_per_cell and
          cells_per_block.
  
      References
      ----------
      .. [1] https://en.wikipedia.org/wiki/Histogram_of_oriented_gradients
  
      .. [2] Dalal, N and Triggs, B, Histograms of Oriented Gradients for
             Human Detection, IEEE Computer Society Conference on Computer
             Vision and Pattern Recognition 2005 San Diego, CA, USA,
             https://lear.inrialpes.fr/people/triggs/pubs/Dalal-cvpr05.pdf,
             :DOI:`10.1109/CVPR.2005.177`
  
      .. [3] Lowe, D.G., Distinctive image features from scale-invatiant
             keypoints, International Journal of Computer Vision (2004) 60: 91,
             http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf,
             :DOI:`10.1023/B:VISI.0000029664.99615.94`
  
      .. [4] Dalal, N, Finding People in Images and Videos,
             Human-Computer Interaction [cs.HC], Institut National Polytechnique
             de Grenoble - INPG, 2006,
             https://tel.archives-ouvertes.fr/tel-00390303/file/NavneetDalalThesis.pdf
  
      Notes
      -----
      The presented code implements the HOG extraction method from [2]_ with
      the following changes: (I) blocks of (3, 3) cells are used ((2, 2) in the
      paper); (II) no smoothing within cells (Gaussian spatial window with sigma=8pix
      in the paper); (III) L1 block normalization is used (L2-Hys in the paper).
  
      Power law compression, also known as Gamma correction, is used to reduce
      the effects of shadowing and illumination variations. The compression makes
      the dark regions lighter. When the kwarg `transform_sqrt` is set to
      ``True``, the function computes the square root of each color channel
      and then applies the hog algorithm to the image.
      """
      image = np.atleast_2d(image)
      float_dtype = utils._supported_float_type(image.dtype)
      image = image.astype(float_dtype, copy=False)
  
      multichannel = channel_axis is not None
      ndim_spatial = image.ndim - 1 if multichannel else image.ndim
      if ndim_spatial != 2:
          raise ValueError(
              "Only images with two spatial dimensions are "
              "supported. If using with color/multichannel "
              "images, specify `channel_axis`."
          )
  
      """
      The first stage applies an optional global image normalization
      equalisation that is designed to reduce the influence of illumination
      effects. In practice we use gamma (power law) compression, either
      computing the square root or the log of each color channel.
      Image texture strength is typically proportional to the local surface
      illumination so this compression helps to reduce the effects of local
      shadowing and illumination variations.
      """
  
      if transform_sqrt:
          image = np.sqrt(image)
  
      """
      The second stage computes first order image gradients. These capture
      contour, silhouette and some texture information, while providing
      further resistance to illumination variations. The locally dominant
      color channel is used, which provides color invariance to a large
      extent. Variant methods may also include second order image derivatives,
      which act as primitive bar detectors - a useful feature for capturing,
      e.g. bar like structures in bicycles and limbs in humans.
      """
  
      if multichannel:
          g_row_by_ch = np.empty_like(image, dtype=float_dtype)
          g_col_by_ch = np.empty_like(image, dtype=float_dtype)
          g_magn = np.empty_like(image, dtype=float_dtype)
  
          for idx_ch in range(image.shape[2]):
              (
                  g_row_by_ch[:, :, idx_ch],
                  g_col_by_ch[:, :, idx_ch],
              ) = _hog_channel_gradient(image[:, :, idx_ch])
              g_magn[:, :, idx_ch] = np.hypot(
                  g_row_by_ch[:, :, idx_ch], g_col_by_ch[:, :, idx_ch]
              )
  
          # For each pixel select the channel with the highest gradient magnitude
          idcs_max = g_magn.argmax(axis=2)
          rr, cc = np.meshgrid(
              np.arange(image.shape[0]),
              np.arange(image.shape[1]),
              indexing="ij",
              sparse=True,
          )
          g_row = g_row_by_ch[rr, cc, idcs_max]
          g_col = g_col_by_ch[rr, cc, idcs_max]
      else:
          g_row, g_col = _hog_channel_gradient(image)
  
      """
      The third stage aims to produce an encoding that is sensitive to
      local image content while remaining resistant to small changes in
      pose or appearance. The adopted method pools gradient orientation
      information locally in the same way as the SIFT [Lowe 2004]
      feature. The image window is divided into small spatial regions,
      called "cells". For each cell we accumulate a local 1-D histogram
      of gradient or edge orientations over all the pixels in the
      cell. This combined cell-level 1-D histogram forms the basic
      "orientation histogram" representation. Each orientation histogram
      divides the gradient angle range into a fixed number of
      predetermined bins. The gradient magnitudes of the pixels in the
      cell are used to vote into the orientation histogram.
      """
  
      s_row, s_col = image.shape[:2]
      c_row, c_col = pixels_per_cell
      b_row, b_col = cells_per_block
  
      n_cells_row = int(
          s_row // c_row
      )  # number of cells along row-axis
      n_cells_col = int(
          s_col // c_col
      )  # number of cells along col-axis
  
      # compute orientations integral images
      orientation_histogram = np.zeros(
          (n_cells_row, n_cells_col, orientations), dtype=float
      )
      g_row = g_row.astype(float, copy=False)
      g_col = g_col.astype(float, copy=False)
  
      _hoghistogram.hog_histograms(
          g_col,
          g_row,
          c_col,
          c_row,
          s_col,
          s_row,
          n_cells_col,
          n_cells_row,
          orientations,
          orientation_histogram,
      )
  
      # now compute the histogram for each cell
      hog_image = None
  
      if visualize:
          from .. import draw
  
          radius = min(c_row, c_col) // 2 - 1
          orientations_arr = np.arange(orientations)
          # set dr_arr, dc_arr to correspond to midpoints of orientation bins
          orientation_bin_midpoints = (
              np.pi * (orientations_arr + 0.5) / orientations
          )
          dr_arr = radius * np.sin(orientation_bin_midpoints)
          dc_arr = radius * np.cos(orientation_bin_midpoints)
          hog_image = np.zeros((s_row, s_col), dtype=float_dtype)
          for r in range(n_cells_row):
              for c in range(n_cells_col):
                  for o, dr, dc in zip(
                      orientations_arr, dr_arr, dc_arr
                  ):
                      centre = tuple(
                          [
                              r * c_row + c_row // 2,
                              c * c_col + c_col // 2,
                          ]
                      )
                      rr, cc = draw.line(
                          int(centre[0] - dc),
                          int(centre[1] + dr),
                          int(centre[0] + dc),
                          int(centre[1] - dr),
                      )
                      hog_image[rr, cc] += orientation_histogram[
                          r, c, o
                      ]
  
      """
      The fourth stage computes normalization, which takes local groups of
      cells and contrast normalizes their overall responses before passing
      to next stage. Normalization introduces better invariance to illumination,
      shadowing, and edge contrast. It is performed by accumulating a measure
      of local histogram "energy" over local groups of cells that we call
      "blocks". The result is used to normalize each cell in the block.
      Typically each individual cell is shared between several blocks, but
      its normalizations are block dependent and thus different. The cell
      thus appears several times in the final output vector with different
      normalizations. This may seem redundant but it improves the performance.
      We refer to the normalized block descriptors as Histogram of Oriented
      Gradient (HOG) descriptors.
      """
  
      n_blocks_row = (n_cells_row - b_row) + 1
      n_blocks_col = (n_cells_col - b_col) + 1
      if n_blocks_col <= 0 or n_blocks_row <= 0:
          min_row = b_row * c_row
          min_col = b_col * c_col
          raise ValueError(
              "The input image is too small given the values of "
              "pixels_per_cell and cells_per_block. "
              "It should have at least: "
              f"{min_row} rows and {min_col} cols."
          )
      normalized_blocks = np.zeros(
          (n_blocks_row, n_blocks_col, b_row, b_col, orientations),
          dtype=float_dtype,
      )
  
      for r in range(n_blocks_row):
          for c in range(n_blocks_col):
              block = orientation_histogram[
                  r : r + b_row, c : c + b_col, :
              ]
              normalized_blocks[r, c, :] = _hog_normalize_block(
                  block, method=block_norm
              )
  
      """
      The final step collects the HOG descriptors from all blocks of a dense
      overlapping grid of blocks covering the detection window into a combined
      feature vector for use in the window classifier.
      """
  
      if feature_vector:
          normalized_blocks = normalized_blocks.ravel()
  
      if visualize:
          return normalized_blocks, hog_image
      else:
          return normalized_blocks
  
imports: import numpy
  from .None import _hoghistogram
  from .._shared import utils
label_desc: Use image node_id 3 for calling a global function with example usage: hog(image, orientations, pixels_per_cell, cells_per_block, block_norm, visualize, transform_sqrt, feature_vector) and returns: normalized_blocks,  hog_image, normalized_blocks