title: HOG Feature extraction
body: <p>I want to extract HOG features of Line images of Arabic Handwriting. The code is as follows. So , I want help regarding how to input the image and how to output the features . Can anyone please help me regarding this.</p>
  
  <pre><code>import numpy as np
  from scipy import sqrt, pi, arctan2, cos, sin
  from scipy.ndimage import uniform_filter
  
  def hog(image, orientations=9, pixels_per_cell=(8, 8),
      cells_per_block=(3, 3), visualise=False, normalise=False):
  """Extract Histogram of Oriented Gradients (HOG) for a given image.
  
  Compute a Histogram of Oriented Gradients (HOG) by
  
      1. (optional) global image normalisation
      2. computing the gradient image in x and y
      3. computing gradient histograms
      4. normalising across blocks
      5. flattening into a feature vector
  
  Parameters
  ----------
  image : (M, N) ndarray
      Input image (greyscale).
  orientations : int
      Number of orientation bins.
  pixels_per_cell : 2 tuple (int, int)
      Size (in pixels) of a cell.
  cells_per_block  : 2 tuple (int,int)
      Number of cells in each block.
  visualise : bool, optional
      Also return an image of the HOG.
  normalise : bool, optional
      Apply power law compression to normalise the image before
      processing.
  
  Returns
  -------
  newarr : ndarray
      HOG for the image as a 1D (flattened) array.
  hog_image : ndarray (if visualise=True)
      A visualisation of the HOG image.
  
  References
  ----------
  * http://en.wikipedia.org/wiki/Histogram_of_oriented_gradients
  
  * 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
  
  """
  image = np.atleast_2d(image)
  
  """
  The first stage applies an optional global image normalisation
  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 colour 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 image.ndim &gt; 3:
      raise ValueError("Currently only supports grey-level images")
  
  if normalise:
      image = 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
  colour channel is used, which provides colour 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.
  """
  
  gx = np.zeros(image.shape)
  gy = np.zeros(image.shape)
  gx[:, :-1] = np.diff(image, n=1, axis=1)
  gy[:-1, :] = np.diff(image, n=1, axis=0)
  
  """
  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.
  """
  
  magnitude = sqrt(gx ** 2 + gy ** 2)
  orientation = arctan2(gy, (gx + 1e-15)) * (180 / pi) + 90
  
  sy, sx = image.shape
  cx, cy = pixels_per_cell
  bx, by = cells_per_block
  
  n_cellsx = int(np.floor(sx // cx))  # number of cells in x
  n_cellsy = int(np.floor(sy // cy))  # number of cells in y
  
  # compute orientations integral images
  orientation_histogram = np.zeros((n_cellsy, n_cellsx, orientations))
  for i in range(orientations):
      #create new integral image for this orientation
      # isolate orientations in this range
  
      temp_ori = np.where(orientation &lt; 180 / orientations * (i + 1),
                          orientation, 0)
      temp_ori = np.where(orientation &gt;= 180 / orientations * i,
                          temp_ori, 0)
      # select magnitudes for those orientations
      cond2 = temp_ori &gt; 0
      temp_mag = np.where(cond2, magnitude, 0)
  
      orientation_histogram[:,:,i] = uniform_filter(temp_mag, size=(cy, cx))[cy/2::cy, cx/2::cx]
  
  
  # now for each cell, compute the histogram
  #orientation_histogram = np.zeros((n_cellsx, n_cellsy, orientations))
  
  radius = min(cx, cy) // 2 - 1
  hog_image = None
  if visualise:
      hog_image = np.zeros((sy, sx), dtype=float)
  
  if visualise:
      from skimage import draw
  
      for x in range(n_cellsx):
          for y in range(n_cellsy):
              for o in range(orientations):
                  centre = tuple([y * cy + cy // 2, x * cx + cx // 2])
                  dx = radius * cos(float(o) / orientations * np.pi)
                  dy = radius * sin(float(o) / orientations * np.pi)
                  rr, cc = draw.bresenham(centre[0] - dx, centre[1] - dy,
                                          centre[0] + dx, centre[1] + dy)
                  hog_image[rr, cc] += orientation_histogram[y, x, o]
  
  """
  The fourth stage computes normalisation, which takes local groups of
  cells and contrast normalises their overall responses before passing
  to next stage. Normalisation 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 normalise each cell in the block.
  Typically each individual cell is shared between several blocks, but
  its normalisations are block dependent and thus different. The cell
  thus appears several times in the final output vector with different
  normalisations. This may seem redundant but it improves the performance.
  We refer to the normalised block descriptors as Histogram of Oriented
  Gradient (HOG) descriptors.
  """
  
  n_blocksx = (n_cellsx - bx) + 1
  n_blocksy = (n_cellsy - by) + 1
  normalised_blocks = np.zeros((n_blocksy, n_blocksx,
                                by, bx, orientations))
  
  for x in range(n_blocksx):
      for y in range(n_blocksy):
          block = orientation_histogram[y:y + by, x:x + bx, :]
          eps = 1e-5
          normalised_blocks[y, x, :] = block / sqrt(block.sum() ** 2 + eps)
  
  """
  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 visualise:
      return normalised_blocks.ravel(), hog_image
  else:
      return normalised_blocks.ravel()
  </code></pre>