```
from __future__ import division
import numpy as np 
import scipy.fftpack
import scipy.ndimage
import cv2
import matplotlib.pyplot as plt 
#sns.set()


def DST(x):
  """
  Converts Scipy's DST output to Matlab's DST (scaling).
  """
  X = scipy.fftpack.dst(x,type=1,axis=0)
  return X/2.0

def IDST(X):
  """
  Inverse DST. Python -> Matlab
  """
  n = X.shape[0]
  x = np.real(scipy.fftpack.idst(X,type=1,axis=0))
  return x/(n+1.0)

def get_grads(im):
  """
  return the x and y gradients.
  """
  [H,W] = im.shape
  Dx,Dy = np.zeros((H,W),'float32'), np.zeros((H,W),'float32')
  j,k = np.atleast_2d(np.arange(0,H-1)).T, np.arange(0,W-1)
  Dx[j,k] = im[j,k+1] - im[j,k]
  Dy[j,k] = im[j+1,k] - im[j,k]
  return Dx,Dy

def get_laplacian(Dx,Dy):
  """
  return the laplacian
  """
  [H,W] = Dx.shape
  Dxx, Dyy = np.zeros((H,W)), np.zeros((H,W))
  j,k = np.atleast_2d(np.arange(0,H-1)).T, np.arange(0,W-1)
  Dxx[j,k+1] = Dx[j,k+1] - Dx[j,k] 
  Dyy[j+1,k] = Dy[j+1,k] - Dy[j,k]
  return Dxx+Dyy

def poisson_solve(gx,gy,bnd):
  # convert to double:
  gx = gx.astype('float32')
  gy = gy.astype('float32')
  bnd = bnd.astype('float32')

  H,W = bnd.shape
  L = get_laplacian(gx,gy)

  # set the interior of the boundary-image to 0:
  bnd[1:-1,1:-1] = 0
  # get the boundary laplacian:
  L_bp = np.zeros_like(L)
  L_bp[1:-1,1:-1] = -4*bnd[1:-1,1:-1] \
           + bnd[1:-1,2:] + bnd[1:-1,0:-2] \
           + bnd[2:,1:-1] + bnd[0:-2,1:-1] # delta-x
  L = L - L_bp
  L = L[1:-1,1:-1]

  # compute the 2D DST:
  L_dst = DST(DST(L).T).T #first along columns, then along rows

  # normalize:
  [xx,yy] = np.meshgrid(np.arange(1,W-1),np.arange(1,H-1))
  D = (2*np.cos(np.pi*xx/(W-1))-2) + (2*np.cos(np.pi*yy/(H-1))-2)
  L_dst = L_dst/D

  img_interior = IDST(IDST(L_dst).T).T # inverse DST for rows and columns

  img = bnd.copy()

  img[1:-1,1:-1] = img_interior

  return img

def blit_images(im_top,im_back,scale_grad=1.0,mode='max'):
  """
  combine images using poission editing.
  IM_TOP and IM_BACK should be of the same size.
  """
  assert np.all(im_top.shape==im_back.shape)

  im_top = im_top.copy().astype('float32')
  im_back = im_back.copy().astype('float32')
  im_res = np.zeros_like(im_top)

  # frac of gradients which come from source:
  for ch in xrange(im_top.shape[2]):
    ims = im_top[:,:,ch]
    imd = im_back[:,:,ch]

    [gxs,gys] = get_grads(ims)
    [gxd,gyd] = get_grads(imd)

    gxs *= scale_grad
    gys *= scale_grad

    gxs_idx = gxs!=0
    gys_idx = gys!=0
    # mix the source and target gradients:
    if mode=='max':
      gx = gxs.copy()
      gxm = (np.abs(gxd))>np.abs(gxs)
      gx[gxm] = gxd[gxm]

      gy = gys.copy()
      gym = np.abs(gyd)>np.abs(gys)
      gy[gym] = gyd[gym]

      # get gradient mixture statistics:
      f_gx = np.sum((gx[gxs_idx]==gxs[gxs_idx]).flat) / (np.sum(gxs_idx.flat)+1e-6)
      f_gy = np.sum((gy[gys_idx]==gys[gys_idx]).flat) / (np.sum(gys_idx.flat)+1e-6)
      if min(f_gx, f_gy) <= 0.35:
        m = 'max'
        if scale_grad > 1:
          m = 'blend'
        return blit_images(im_top, im_back, scale_grad=1.5, mode=m)

    elif mode=='src':
      gx,gy = gxd.copy(), gyd.copy()
      gx[gxs_idx] = gxs[gxs_idx]
      gy[gys_idx] = gys[gys_idx]

    elif mode=='blend': # from recursive call:
      # just do an alpha blend
      gx = gxs+gxd
      gy = gys+gyd

    im_res[:,:,ch] = np.clip(poisson_solve(gx,gy,imd),0,255)

  return im_res.astype('uint8')


def contiguous_regions(mask):
  """
  return a list of (ind0, ind1) such that mask[ind0:ind1].all() is
  True and we cover all such regions
  """
  in_region = None
  boundaries = []
  for i, val in enumerate(mask):
    if in_region is None and val:
      in_region = i
    elif in_region is not None and not val:
      boundaries.append((in_region, i))
      in_region = None

  if in_region is not None:
    boundaries.append((in_region, i+1))
  return boundaries


if __name__=='__main__':
  """
  example usage:
  """
  import seaborn as sns

  im_src = cv2.imread('../f01006.jpg').astype('float32')

  im_dst = cv2.imread('../f01006-5.jpg').astype('float32')

  mu = np.mean(np.reshape(im_src,[im_src.shape[0]*im_src.shape[1],3]),axis=0)
  # print mu
  sz = (1920,1080)
  im_src = cv2.resize(im_src,sz)
  im_dst = cv2.resize(im_dst,sz)

  im0 = im_dst[:,:,0] > 100
  im_dst[im0,:] = im_src[im0,:]
  im_dst[~im0,:] = 50
  im_dst = cv2.GaussianBlur(im_dst,(5,5),5)

  im_alpha = 0.8*im_dst + 0.2*im_src

  # plt.imshow(im_dst)
  # plt.show()

  im_res = blit_images(im_src,im_dst)

  import scipy
  scipy.misc.imsave('orig.png',im_src[:,:,::-1].astype('uint8'))
  scipy.misc.imsave('alpha.png',im_alpha[:,:,::-1].astype('uint8'))
  scipy.misc.imsave('poisson.png',im_res[:,:,::-1].astype('uint8'))

  im_actual_L = cv2.cvtColor(im_src.astype('uint8'),cv2.cv.CV_BGR2Lab)[:,:,0]
  im_alpha_L = cv2.cvtColor(im_alpha.astype('uint8'),cv2.cv.CV_BGR2Lab)[:,:,0]
  im_poisson_L = cv2.cvtColor(im_res.astype('uint8'),cv2.cv.CV_BGR2Lab)[:,:,0]

  # plt.imshow(im_alpha_L)
  # plt.show()
  for i in xrange(500,im_alpha_L.shape[1],5):
    l_actual = im_actual_L[i,:]#-im_actual_L[i,:-1]
    l_alpha = im_alpha_L[i,:]#-im_alpha_L[i,:-1]
    l_poisson = im_poisson_L[i,:]#-im_poisson_L[i,:-1]


    with sns.axes_style("darkgrid"):
      plt.subplot(2,1,2)
      #plt.plot(l_alpha,label='alpha')

      plt.plot(l_poisson,label='poisson')
      plt.hold(True)
      plt.plot(l_actual,label='actual')
      plt.legend()

      # find "text regions":
      is_txt = ~im0[i,:]
      t_loc = contiguous_regions(is_txt)
      ax = plt.gca()
      for b0,b1 in t_loc:
        ax.axvspan(b0, b1, facecolor='red', alpha=0.1)

    with sns.axes_style("white"):
      plt.subplot(2,1,1)
      plt.imshow(im_alpha[:,:,::-1].astype('uint8'))
      plt.hold(True)
      plt.plot([0,im_alpha_L.shape[0]-1],[i,i],'r')
      plt.axis('image')
      plt.show()


  plt.subplot(1,3,1)
  plt.imshow(im_src[:,:,::-1].astype('uint8'))
  plt.subplot(1,3,2)
  plt.imshow(im_alpha[:,:,::-1].astype('uint8'))
  plt.subplot(1,3,3)  
  plt.imshow(im_res[:,:,::-1]) #cv2 reads in BGR
  plt.show()