Affine_transform.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from transform_helpers import *\n",
    "# %gui qt5\n",
    "# from spimagine import volshow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Z, Y, X\n",
    "test_vol = np.zeros((200,400,800), dtype = np.uint16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# put origin in the centre\n",
    "\n",
    "imprint_coordinate_system(test_vol, ( 100, 200, 400))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plot_all(get_projections(test_vol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<spimagine.gui.mainwidget.MainWidget at 0x1505faca798>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# volshow(test_vol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gputools\n",
    "import scipy.ndimage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1.,    0.,    0., -100.],\n",
       "       [   0.,    1.,    0.,    0.],\n",
       "       [   0.,    0.,    1.,    0.],\n",
       "       [   0.,    0.,    0.,    1.]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "move_z = np.eye(4)\n",
    "move_z[0,3]  = -100\n",
    "move_z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "gpu_trans_mz = gputools.affine(test_vol, move_z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "scipy_trans_mz = scipy.ndimage.affine_transform(test_vol, move_z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  scipy actually expects the affine transform from output to input, i.e. the inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "scipy_trans_mz_inv = scipy.ndimage.affine_transform(test_vol, scipy.linalg.inv(move_z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(get_projections(gpu_trans_mz))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(get_projections(scipy_trans_mz))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(get_projections(scipy_trans_mz_inv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1.,    0.,    0.,    0.],\n",
       "       [   0.,    1.,    0., -200.],\n",
       "       [   0.,    0.,    1.,    0.],\n",
       "       [   0.,    0.,    0.,    1.]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "move_y = np.eye(4)\n",
    "move_y[1,3]  = -200\n",
    "move_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gpu_trans_my = scipy.ndimage.affine_transform(test_vol, move_y)\n",
    "scipy_trans_my_inv = scipy.ndimage.affine_transform(test_vol, scipy.linalg.inv(move_y))\n",
    "plot_all(get_projections(gpu_trans_my))\n",
    "plot_all(get_projections(scipy_trans_my_inv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1.,    0.,    0.,    0.],\n",
       "       [   0.,    1.,    0.,    0.],\n",
       "       [   0.,    0.,    1., -400.],\n",
       "       [   0.,    0.,    0.,    1.]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "move_x = np.eye(4)\n",
    "move_x[2,3]  = -400\n",
    "move_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Bd1bVj/Y0dY6xfVJnVT1VVSvo/YZ9MvDyPdQylTozsNJ9cHgPtUzzeT+1qk4EzgIuTPKaPcydVp0H0juNellVnQD8D3v+KPi0f44WAW8E/m1vU+cYm2id7f2H1cBxwIuAQ+k99/PV8axrnHYA9FcN9w2uKJ4VjyRZBtCud7bxqdWe5CB6//l/uqo+N6t19lXVY8CX6Z07XZLeCvHda9lVZ/btCvL+SvdtwNX0TgPtWuk+Q3VSVQ+3653A5+mF6qw979uB7VV1a9tfRy8QZq3OvrOAu6rqkbY/S3W+Fniwqr5XVT8DPgf8NmN8bU47AG4Hlrd3tRfROxRbP+Wadje4snn3Fc/ntk8HrAQe7x86TlKS0Ftst6WqPjzDdR6RZEnbfg69F/MWZmwFee0nK92THJrksP42vfPWm5mx572qvgt8O0n/j5SdAdw7a3UOOIenT//065mVOh8CViY5pP3c9/8tx/fa3JdvtszzRscqep9k+Sbwt1Ou5Sp659p+Ri9Nz6d3Du0m4IF2vbTNDfDPre6vAyftoxp/h95h3SZgY7usmsE6fxP4WqtzM/B3bfx44DZgK73D7sVt/OC2v7XdfvwUnv/TePpTQDNVZ6vn7na5p/+zMmvPe3vsFcAd7bn/d+DwGa3zEOAHwPMHxmaqTuC9wH3tZ+hTwOJxvjZdCSxJHTXtU0CSpCkxACSpowwASeooA0CSOsoAkKSOMgAkqaMMAEnqKANAkjrq/wH5D5iyDoFVEQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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W3m/XU1dnO61yF7AVuJ7e0d5AK8iBmRXku8PMSveft/2BV7rv5joL+FKSO9JbSQ/T97wfA3wP+EQ7pfbxJPtPYZ391gCXt+2pqbOqvgN8CHgU2ELvtXYHY3xtLnQADLRqeEotaO1JXgB8DnhXVf1oR1PnGNstdVbVc1W1gt5v2CcAr9hBLQtSZ/pWuvcP76CWhXzeT6qq44AzgPOSvHYHcxeqzr3onUa9uKqOBf6HHX8UfKF/jhYDbwL+bWdT5xibaJ3t/YfVwNHAi4H96T3389WxyzUudADMrBqe0b+ieFo8nmQZQLve2sYXrPYke9P7z/8zVfX5aa1zRlU9CXyZ3rnTpemtEJ9dy7Y6s3tXkM+sdH8EuILeaaBtK92nqE6q6rF2vRX4Ar1QnbbnfTOwuapuafvr6QXCtNU54wzgzqp6vO1PU52vAx6uqu9V1TPA54HfYYyvzYUOgNuA5e1d7cX0DsU2LHBNs/WvbJ694vns9umAlcBTM4eOk5Qk9Bbb3V9VH5niOg9NsrRt70vvxXw/U7aCvPaQle5J9k9ywMw2vfPWG5my572qvgt8O8nMHyk7Fbhv2urscxbbT//M1DMtdT4KrEyyX/u5n/m3HN9rc3e+2TLPGx2r6H2S5ZvA3y5wLZfTO9f2DL00PZfeObQbgYfa9cFtboB/bnV/HTh+N9X4u/QO6+4B7mqXVVNY528BX2t1bgT+ro0fA9wKbKJ32L2kje/T9je1249ZgOf/ZLZ/Cmiq6mz13N0u9878rEzb894eewVwe3vu/x04aErr3A/4AXBg39hU1Qm8D3ig/Qx9GlgyztemK4ElqaMW+hSQJGmBGACS1FEGgCR1lAEgSR1lAEhSRxkAktRRBoAkdZQBIEkd9f/U46cDm9AiPwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gpu_trans_mx = scipy.ndimage.affine_transform(test_vol, move_x)\n",
    "scipy_trans_mx_inv = scipy.ndimage.affine_transform(test_vol, scipy.linalg.inv(move_x))\n",
    "plot_all(get_projections(gpu_trans_mx))\n",
    "plot_all(get_projections(scipy_trans_mx_inv))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Now try and find out how to get gputools transforms working as expected ....\n",
    "\n",
    "\n",
    "* shifting dimension 0 (Z) has actually shifted dimension 2 (X)\n",
    "* use smaller shifts to get to the bottom of it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   0.,   0., -10.],\n",
       "       [  0.,   1.,   0., -40.],\n",
       "       [  0.,   0.,   1., -90.],\n",
       "       [  0.,   0.,   0.,   1.]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shift_all = np.eye(4)\n",
    "shift_all[0,3] = -10\n",
    "shift_all[1,3] = -40\n",
    "shift_all[2,3] = -90\n",
    "shift_all\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gpu_trans_all = gputools.affine(test_vol, shift_all)\n",
    "plot_all(get_projections(gpu_trans_all))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So it appears that \n",
    "* the shift of 10 happens along dimension 2 (supposed to be along dimension 0)\n",
    "* the shift of 40 happens along dimension 1 (supposed to be along dimension 1)\n",
    "* the shift of 90 happens along dimension 0 (supposed to be along \n",
    "dimension 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

transform_helpers.py

import numpy as np
import matplotlib.pyplot as plt

def get_transformed_corners(aff, vol, zeroindex=True):
    ''' given an affine transformation matrix for a volume
    and a corresponding volume vol. This function will return
    the positions of the corner points after the mapping.
    '''

    d0, d1, d2 = vol.shape
    # these give the dimensions of the array
    # the maximum index is one less
    if zeroindex:
        d0 -= 1
        d1 -= 1
        d2 -= 1
    # all corners of the input volume
    corners_in = [ ( 0,  0,  0, 1), \
                   (d0,  0,  0, 1), \
                   ( 0, d1,  0, 1), \
                   ( 0,  0, d2, 1), \
                   ( d0, d1, 0, 1), \
                   ( d0,  0,d2, 1), \
                   (  0, d1, d2, 1),\
                   ( d0, d1, d2, 1)] \
    
    corners_out = list(map(lambda c: aff @ np.array(c), corners_in))

    corner_array =  np.concatenate(corners_out).reshape((-1,4))
    #print(corner_array)
    return(corner_array)    

def get_projections(in_array, fun=np.max):
    """ given an array, projects along each axis using the function fun (defaults to np.max).
    Returns a mapping (iterator) of projections """

    projections = map(lambda ax: fun(in_array, axis=ax), range(in_array.ndim))
    return projections

def plot_all(imlist, backend = "matplotlib"):
    """ given a list of images, plots all of them in order
    Will add different backends later """
    for im in imlist:
        plt.imshow(im)
        plt.show()


def imprint_coordinate_system(volume, origin=(0,0,0), l=100, w=5, vals=(6000, 10000, 14000)):
    """ imprints coordinate system axes in a volume at origin
    axes imprints have length l and widht w and intensity values in val """
    o = origin
    volume[o[0]:o[0]+l, o[1]:o[1]+w, o[2]:o[2]+w] = vals[0]
    volume[o[0]:o[0]+w, o[1]:o[1]+l, o[2]:o[2]+w] = vals[1]
    volume[o[0]:o[0]+w, o[1]:o[1]+w, o[2]:o[2]+l] = vals[2]