lhk/3d_volume_trafo

## 3d_volume_trafo
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "transformations.py:1900: UserWarning: failed to import module _transformations\n",
      "  warnings.warn(\"failed to import module %s\" % name)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "from scipy.ndimage import map_coordinates\n",
    "\n",
    "# this is code from here: http://www.lfd.uci.edu/~gohlke/code/transformations.py.html\n",
    "from transformations import rotation_matrix, translation_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First in 2D:\n",
    "\n",
    "Create a meshgrid for the coordinates, stack it to create \"position vectors\", transform them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8298b4fb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim=100\n",
    "\n",
    "img=np.zeros((dim,dim))\n",
    "img[dim/5:dim/4,dim/4:dim*3/4]=1\n",
    "\n",
    "%matplotlib inline\n",
    "plt.figure(\"2d before trafo\")\n",
    "plt.imshow(img, interpolation=\"none\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# create a meshgrid for the coordinates\n",
    "line=np.arange(dim)\n",
    "coords=np.meshgrid(line, line)\n",
    "xy_coords=np.vstack([coords[0].reshape(-1), coords[1].reshape(-1)])\n",
    "\n",
    "# create a transformation matrix\n",
    "angle=30./180.*np.pi\n",
    "c=np.cos(angle)\n",
    "s=np.sin(angle)\n",
    "mat=np.array([[c,s],[-s,c]])\n",
    "\n",
    "# apply the transformation matrix\n",
    "# please note: the coordinates are not homogeneous.\n",
    "# for the 3D case, I've added code for homogeneous coordinates, you might want to look at that\n",
    "# please also note: rotation is always around the origin:\n",
    "# since I want the origin to be in the image center, I had to substract dim/2, rotate, then add it again\n",
    "xy_coords=np.dot(mat, xy_coords-dim/2)+dim/2\n",
    "\n",
    "# undo the stacking and reshaping\n",
    "x=xy_coords[0,:]\n",
    "y=xy_coords[1,:]\n",
    "x=x.reshape((dim,dim))\n",
    "y=y.reshape((dim,dim))\n",
    "\n",
    "# create a list for map_coordinates\n",
    "# ATTENTION: the coordinate system for map_coordinates seems messed up\n",
    "# it is necessary to reorder the dimensions like this\n",
    "# probably my fault, but I haven't figured out why, yet\n",
    "new_coords=[y,x]\n",
    "\n",
    "# use map_coordinates to sample values for the new image\n",
    "new_img=scipy.ndimage.map_coordinates(img,new_coords, order=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8298b4f8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(\"2d after trafo\")\n",
    "plt.imshow(new_img, interpolation=\"none\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the 3D case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GryQFMHwlKYDhK0kBDF9JCmD4SlIAw1eSAhi+khTA8JWkAIavJAUwfCUpgOErSQEMX0kK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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f829683b610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim=40\n",
    "\n",
    "vol=np.zeros((dim,dim,dim))\n",
    "vol[:,dim/5:dim/4,dim/4:dim*3/4]=1\n",
    "\n",
    "plt.figure(\"2d slice of 3d volume, before trafo\")\n",
    "plt.imshow(vol[0,:], interpolation=\"none\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ax=np.arange(dim)\n",
    "coords=np.meshgrid(ax,ax,ax)\n",
    "\n",
    "# stack the meshgrid to position vectors, center them around 0 by substracting dim/2\n",
    "xyz=np.vstack([coords[0].reshape(-1)-float(dim)/2,     # x coordinate, centered\n",
    "               coords[1].reshape(-1)-float(dim)/2,     # y coordinate, centered\n",
    "               coords[2].reshape(-1)-float(dim)/2,     # z coordinate, centered\n",
    "               np.ones((dim,dim,dim)).reshape(-1)])    # 1 for homogeneous coordinates\n",
    "\n",
    "# create transformation matrix\n",
    "mat=rotation_matrix(0.1*np.pi,(0,1,0))\n",
    "#mat=translation_matrix(np.array([1,0,0]).transpose(1,0,2))\n",
    "\n",
    "# apply transformation\n",
    "transformed_xyz=np.dot(mat, xyz)\n",
    "\n",
    "# extract coordinates, don't use transformed_xyz[3,:] that's the homogeneous coordinate, always 1\n",
    "x=transformed_xyz[0,:]+float(dim)/2\n",
    "y=transformed_xyz[1,:]+float(dim)/2\n",
    "z=transformed_xyz[2,:]+float(dim)/2\n",
    "\n",
    "x=x.reshape((dim,dim,dim))\n",
    "y=y.reshape((dim,dim,dim))\n",
    "z=z.reshape((dim,dim,dim))\n",
    "\n",
    "# the coordinate system seems to be strange, it has to be ordered like this\n",
    "new_xyz=[y,x,z]\n",
    "\n",
    "# sample\n",
    "new_vol=scipy.ndimage.map_coordinates(vol,new_xyz, order=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f829699fe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(\"2d slice of 3d volume, after trafo\")\n",
    "plt.imshow(new_vol[20,:,:], interpolation=\"none\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
No results found