StructureTensor3D_Examples.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# 3D structure tensor - a small example\n",
    "A small example demonstrating the use of 3D structure tensor for visualizing and clustering dominant orientation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import scipy.io\n",
    "import st3d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading the data\n",
    "\n",
    "The data is a small cube from a volumetric image og fibre composite. The cube contains five bundles in layers: UD fibre (0 deg), crossing fibre (45 deg), 90 deg fibre, -45 deg bundle, UD bundle (0 deg)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 150, 150)\n"
     ]
    }
   ],
   "source": [
    "volume = scipy.io.loadmat('example_data_3D/multi_cube.mat')['vol']\n",
    "print(volume.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the structure tensor and the dominant orientation\n",
    "Computation of structure tensor requires only two parameters: the noise scale sigma and the integration scale rho. Parameter sigma controls smothing while computing gradientes, and structures smaller than sigma will be removed by smoothing. Parameter rho gives the size over the neighborhood in which the orientation is to be analysed for every volume voxel. Larger rho will result in a smoother orientation field.\n",
    "\n",
    "Structure tensor is a 3x3 matrix, but as it is symmetrical we only carry values of 6 elements: $s_{xx}$, $s_{yy}$, $s_{zz}$, $s_{xy}$, $s_{xz}$ and $s_{yz}$.\n",
    "\n",
    "Eigenvalues (val) carry the information about the degree of anisotropy - this is not used or visualized here. Eigenvectors (vec) carry the orientation information, as $x$, $y$, and $z$ component of the orientation vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7673420906066895\n",
      "0.5525798797607422\n",
      "The volume has a shape (150, 150, 150), i.e. 3375000 voxels.\n",
      "Structure tensor information is carried in a (6, 3375000) array.\n",
      "Orientation information is carried in a (3, 3375000) array.\n"
     ]
    }
   ],
   "source": [
    "sigma = 0.5; # noise scale\n",
    "rho = 2; # integration scale\n",
    "S = st3d.structure_tensor(volume, sigma, rho)\n",
    "val,vec = st3d.eig_special(S)\n",
    "print(f'The volume has a shape {volume.shape}, i.e. {volume.size} voxels.')\n",
    "print(f'Structure tensor information is carried in a {S.shape} array.')\n",
    "print(f'Orientation information is carried in a {vec.shape} array.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the dominant orientation\n",
    "Here we show only dominant orientation, ignoring shape measures. \n",
    "\n",
    "Since slicng is in $z$ direction, the arrows show $x$ and $y$ component of orientation vectors, on top of every slice.\n",
    "\n",
    "To interactively inspect the volume use arrow keys."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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