Watershed_on_a_Mesh_Trimesh.ipynb

{
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   "source": [
    "# Watershed on a mesh\n",
    "\n",
    "The notebook uses [trimesh](https://trimsh.org) and [higra](https://higra.readthedocs.io/en/stable/). Trimesh is a pure python library that deals with triangular mesh. It is a bit slow with large model, and under colab, does not have enough memory for larger model. Please have a look at the Higra example that uses the igl library for solving those issues.\n",
    "\n",
    "We are going to read a mesh file, compute a curvature measure on the mesh, and compute a watershed on the dual graph of the mesh.\n",
    "\n",
    "Reference paper:\n",
    "> Jean Cousty,  Gilles Bertrand,  Michel Couprie,  Laurent Najman\n",
    "> Collapses and watersheds in pseudomanifolds of arbitrary dimension.\n",
    "> Journal of Mathematical Imaging and Vision volume 50, pages 261–285 (2014) [10.1007/s10851-014-0498-z](https://doi.org/10.1007/s10851-014-0498-z). [hal-00871498v2](https://hal.science/hal-00871498/)\n",
    "\n",
    "For an application of the hierarchical  watershed on a mesh, you can look at:\n",
    "\n",
    "> Sylvie Philipp-Foliguet, Michel M. Jordan, Laurent Najman, Jean Cousty. \n",
    "> Artwork 3D model database indexing and classification. \n",
    "> Pattern Recognition, 2011, 44 (3), pp.588-597.  [10.1016/j.patcog.2010.09.016](https://doi.org/10.1016/j.patcog.2010.09.016). [hal-00538470](https://hal.science/hal-00538470/)"
   ]
  },
  {
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     "base_uri": "https://localhost:8080/"
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    "id": "EWiB1O-QAtit",
    "outputId": "efb05904-46f5-4db1-d462-bae538a23b2c"
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     "text": [
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   ],
   "source": [
    "# Trimesh is a simple python package for dealing with meshes.\n",
    "!pip install trimesh[easy]\n",
    "# WARNING: trimesh is slow for large meshes\n",
    "# An alternative can be igl https://libigl.github.io/libigl-python-bindings/\n",
    "# Also, plotly, the viewer we are using in this notebook, is not made for large mesh\n",
    "# An alternative is meshplot https://skoch9.github.io/meshplot/\n",
    "# Another Higra example uses igl and meshplot, please have a look\n",
    "\n",
    "# Higra is for the watershed and related operators on graphs\n",
    "!pip install higra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "Od6I87OcA7Vi"
   },
   "outputs": [],
   "source": [
    "import trimesh\n",
    "# We need a curvature operator for weighting the mesh\n",
    "from trimesh.curvature import discrete_gaussian_curvature_measure, discrete_mean_curvature_measure, sphere_ball_intersection\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9QAG5H9ZBezb"
   },
   "source": [
    "As a first example, we will work with a coarse bunny model from Standford repository. A copy of this model in obj format, preprocessed with [MeshFix](https://github.com/MarcoAttene/MeshFix-V2.1), is located at the following address"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "QZhUXAayBZoI"
   },
   "outputs": [],
   "source": [
    "# This model is from pyvista, it works fine, but resolution is not so good\n",
    "mesh = trimesh.load_remote('https://raw.githubusercontent.com/higra/Higra-Notebooks/master/data/BunnyCoarse.obj', force='mesh')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "wurUeepnvKU2"
   },
   "outputs": [],
   "source": [
    "assert(mesh.is_watertight) # Notebook can only process watertight mesh for the watershed (normal, don't you think so?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "O8V5CeWgCB6v"
   },
   "source": [
    "The mesh viewer in trimesh is less powerfull that plotly, hence we are going to use plotly. Here are some helper functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "DK9oZ2GGBp_q"
   },
   "outputs": [],
   "source": [
    "# Adapted from https://plotly.com/python/v3/surface-triangulation/\n",
    "import matplotlib.cm as cm\n",
    "from functools import reduce\n",
    "import numpy as np\n",
    "import plotly.graph_objects as go\n",
    "import plotly\n",
    "\n",
    "def map_z2color(zval, colormap, vmin, vmax):\n",
    "    #map the normalized value zval to a corresponding color in the colormap\n",
    "\n",
    "    if vmin>vmax:\n",
    "        raise ValueError('incorrect relation between vmin and vmax')\n",
    "    t=(zval-vmin)/float((vmax-vmin))#normalize val\n",
    "    R, G, B, alpha=colormap(t)\n",
    "    return 'rgb('+'{:d}'.format(int(R*255+0.5))+','+'{:d}'.format(int(G*255+0.5))+\\\n",
    "           ','+'{:d}'.format(int(B*255+0.5))+')'\n",
    "\n",
    "# Plot a mesh, with or without the edges of the triangles\n",
    "# If color is None, the mesh is plotted with a color depending on the height (z axis)\n",
    "def plotly_trisurf(mesh, colors=None, colormap=cm.RdBu, plot_edges=False):\n",
    "    # colors is defined on the vertices\n",
    "\n",
    "    #x, y, z are lists of coordinates of the triangle vertices \n",
    "    #simplices are the simplices that define the triangularization;\n",
    "    #simplices  is a numpy array of shape (no_triangles, 3)\n",
    "    #insert here the  type check for input data\n",
    "    x, y, z = mesh.vertices.T\n",
    "    simplices = mesh.faces\n",
    "    points3D=np.vstack((x,y,z)).T\n",
    "    tri_vertices=list(map(lambda index: points3D[index], simplices))# vertices of the surface triangles \n",
    "\n",
    "    if colors is None:    \n",
    "        zmean=[np.mean(tri[:,2]) for tri in tri_vertices]# mean values of z-coordinates of \n",
    "                                                          #triangle vertices\n",
    "        min_zmean=np.min(zmean)\n",
    "        max_zmean=np.max(zmean)\n",
    "        facecolor=[map_z2color(zz,  colormap, min_zmean, max_zmean) for zz in zmean]\n",
    "    else:\n",
    "        zmean=[(colors[i]+colors[j]+colors[k])/3. for i,j,k in simplices] # Mean of the color of the vertices\n",
    "        min_zmean=np.min(zmean)\n",
    "        max_zmean=np.max(zmean)\n",
    "        facecolor=[map_z2color(zz,  colormap, min_zmean, max_zmean) for zz in zmean]\n",
    "    \n",
    "    #I,J,K=tri_indices(simplices)\n",
    "    I,J,K = mesh.faces.T\n",
    "\n",
    "    triangles=go.Mesh3d(x=x,\n",
    "                     y=y,\n",
    "                     z=z,\n",
    "                     facecolor=facecolor,\n",
    "                     i=I,\n",
    "                     j=J,\n",
    "                     k=K,\n",
    "                     name=''\n",
    "                    )\n",
    "\n",
    "    if plot_edges is False:# the triangle sides are not plotted \n",
    "        return [triangles]\n",
    "    else:\n",
    "        #define the lists Xe, Ye, Ze, of x, y, resp z coordinates of edge end points for each triangle\n",
    "        #None separates data corresponding to two consecutive triangles\n",
    "        lists_coord=[[[T[k%3][c] for k in range(4)]+[ None]   for T in tri_vertices]  for c in range(3)]\n",
    "        Xe, Ye, Ze=[reduce(lambda x,y: x+y, lists_coord[k]) for k in range(3)]\n",
    "\n",
    "        #define the lines to be plotted\n",
    "        lines=go.Scatter3d(x=Xe,\n",
    "                        y=Ye,\n",
    "                        z=Ze,\n",
    "                        mode='lines',\n",
    "                        line=dict(color= 'rgb(50,50,50)', width=1.5)\n",
    "               )\n",
    "        return [triangles, lines]\n",
    "\n",
    "# For ploting a saliency map\n",
    "def plotly_trisurf_saliency(mesh, edges, saliency):\n",
    "\n",
    "    # Remove saliency edges with 0 weight\n",
    "    edges = edges[saliency>0]\n",
    "    saliency = saliency[saliency>0]\n",
    "\n",
    "    #x, y, z are lists of coordinates of the triangle vertices \n",
    "    #simplices are the simplices that define the triangularization;\n",
    "    #simplices  is a numpy array of shape (no_triangles, 3)\n",
    "    x, y, z = mesh.vertices.T\n",
    "    simplices = mesh.faces\n",
    "    points3D=np.vstack((x,y,z)).T\n",
    "    tri_vertices=list(map(lambda index: points3D[index], simplices)) # vertices of the surface triangles \n",
    "    \n",
    "    I,J,K = mesh.faces.T\n",
    "\n",
    "    triangles = go.Mesh3d(x=x, y=y, z=z, \n",
    "                          i=I,j=J,k=K,\n",
    "                          color='darkgray', opacity=1.,\n",
    "                          name='')\n",
    "    \n",
    "    result = [triangles]\n",
    "    from plotly.express.colors import sample_colorscale\n",
    "    col = sample_colorscale('peach', list(np.linspace(0, 1, 256)))\n",
    "    sal = saliency/saliency.max()\n",
    "    uniq_saliency = np.unique(sal)\n",
    "    for i in np.arange(uniq_saliency.shape[0]):\n",
    "      edge_vertices = list(map(lambda index: points3D[index], edges[sal==uniq_saliency[i]])) # Vertices of the edge set\n",
    "      #define the lists Xe, Ye, Ze, of x, y, resp z coordinates of edge end points for each edge\n",
    "      #None separates data corresponding to two consecutive edges\n",
    "      lists_coord = [[[e[k%2][c] for k in range(3)]+[ None]   for e in edge_vertices]  for c in range(3)]\n",
    "      Xe, Ye, Ze=[reduce(lambda x,y: x+y, lists_coord[k]) for k in range(3)]\n",
    "\n",
    "      #define the lines to be plotted\n",
    "      lines=go.Scatter3d(x=Xe,\n",
    "                      y=Ye,\n",
    "                      z=Ze,\n",
    "                      mode='lines',\n",
    "                      line=dict(color= col[int(uniq_saliency[i]*255)], width=3.), #1.5\n",
    "                      name = f'{(uniq_saliency[i]*saliency.max()):.2f}'\n",
    "               )\n",
    "      result.append(lines)\n",
    "    return result\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "Jy8abRSwChZV"
   },
   "outputs": [],
   "source": [
    "data1=plotly_trisurf(mesh, colormap=cm.RdBu, plot_edges=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "ZPIbq6LJCoUF"
   },
   "outputs": [],
   "source": [
    "#Set up the scene, all plot will share that setting\n",
    "axis = dict(\n",
    "showbackground=True,\n",
    "backgroundcolor=\"rgb(230, 230,230)\",\n",
    "gridcolor=\"rgb(255, 255, 255)\",\n",
    "zerolinecolor=\"rgb(255, 255, 255)\",\n",
    "    )\n",
    "\n",
    "layout = go.Layout(\n",
    "         title='Mesh triangulation',\n",
    "         width=800,\n",
    "         height=800,\n",
    "         scene=dict(\n",
    "         xaxis=dict(axis),\n",
    "         yaxis=dict(axis),\n",
    "         zaxis=dict(axis),\n",
    "        aspectratio=dict(\n",
    "            x=1,\n",
    "            y=1,\n",
    "            z=1\n",
    "        ),\n",
    "        )\n",
    "        )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 817
    },
    "id": "7KwKsmSqX7MA",
    "outputId": "75ab7740-9934-4a95-b933-60f68f1485fe"
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   "outputs": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = go.Figure(data=data1, layout=layout)\n",
    "fig1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "aDuOzxjQC5qS"
   },
   "outputs": [],
   "source": [
    "# Choose a curvature, and compute it (on the vertices of the mesh)\n",
    "curvature = discrete_mean_curvature_measure(mesh, mesh.vertices, .1) #/sphere_ball_intersection(1, .1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "uCs836dLWAGJ"
   },
   "outputs": [],
   "source": [
    "#Plot data with curvature\n",
    "data2=plotly_trisurf(mesh, colors=curvature, colormap=cm.RdBu, plot_edges=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
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     "height": 817
    },
    "id": "fycSXm6qWKs7",
    "outputId": "94a2367f-9690-4930-a15a-8a2f7b519925"
   },
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2 = go.Figure(data=data2, layout=layout)\n",
    "fig2.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "8h-WRPE8DeiD"
   },
   "outputs": [],
   "source": [
    "# Compute the dual graph\n",
    "adjacency, edges = trimesh.graph.face_adjacency(faces=None, mesh=mesh, return_edges=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "rEN8bDgEDyj1"
   },
   "outputs": [],
   "source": [
    "#We need a curvature on each edge\n",
    "edge_weights= (curvature[edges[:,0]] + curvature[edges[:,1]])/2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "85_zqLSvSfKn"
   },
   "outputs": [],
   "source": [
    "import higra as hg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "Lb_XbvjyX4uo"
   },
   "outputs": [],
   "source": [
    "g = hg.UndirectedGraph(mesh.faces.shape[0]) # Number of points is the number of faces in the mesh\n",
    "g.add_edges(adjacency[:,0].tolist(), adjacency[:,1].tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "iQ8kWlRJX-Sb"
   },
   "outputs": [],
   "source": [
    "# Compute the hierarchy\n",
    "tree, altitudes = hg.watershed_hierarchy_by_area(g, edge_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "BqwX2OneZXcF"
   },
   "outputs": [],
   "source": [
    "# Compute the saliency map\n",
    "sal = hg.saliency(tree, altitudes)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 817
    },
    "id": "bua3-VlyhDHU",
    "outputId": "cda59855-0752-41dc-e0af-1b041d50eca9"
   },
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot it\n",
    "# You can click on the legend to hide/show a level of the saliency map\n",
    "data3=plotly_trisurf_saliency(mesh, edges=edges, saliency=sal)\n",
    "fig3 = go.Figure(data=data3, layout=layout)\n",
    "fig3.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "id": "T2d1snRk3Bq-"
   },
   "outputs": [],
   "source": []
  }
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