{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "-P3OUvJirQdR"
   },
   "outputs": [],
   "source": [
    "# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "44lB2sH-rQdW"
   },
   "source": [
    "# Camera position optimization using differentiable rendering\n",
    "\n",
    "In this tutorial we will learn the [x, y, z] position of a camera given a reference image using differentiable rendering. \n",
    "\n",
    "We will first initialize a renderer with a starting position for the camera. We will then use this to generate an image, compute a loss with the reference image, and finally backpropagate through the entire pipeline to update the position of the camera. \n",
    "\n",
    "This tutorial shows how to:\n",
    "- load a mesh from an `.obj` file\n",
    "- initialize a `Camera`, `Shader` and `Renderer`,\n",
    "- render a mesh\n",
    "- set up an optimization loop with a loss function and optimizer\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AZGmIlmWrQdX"
   },
   "source": [
    "##  0. Install and import modules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qkX7DiM6rmeM"
   },
   "source": [
    "If `torch`, `torchvision` and `pytorch3d` are not installed, run the following cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 717
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "sEVdNGFwripM",
    "outputId": "27047061-a29b-4562-c164-c1288e24c266"
   },
   "outputs": [],
   "source": [
    "!pip install torch torchvision\n",
    "!pip install 'git+https://github.com/facebookresearch/pytorch3d.git@stable'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "w9mH5iVprQdZ"
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import torch\n",
    "import numpy as np\n",
    "from tqdm import tqdm_notebook\n",
    "import imageio\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import matplotlib.pyplot as plt\n",
    "from skimage import img_as_ubyte\n",
    "\n",
    "# io utils\n",
    "from pytorch3d.io import load_obj\n",
    "\n",
    "# datastructures\n",
    "from pytorch3d.structures import Meshes, Textures\n",
    "\n",
    "# 3D transformations functions\n",
    "from pytorch3d.transforms import Rotate, Translate\n",
    "\n",
    "# rendering components\n",
    "from pytorch3d.renderer import (\n",
    "    OpenGLPerspectiveCameras, look_at_view_transform, look_at_rotation, \n",
    "    RasterizationSettings, MeshRenderer, MeshRasterizer, BlendParams,\n",
    "    SoftSilhouetteShader, HardPhongShader, PointLights\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cpUf2UvirQdc"
   },
   "source": [
    "## 1. Load the Obj\n",
    "\n",
    "We will load an obj file and create a **Meshes** object. **Meshes** is a unique datastructure provided in PyTorch3D for working with **batches of meshes of different sizes**. It has several useful class methods which are used in the rendering pipeline. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8d-oREfkrt_Z"
   },
   "source": [
    "If you are running this notebook locally after cloning the PyTorch3D repository, the mesh will already be available. **If using Google Colab, fetch the mesh and save it at the path `data/`**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "sD5KcLuJr0PL",
    "outputId": "e65061fa-dbd5-4c06-b559-3592632983ee"
   },
   "outputs": [],
   "source": [
    "!mkdir -p data\n",
    "!wget -P data https://dl.fbaipublicfiles.com/pytorch3d/data/teapot/teapot.obj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "VWiPKnEIrQdd"
   },
   "outputs": [],
   "source": [
    "# Set the cuda device \n",
    "device = torch.device(\"cuda:0\")\n",
    "torch.cuda.set_device(device)\n",
    "\n",
    "# Load the obj and ignore the textures and materials.\n",
    "verts, faces_idx, _ = load_obj(\"./data/teapot.obj\")\n",
    "faces = faces_idx.verts_idx\n",
    "\n",
    "# Initialize each vertex to be white in color.\n",
    "verts_rgb = torch.ones_like(verts)[None]  # (1, V, 3)\n",
    "textures = Textures(verts_rgb=verts_rgb.to(device))\n",
    "\n",
    "# Create a Meshes object for the teapot. Here we have only one mesh in the batch.\n",
    "teapot_mesh = Meshes(\n",
    "    verts=[verts.to(device)],   \n",
    "    faces=[faces.to(device)], \n",
    "    textures=textures\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mgtGbQktrQdh"
   },
   "source": [
    "\n",
    "\n",
    "## 2. Optimization setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Q6PzKD_NrQdi"
   },
   "source": [
    "### Create a renderer\n",
    "\n",
    "A **renderer** in PyTorch3D is composed of a **rasterizer** and a **shader** which each have a number of subcomponents such as a **camera** (orthgraphic/perspective). Here we initialize some of these components and use default values for the rest. \n",
    "\n",
    "For optimizing the camera position we will use a renderer which produces a **silhouette** of the object only and does not apply any **lighting** or **shading**. We will also initialize another renderer which applies full **phong shading** and use this for visualizing the outputs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "KPlby75GrQdj"
   },
   "outputs": [],
   "source": [
    "# Initialize an OpenGL perspective camera.\n",
    "cameras = OpenGLPerspectiveCameras(device=device)\n",
    "\n",
    "# To blend the 100 faces we set a few parameters which control the opacity and the sharpness of \n",
    "# edges. Refer to blending.py for more details. \n",
    "blend_params = BlendParams(sigma=1e-4, gamma=1e-4)\n",
    "\n",
    "# Define the settings for rasterization and shading. Here we set the output image to be of size\n",
    "# 256x256. To form the blended image we use 100 faces for each pixel. We also set bin_size and max_faces_per_bin to None which ensure that \n",
    "# the faster coarse-to-fine rasterization method is used. Refer to rasterize_meshes.py for \n",
    "# explanations of these parameters. Refer to docs/notes/renderer.md for an explanation of \n",
    "# the difference between naive and coarse-to-fine rasterization. \n",
    "raster_settings = RasterizationSettings(\n",
    "    image_size=256, \n",
    "    blur_radius=np.log(1. / 1e-4 - 1.) * blend_params.sigma, \n",
    "    faces_per_pixel=100, \n",
    ")\n",
    "\n",
    "# Create a silhouette mesh renderer by composing a rasterizer and a shader. \n",
    "silhouette_renderer = MeshRenderer(\n",
    "    rasterizer=MeshRasterizer(\n",
    "        cameras=cameras, \n",
    "        raster_settings=raster_settings\n",
    "    ),\n",
    "    shader=SoftSilhouetteShader(blend_params=blend_params)\n",
    ")\n",
    "\n",
    "\n",
    "# We will also create a phong renderer. This is simpler and only needs to render one face per pixel.\n",
    "raster_settings = RasterizationSettings(\n",
    "    image_size=256, \n",
    "    blur_radius=0.0, \n",
    "    faces_per_pixel=1, \n",
    ")\n",
    "# We can add a point light in front of the object. \n",
    "lights = PointLights(device=device, location=((2.0, 2.0, -2.0),))\n",
    "phong_renderer = MeshRenderer(\n",
    "    rasterizer=MeshRasterizer(\n",
    "        cameras=cameras, \n",
    "        raster_settings=raster_settings\n",
    "    ),\n",
    "    shader=HardPhongShader(device=device, lights=lights)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "osOy2OIJrQdn"
   },
   "source": [
    "### Create a reference image\n",
    "\n",
    "We will first position the teapot and generate an image. We use helper functions to rotate the teapot to a desired viewpoint. Then we can use the renderers to produce an image. Here we will use both renderers and visualize the silhouette and full shaded image. \n",
    "\n",
    "The world coordinate system is defined as +Y up, +X left and +Z in. The teapot in world coordinates has the spout pointing to the left. \n",
    "\n",
    "We defined a camera which is positioned on the positive z axis hence sees the spout to the right. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 305
    },
    "colab_type": "code",
    "id": "EjJrW7qerQdo",
    "outputId": "93545b65-269e-4719-f4a2-52cbc6c9c974"
   },
   "outputs": [
    {
     "data": {
      "image/png": "[encoded data, 36416 characters]\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "139625337525584",
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Select the viewpoint using spherical angles  \n",
    "distance = 3   # distance from camera to the object\n",
    "elevation = 50.0   # angle of elevation in degrees\n",
    "azimuth = 0.0  # No rotation so the camera is positioned on the +Z axis. \n",
    "\n",
    "# Get the position of the camera based on the spherical angles\n",
    "R, T = look_at_view_transform(distance, elevation, azimuth, device=device)\n",
    "\n",
    "# Render the teapot providing the values of R and T. \n",
    "silhouete = silhouette_renderer(meshes_world=teapot_mesh, R=R, T=T)\n",
    "image_ref = phong_renderer(meshes_world=teapot_mesh, R=R, T=T)\n",
    "\n",
    "silhouete = silhouete.cpu().numpy()\n",
    "image_ref = image_ref.cpu().numpy()\n",
    "\n",
    "plt.figure(figsize=(10, 10))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(silhouete.squeeze()[..., 3])  # only plot the alpha channel of the RGBA image\n",
    "plt.grid(False)\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(image_ref.squeeze())\n",
    "plt.grid(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "plBJwEslrQdt"
   },
   "source": [
    "### Set up a basic model \n",
    "\n",
    "Here we create a simple model class and initialize a parameter for the camera position. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "YBbP1-EDrQdu"
   },
   "outputs": [],
   "source": [
    "class Model(nn.Module):\n",
    "    def __init__(self, meshes, renderer, image_ref):\n",
    "        super().__init__()\n",
    "        self.meshes = meshes\n",
    "        self.device = meshes.device\n",
    "        self.renderer = renderer\n",
    "        \n",
    "        # Get the silhouette of the reference RGB image by finding all the non zero values. \n",
    "        image_ref = torch.from_numpy((image_ref[..., :3].max(-1) != 0).astype(np.float32))\n",
    "        self.register_buffer('image_ref', image_ref)\n",
    "        \n",
    "        # Create an optimizable parameter for the x, y, z position of the camera. \n",
    "        self.camera_position = nn.Parameter(\n",
    "            torch.from_numpy(np.array([3.0,  6.9, +2.5], dtype=np.float32)).to(meshes.device))\n",
    "\n",
    "    def forward(self):\n",
    "        \n",
    "        # Render the image using the updated camera position. Based on the new position of the \n",
    "        # camer we calculate the rotation and translation matrices\n",
    "        R = look_at_rotation(self.camera_position[None, :], device=self.device)  # (1, 3, 3)\n",
    "        T = -torch.bmm(R.transpose(1, 2), self.camera_position[None, :, None])[:, :, 0]   # (1, 3)\n",
    "        \n",
    "        image = self.renderer(meshes_world=self.meshes.clone(), R=R, T=T)\n",
    "        \n",
    "        # Calculate the silhouette loss\n",
    "        loss = torch.sum((image[..., 3] - self.image_ref) ** 2)\n",
    "        return loss, image\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qCGLSJtfrQdy"
   },
   "source": [
    "## 3. Initialize the model and optimizer\n",
    "\n",
    "Now we can create an instance of the **model** above and set up an **optimizer** for the camera position parameter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "srZPBU7_rQdz"
   },
   "outputs": [],
   "source": [
    "# We will save images periodically and compose them into a GIF.\n",
    "filename_output = \"./teapot_optimization_demo.gif\"\n",
    "writer = imageio.get_writer(filename_output, mode='I', duration=0.3)\n",
    "\n",
    "# Initialize a model using the renderer, mesh and reference image\n",
    "model = Model(meshes=teapot_mesh, renderer=silhouette_renderer, image_ref=image_ref).to(device)\n",
    "\n",
    "# Create an optimizer. Here we are using Adam and we pass in the parameters of the model\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dvTLnrWorQd2"
   },
   "source": [
    "### Visualize the starting position and the reference position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 335
    },
    "colab_type": "code",
    "id": "qyRXpP3mrQd3",
    "outputId": "47ecb12a-e68c-47f5-92fc-821a7a9bd661"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Reference silhouette')"
      ]
     },
     "execution_count": 19,
     "metadata": {
      "bento_obj_id": "140046464048336"
     },
     "output_type": "execute_result"
    },
    {
     "data": {
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mlJ5MKXUDNwMHldROSRoJ61eHW7pwX8NDHW6X9jVkj1VKqQfoiTHWzjoxxngy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\nkiSV5P8D4F92xJykcVkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140047413426192"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 10))\n",
    "\n",
    "_, image_init = model()\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(image_init.detach().squeeze().cpu().numpy()[..., 3])\n",
    "plt.grid(False)\n",
    "plt.title(\"Starting position\")\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(model.image_ref.cpu().numpy().squeeze())\n",
    "plt.grid(False)\n",
    "plt.title(\"Reference silhouette\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aGJu7h-lrQd5"
   },
   "source": [
    "## 4. Run the optimization \n",
    "\n",
    "We run several iterations of the forward and backward pass and save outputs every 10 iterations. When this has finished take a look at `./teapot_optimization_demo.gif` for a cool gif of the optimization process!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000,
     "referenced_widgets": [
      "79d7fc84b5564206ab64b2759474da04",
      "02acadb61c3949fcaeab177fd184c388",
      "efd9860908c64bfe9d47118be4734648",
      "f8df7c6efb7d47f5be760a39b4bdbcf8",
      "d8a109658c364a00ab4d298112dac6db",
      "2d05db82cc99482bb3d62b6d4e5b1a98",
      "c621d425e2c8426c8cd4f9136d392af1",
      "3df8063f307040ebb8ff8e2f26ccf729"
     ]
    },
    "colab_type": "code",
    "id": "HvnK5VI5rQd6",
    "outputId": "4019c697-3fc6-4c7b-cdfe-225633cc0d60"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "78b2d6baaf28479c8aebf3b35cd9cf74",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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cF0PI4tNh7QkoH0230TT7TQfZb9/LHnfzzTcf8fxur5n9/dxzz9X/DXoc6P9KOUnNNbpp\n9ItPcYoEpQkhkROM4hQJSnGKBKU4RYJSnCJBKU6RoBSnSFCKUyQoxSkSlOIUCUpxigSlOEWCUpwi\nQSlOkaAUp0hQilMkKMUpEpTiFAlKcYoEpThFglKcIkEpTpGgFKdIUIpTJCjFKRKU4hQJSnGKBKU4\nRYJSnCJBKU6RoBSnSFCKUyQoxSkSlOIUCUpxigSlOEWCUpwiQSlOkaAUp0hQilMkKMUpEpTiFAlK\ncYoEpThFglKcIkEpTpGgFKdIUIpTJCjFKRKU4hQJSnGKBKU4RYJSnCJBKU6RoBSnSFCKUyQoxSkS\nlOIUCUpxigSlOEWCUpwiQSlOkaAUp0hQilMkKMUpEpTiFAlKcYoEpThFglKcIkEpTpGgFKdIUIpT\nJCjFKRKU4hQJSnGKBKU4RYJSnCJBKU6RoBSnSFCKUyQoxSkSlOIUCUpxigSlOEWCUpwiQSlOkaAU\np0hQilMkKMUpEpTiFAlKcYoEpThFglKcIkEpTpGgFKdIUIpTJCjFKRKUuXuvt0FEutDIKRKU4hQJ\nSnGKBKU4RYJSnCJBKU6RoP4PtK1qrRux1HYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046487997712"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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B6UDOFcx2f7AtnaU+p2PpgDLLvbftlpltyvY1jx8/3rqRYcmSJR2rp7SnltOp9KntXK1l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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046488867728"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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htpfYZWVbxVqtxujoKDt27GDnzp0MDw+ze/duKpVKq1VNzk/TFzN0GgBKt6SVSmWGXwXJ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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046463357264"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vWWDSV52Uy2WKxSL5fB7nXOMjTuKOo3i4ZCrpzqHkY2/cuPE4HLXMhGrOjCQnFQBs2bKl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\nBOr/AHYKWRdVX+yiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046463617296"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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J0AExp02imBKzWq0G3foQEjp7eKVSwZo1a+a06NqhdktkpRTK5TJyuRzGx8cbWn+ff/75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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046462817104"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RLBbR0dGB9vZ2vOENb8Dw8DByuRyefvppXHDBBXP6/lM9htMS1bNpBuihS0S7TeeGMGr+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\nA9Dty2EIq8KlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046462421328"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046449306128"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/dtTKHNe4zMU+Xe1YaA/pmg58+t4soT+4Oq676Vqn0+pk9lYnyCsoysZh+t4s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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046462420496"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wPj6OyclJHHroochkMjjrrLPadKYb55577kG5XJ53w4DtFUgpkU6ng2VoaAgXX3zxotUz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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140047413338448"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7bMXF46GHHornnEdHR3HZZZctdZWccMw5T7Zu3QoAOO+88/Dzn/8chw4dipe/6WmTgYEB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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046448682192"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046448559248"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LC9htWfYSPlrM3sFFCEuMvpjj1qxGkVRMnc5nRuWPuoOFwlxcaDmXEB0wQhcu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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046448290512"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Q0+Lori49jNZ2GeYrILCAfVMRoTA9hZazS0niepr/LQXoL3RrCfEUurWEdBkU\nJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGe\nQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES\n4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikU\nJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGe\nQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES\n4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4ikU\nJyGeQnES4ikUJyGeQnES4ikUJyGeQnES4imilFrqOhBCHNByEuIpFCchnkJxEuIpFCchnkJxEuIp\nFCchnvL/tMIznaGp+z4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046447898384"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wY2PPldWzj2q1GrLZbJCvGZSKg11m0z3WgaJsNhsc9+jRo8jn84ny6CT33XcfJicncfDg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\nQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046434818256"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kkkvmvI0u6Na2yNDQEBKJBE477TTs3LkTr7/+OqSUsybu9YIAOBYcwGEFbUtpilTPX4ah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\nIZ5CcRLiKRQnIZ5CcRLiKf8PphZo5rDxwscAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046434053200"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mkhpjXCdoT1MkkbTQPQnzCZFBRnVBYQ4UinOAxI2x0kyP2PgWj8OymK75037p\n91y7XF0fCnNw0K1dBlwijVsJdLowRWS7wa6VP/3WkQGgxcFXYw4B+4d8NYsZJ5oMKgrrWuvrqmcS\nFOXS4JhzCOhGa4/vfOtT0zIoqxsXcfVFeu36UpjLBy3nacJcj+tyHU/H85hJpHFn9TEcWw4OPpUS\nAPY61LinOvp1XQfh6qZZC7xYa0/6h5bzNLOYn3bQ9Cs+37lxQk4KXNGNHTwMCAWKdneTVvOYnE6X\nl2JcfijOwLFF6rJ6S3Vd+1mTyzHl6YPiXEH4rGkaliJgWsnhQHGuQJLeubOY9w65pnMoyuFCcY4I\nPsGmnZKhEMPDJ84FayStdZqS28rZdu/ePfQ6cOt/8+mPlpOQIcPle4SsMChOQgKF4iQkUChOQgKF\n4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQk\nUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChO\nQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF\n4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQk\nUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChO\nQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF4iQkUChOQgKF\n4iQkUChOQgJFSCmHXQdCiANaTkICheIkJFAoTkICheIkJFAoTkICheIkJFD+PzLLcVKOYxs6AAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046434176144"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sdrIlycKBqAvAQqEoWwctZ4ex18dG7edaXRNlNcPWybr2S3JxaNRX0l5oOReZ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\nIZ5CcRLiKRQnIZ5CcRLiKf8PHKmZncHcDcYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046434051856"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3N+5dIe1MXG8GWsvuQcvpGY0sW9hEhG4EeBrRasSYtAct5xzjo8VpZojHx/ov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\nnikmekEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046433628112"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JjI+PY9++fSgUCk6LZgszTtxpx5wAAoHp8biuOszkT61WaxC0nbGN6jN1tdecryedQU4m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\nCsVJiKf8P8ZamgYBgyMkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "bento_obj_id": "140046433023312"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kTbCgO9sefMHXAmHPHrJJO8XPd2zc/nHHx5XRasw1zRTBJKHLMntrXregOBeY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\nOAkJlP8HtUg08UdcRyYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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    "loop = tqdm_notebook(range(200))\n",
    "for i in loop:\n",
    "    optimizer.zero_grad()\n",
    "    loss, _ = model()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    \n",
    "    loop.set_description('Optimizing (loss %.4f)' % loss.data)\n",
    "    \n",
    "    if loss.item() < 200:\n",
    "        break\n",
    "    \n",
    "    # Save outputs to create a GIF. \n",
    "    if i % 10 == 0:\n",
    "        R = look_at_rotation(model.camera_position[None, :], device=model.device)\n",
    "        T = -torch.bmm(R.transpose(1, 2), model.camera_position[None, :, None])[:, :, 0]   # (1, 3)\n",
    "        image = phong_renderer(meshes_world=model.meshes.clone(), R=R, T=T)\n",
    "        image = image[0, ..., :3].detach().squeeze().cpu().numpy()\n",
    "        image = img_as_ubyte(image)\n",
    "        writer.append_data(image)\n",
    "        \n",
    "        plt.figure()\n",
    "        plt.imshow(image[..., :3])\n",
    "        plt.title(\"iter: %d, loss: %0.2f\" % (i, loss.data))\n",
    "        plt.grid(\"off\")\n",
    "        plt.axis(\"off\")\n",
    "    \n",
    "writer.close()"
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    "## 5. Conclusion \n",
    "\n",
    "In this tutorial we learnt how to **load** a mesh from an obj file, initialize a PyTorch3D datastructure called **Meshes**, set up an **Renderer** consisting of a **Rasterizer** and a **Shader**, set up an optimization loop including a **Model** and a **loss function**, and run  the optimization. "
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  }
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