Attempt to fix equation in object_pose_estimation tuto

Author: Speierers

inverse_rendering/object_pose_estimation.ipynb

@@ -19,15 +19,15 @@
     "In this tutorial, we will show how to optimize the pose of an object while correctly accounting for the visibility discontinuities. We are going to optimize several latent variables that control the translation and rotation of the object.\n",
     "\n",
     "In differentiable rendering, we aim to evaluate the derivative of a pixel intensity integral with respect to a scene parameter $\\pi$ as follows:\n",
-    "$$\n",
-    "\\partial_\\pi I(\\pi) = \\partial_\\pi \\int_P f(\\textbf{x}, \\pi) ~ d\\textbf{x}\n",
-    "$$\n",
-    "where $\\textbf{x}$ is a light path in the path space $P$. \n",
+    "\n",
+    "$$\\partial_\\pi I(\\pi) = \\partial_\\pi \\int_P f(\\textbf{x}, \\pi) ~ d\\textbf{x}$$\n",
+    "\n",
+    "where $\\textbf{x}$ is a light path in the path space $P$.\n",
     "\n",
     "When the function $f(\\cdot)$ is continuous w.r.t. $\\pi$, we can move the derivative into the integral and then apply Monte Carlo integration. Under this assumption, differentiating the rendering process via automatic differentiation, as in the previous tutorials, is correct.\n",
     "\n",
     "However, if $f(\\cdot)$ has discontinuities w.r.t. $\\pi$, direct application of automatic differentiation is not correct anymore, as it omits an integral term given by the [Reynolds transport theorem](https://en.wikipedia.org/wiki/Reynolds_transport_theorem). This needs to be considered when differentiating shape-related parameters (e.g., position), as the discontinuities in the visiblity function (the silhouette of the object) are then dependent on the differentiated parameter.\n",
-    "      \n",
+    "\n",
     "In the last years, several works tried to address this issue (e.g., <cite data-cite=\"Li2018\">Li et al. (2018)</cite>, <cite data-cite=\"Zhang2020\">Zhang et al. (2020)</cite>, <cite data-cite=\"Loubet2019Reparameterizing\">Loubet et al. (2019)</cite>, <cite data-cite=\"Bangaru2020\">Bangaru et al. (2020)</cite>, ...). Mitsuba provides dedicated integrators implementing the *reparameterization*-based approach (<cite data-cite=\"Loubet2019Reparameterizing\">Loubet et al. (2019)</cite>, <cite data-cite=\"Bangaru2020\">Bangaru et al. (2020)</cite>, <cite data-cite=\"Zeltner2021\">Zeltner et al. (2021)</cite>):\n",
     "\n",
     "- [<code>prb_reparam</code>][1]: reparameterized Path Replay Backpropagation (PRB) integrator\n",