|  | 
| 63 | 63 |         "\n", | 
| 64 | 64 |         "\n", | 
| 65 | 65 |         "\n", | 
| 66 |  | -        " This model is composed of two parameters that are often refered to as intrinsic parameters:\n", | 
|  | 66 | +        " This model is composed of two parameters that are often referred to as intrinsic parameters:\n", | 
| 67 | 67 |         "- the principal point, which is the projection of the optical center on the image. Ideally, the principal point is close to the center of the image.\n", | 
| 68 | 68 |         "- the focal length, which is the distance between the optical center and the image plane. This parameters allows to control the level of zoom.\n", | 
| 69 | 69 |         "\n", | 
| 70 |  | -        "This notebook illustrates how to use [Tensorflow Graphics](https://github.com/tensorflow/graphics) to estimate the intrinsic parameters of a projective camera. Recovering these parameters is particularly imporant to perform several tasks, including 3D reconstruction.\n", | 
|  | 70 | +        "This notebook illustrates how to use [Tensorflow Graphics](https://github.com/tensorflow/graphics) to estimate the intrinsic parameters of a projective camera. Recovering these parameters is particularly important to perform several tasks, including 3D reconstruction.\n", | 
| 71 | 71 |         "\n", | 
| 72 | 72 |         "In this Colab, the goal is to recover the intrinsic parameters of a camera given an observation and correspondences between the observation and the render of the current solution.  Things are kept simple by only inserting a rectangle in the 3D scene, and using it as the source of correspondences during the optimization. The minimization is performed using the Levenberg-Marquardt algorithm." | 
| 73 | 73 |       ] | 
|  | 
| 222 | 222 |         "ideal_principal_point = np.array(\n", | 
| 223 | 223 |         "    (image_width, image_height), dtype=np.float64) / 2.0\n", | 
| 224 | 224 |         "\n", | 
| 225 |  | -        "# Let's see what our scene looks like using the intrinsic paramters defined above.\n", | 
|  | 225 | +        "# Let's see what our scene looks like using the intrinsic parameters defined above.\n", | 
| 226 | 226 |         "render = render_rectangle(rectangle_vertices, focal_lengths, ideal_principal_point,\n", | 
| 227 | 227 |         "                          image_dimensions)\n", | 
| 228 | 228 |         "_ = plt.imshow(render)" | 
|  | 
| 355 | 355 |         "id": "QTdXuY6BapnT" | 
| 356 | 356 |       }, | 
| 357 | 357 |       "source": [ | 
| 358 |  | -        "As described earlier, one can compare how the 3D object would look using the current estimate of the intrinsic parameters, can compare that to the actual observation. The following function captures a distance beween these two images which we will seek to minimize." | 
|  | 358 | +        "As described earlier, one can compare how the 3D object would look using the current estimate of the intrinsic parameters, can compare that to the actual observation. The following function captures a distance between these two images which we will seek to minimize." | 
| 359 | 359 |       ] | 
| 360 | 360 |     }, | 
| 361 | 361 |     { | 
|  | 
| 403 | 403 |         "real_focal_lengths, real_principal_point, estimate_focal_lengths, estimate_principal_point = build_parameters(\n", | 
| 404 | 404 |         ")\n", | 
| 405 | 405 |         "\n", | 
| 406 |  | -        "# Contructs the observed image.\n", | 
|  | 406 | +        "# Constructs the observed image.\n", | 
| 407 | 407 |         "observation = render_rectangle(rectangle_vertices, real_focal_lengths,\n", | 
| 408 | 408 |         "                               real_principal_point, image_dimensions)\n", | 
| 409 | 409 |         "\n", | 
|  | 
| 444 | 444 |       "version": "0.3.2" | 
| 445 | 445 |     }, | 
| 446 | 446 |     "kernelspec": { | 
| 447 |  | -      "display_name": "Python 2", | 
| 448 |  | -      "name": "python2" | 
|  | 447 | +      "display_name": "Python 3", | 
|  | 448 | +      "name": "python3" | 
| 449 | 449 |     } | 
| 450 | 450 |   }, | 
| 451 | 451 |   "nbformat": 4, | 
|  | 
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