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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Spatial Distortions"
]
},
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"cell_type": "code",
"execution_count": 1,
"metadata": {
"nbsphinx": "hidden"
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"outputs": [
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"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from pyrad.cameras.rays import Frustums\n",
"from pyrad.fields.modules.spatial_distortions import SceneContraction\n",
"import torch\n",
"import plotly.graph_objects as go\n",
"import plotly.express.colors as colors\n",
"from plotly.offline import iplot, init_notebook_mode\n",
"from plotly.graph_objs import Mesh3d\n",
"\n",
"init_notebook_mode()\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"nbsphinx": "hidden"
},
"outputs": [],
"source": [
"def gen_ellipse(mean, cov=None, color=None, opacity=0.2, scaling=20, ellipse_res=20):\n",
" phi = torch.linspace(0, 2 * torch.pi, ellipse_res)\n",
" theta = torch.linspace(-torch.pi / 2, torch.pi / 2, ellipse_res)\n",
" phi, theta = torch.meshgrid(phi, theta, indexing=\"ij\")\n",
"\n",
" x = torch.cos(theta) * torch.sin(phi)\n",
" y = torch.cos(theta) * torch.cos(phi)\n",
" z = torch.sin(theta)\n",
"\n",
" pts = torch.stack((x, y, z), axis=-1)\n",
" if cov is not None:\n",
" pts = pts @ cov\n",
" pts = scaling * pts + mean\n",
"\n",
" return Mesh3d(\n",
" {\n",
" \"x\": pts[:, :, 0].flatten(),\n",
" \"y\": pts[:, :, 1].flatten(),\n",
" \"z\": pts[:, :, 2].flatten(),\n",
" \"alphahull\": 0,\n",
" \"opacity\": opacity,\n",
" \"color\": color,\n",
" }\n",
" )\n",
"\n",
"\n",
"def visualize_gaussians(gaussians):\n",
" [num_rays, num_samples, _] = gaussians.mean.shape\n",
" meshes = []\n",
" for ray_idx in range(num_rays):\n",
" centers = go.Scatter3d(\n",
" x=gaussians.mean[ray_idx, :, 0],\n",
" y=gaussians.mean[ray_idx, :, 1],\n",
" z=gaussians.mean[ray_idx, :, 2],\n",
" mode=\"markers\",\n",
" marker=dict(size=2, color=\"black\"),\n",
" )\n",
" meshes.append(centers)\n",
" for sample_idx in range(num_samples):\n",
" color = colors.qualitative.Plotly[ray_idx % len(colors.qualitative.Plotly)]\n",
" ellipse = gen_ellipse(\n",
" gaussians.mean[ray_idx, sample_idx],\n",
" cov=gaussians.cov[ray_idx, sample_idx],\n",
" scaling=scaling,\n",
" color=color,\n",
" )\n",
" meshes.append(ellipse)\n",
"\n",
" ellipse = gen_ellipse(0, scaling=1, color=\"#111111\", opacity=0.03)\n",
" meshes.append(ellipse)\n",
" ellipse = gen_ellipse(0, scaling=2, color=\"#111111\", opacity=0.03)\n",
" meshes.append(ellipse)\n",
" return meshes\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Scene Contraction\n",
"\n",
"Contract unbounded space into a sphere of radius 2. This contraction was proposed in [MipNeRF-360](https://jonbarron.info/mipnerf360/).\n",
" \n",
"We use the following contraction equation:\n",
"\n",
"$$\n",
" f(x) = \\begin{cases}\n",
" x & ||x|| \\leq 1 \\\\\n",
" (2 - \\frac{1}{||x||})(\\frac{x}{||x||}) & ||x|| > 1\n",
" \\end{cases}\n",
"$$\n",
"\n",
"Below we visualize a ray before and after scene contraction. Visualized are gaussians blobs for each sample location."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
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"colorway": [
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"#EF553B",
"#00cc96",
"#ab63fa",
"#FFA15A",
"#19d3f3",
"#FF6692",
"#B6E880",
"#FF97FF",
"#FECB52"
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},
"geo": {
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"lakecolor": "white",
"landcolor": "#E5ECF6",
"showlakes": true,
"showland": true,
"subunitcolor": "white"
},
"hoverlabel": {
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},
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},
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},
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}
}
},
"title": {
"text": "Before Contraction"
}
}
},
"text/html": [
"