PointFlow/docs/index.html

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<title>PointFlow</title>
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<p class="h2 font-weight-normal">PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows</p>
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<a class="col-md-3 col-xs-6" href="http://www.guandaoyang.com"><span>Guandao Yang*</span></a>
<a class="col-md-3 col-xs-6" href="http://www.cs.cornell.edu/~xhuang/"><span>Xun Huang*</span></a>
<a class="col-md-3 col-xs-6" href="http://www.cs.cornell.edu/~zekun/"><span>Zekun Hao</span></a>
<a class="col-md-3 col-xs-6" href="http://mingyuliu.net/"><span>Ming-Yu Liu</span></a>
<a class="col-md-6 col-xs-6" href="http://blogs.cornell.edu/techfaculty/serge-belongie/"><span>Serge Belongie</span></a>
<a class="col-md-6 col-xs-6" href="http://home.bharathh.info/"><span>Bharath Hariharan</span></a>
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<a class="ml-4" href="https://www.cornell.edu/"><span>Cornell University</span></a>
<a class="mr-4 ml-4" href="https://tech.cornell.edu/"><span>Cornell Tech</span></a>
<a class="mr-4 ml-4" href="https://www.nvidia.com/"><span>NVIDIA</span></a>
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<a href="https://arxiv.org/pdf/1906.12320.pdf" style="max-width:200px; margin-left:auto; margin-right:auto">
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<a class="h5" href="https://arxiv.org/abs/1906.12320" style="margin-right:10px">
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<span>[Arxiv]</span>
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<a class="h5" href="https://github.com/stevenygd/PointFlow" style="margin-right:10px">
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<span>[Code]</span>
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</a>
<a class="h5" href="assets/Bibtex.txt" target="_blank">
<span>[Bibtex]</span>
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<p class='h4 font-weight-bold '>Abstract</p>
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<p style='line-height:1;'>
As 3D point clouds become the representation of choice
for multiple vision and graphics applications, the ability to
synthesize or reconstruct high-resolution, high-fidelity point
clouds becomes crucial. Despite the recent success of deep
learning models in discriminative tasks of point clouds,
generating point clouds remains challenging. This paper
proposes a principled probabilistic framework to generate
3D point clouds by modeling them as a distribution of
distributions. Specifically, we learn a two-level hierarchy
of distributions where the first level is the distribution of
shapes and the second level is the distribution of points
given a shape. This formulation allows us to both sample
shapes and sample an arbitrary number of points from
a shape. Our generative model, named PointFlow, learns
each level of the distribution with a continuous normalizing
flow. The invertibility of normalizing flows enables
computation of the likelihood during training and allows us
to train our model in the variational inference framework.
Empirically, we demonstrate that PointFlow achieves stateof-
the-art performance in point cloud generation. We additionally
show that our model can faithfully reconstruct
point clouds and learn useful representations in an unsupervised
manner.
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<p class='h2'>Brief Introduction to the Method</p>
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<p class="text-break">
Each shape can be viewed as a distribution of 3D points.
In such distribution, points on the shape have higher probability and are more likely to be sampled.
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A point cloud can be viewed as a set of points sampled from such distribution.
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<p class="text-break">
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We use two continuous normalizing flows (CNFs) to model the distribution of shapes, while each shape is a distribution of 3D points.
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The latent CNF transforms a vector sampled from the shape prior to a latent shape vector.
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The point CNF transforms 3D points sampled from the point prior to a point cloud conditioned on a shape vector.
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<img src="assets/inference-architecture.gif" class="img-fluid" alt="architecture">
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<p class='h2'>Visulaization of the Flow</p>
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<p class='h2'>Acknowledgements</p>
<p>This work was supported in part by a research gift from Magic Leap. Xun Huang was supported by NVIDIA fellowship.</p>
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