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<!Doctype html>
<html lang="en">
<head>
<title>Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks</title>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="author" content="Despoina Paschalidou">
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</style>
</head>
<body>
<div class="section">
<h1 class="project-title">
Neural Parts: Learning Expressive 3D Shape Abstractions<br />
with Invertible Neural Networks
</h1>
<div class="authors">
<a href=https://paschalidoud.github.io/>
Despoina Paschalidou <sup>1,5,6</sup>
</a>
<a href=https://angeloskath.github.io/>
Angelos Katharopoulos <sup>3,4</sup>
</a>
<a href=http://cvlibs.net/>
Andreas Geiger <sup>1,2,5</sup>
</a>
<a href=https://www.cs.utoronto.ca/~fidler/>
Sanja Fidler <sup>6,7,8</sup>
</a>
</div>
<div class="affiliations">
<span><sup>1</sup> Autonomous Vision Group, MPI for
Intelligent Systems Tübingen</span>
<span><sup>2</sup> University of Tübingen</span> <br/>
<span><sup>3</sup> Idiap Research Institute, Switzerland</span>
<span><sup>4</sup> École Polytechique Fédérale de Lausanne (EPFL)</span> <br/>
<span><sup>5</sup> Max Planck ETH Center for Learning Systems</span>
<span><sup>6</sup> NVIDIA</span>
<span><sup>7</sup> University of Toronto</span>
<span><sup>8</sup> Vector Institute</span>
</div>
<div class="project-conference">
CVPR 2021
</div>
<div class="project-icons">
<a href="https://arxiv.org/pdf/2103.10429.pdf">
<i class="fa fa-file"></i> <br/>
Paper
</a>
<a href="https://github.com/paschalidoud/neural_parts">
<i class="fa fa-github"></i> <br/>
Code
</a>
<a href="https://www.youtube.com/watch?v=6WK3B0IZJsw">
<i class="fa fa-youtube-play"></i> <br/>
Video
</a>
<a href="https://paschalidoud.github.io/data/Paschalidou2021CVPR_poster.pdf">
<i class="fa fa-picture-o"></i> <br/>
Poster
</a>
<a href="http://www.cvlibs.net/publications/Paschalidou2021CVPR_slides.pdf">
<i class="fa fa-file-powerpoint-o"></i> <br/>
Slides
</a>
<a href="https://autonomousvision.github.io/neural-parts/">
<i class="fa fa-newspaper-o"></i> <br/>
Blog
</a>
</div>
<div class="teaser-image">
<img src="projects/neural_parts/teaser.png" style="width:100%;">
<p class="caption">Our model learns to parse 3D objects into
geometrically accurate and semantically consistent part arrangements <strong>
without any part-level supervision</strong>. Our evaluations on ShapeNet objects,
D-FAUST humans and FreiHAND hands demonstrate that our primitives can capture complex
geometries and thus simultaneously achieve geometrically accurate as well as
interpretable reconstructions using an order of magnitude fewer primitives than
state-of-the-art shape abstraction methods.</p>
<figure style="width: 49%;">
<video class="centered" width="100%" controls muted loop autoplay>
<source src="projects/neural_parts/motivation_cvxnet.mp4" type="video/mp4"/>
</video>
<p class="caption">Existing primitive-based methods rely on
simple shapes for decomposing complex 3D shapes into
parts. As a result, they <strong>require a large number of primitives</strong>
for extracting accurate reconstructions. However, this results in <strong>
less interpretable shape abstractions</strong>, namely
<strong>primitives are not semantically meaningful parts</strong>.</p>
</figure>
<figure style="width: 49%;">
<video class="centered" width="100%" controls muted loop autoplay>
<source src="projects/neural_parts/motivation_ours.mp4" type="video/mp4"/>
</video>
<p class="caption">Neural Parts is a novel 3D primitive representation that can
<strong>represent arbitrarily complex genus-zero shapes
</strong> and thus yield more <strong>geometrically accurate</strong> and
<strong>semantically meaningful</strong> shape abstractions compared to simpler primitives.</p>
</figure>
</div>
<div class="section-title">Approach Overview</div>
<div class="video">
<iframe width="860" height="485" src="https://www.youtube.com/embed/6WK3B0IZJsw" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</div>
<div class="content">
<div class="side-text"><p>Primitive-based representations seek to infer
<strong>semantically consistent part arrangements across
different object instances</strong>. Existing primitive-based
methods rely on simple shapes for decomposing complex objects
into parts such as cuboids, superquadrics, spheres or
convexes. <strong>Due to their simple parametrization, these primitives
have limited expressivity and cannot capture arbitrarily
complex geometries</strong>. Therefore, <strong>existing part-based methods
require a large number of primitives for extracting
geometrically accurate reconstructions</strong>. However, using <strong>more
primitives comes at the expense of less interpretable
reconstructions</strong>. Namely, a primitive is not an identifiable
part anymore.</p></div>
<div class="side-image"><img src="projects/neural_parts/convexes_vs_nps.png" style="width:100%;"></div>
<p>We introduce a novel 3D primitive representation that is
defined as <strong>a deformation between shapes</strong> and is
<strong>parametrized as a learned homeomorphic mapping</strong>
implemented with an <strong>Invertible Neural Network
(INN)</strong>. We argue that a primitive should be a non
trivial genus-zero shape with well defined implicit and explicit representations. Using an INN allows us to efficiently compute
the implicit and explicit representation of the predicted shape
and impose various constraints on the predicted parts. In contrast to prior work,
that directly predict the primitive parameters (i.e. centroids and sizes for cuboids
and superquadrics and hyperplanes for convexes), we employ the INN to fully define each primitive.
This allows us to have primitives that capture arbitrarily
complex geometries, hence the ability of our model to parse
objects into expressive shape abstractions that are more
geometrically accurate using an order of magnitude fewer
primitives compared to approaches that rely on simple convex
shape primitives.
</p>
<img src="projects/neural_parts/architecture.png" style="width:100%;">
<p class="caption">Given an input image and a watertight mesh
of the target object we seek to learn a representation with M
primitives that best describes the target object. We define our
primitives via a deformation between shapes that is
parametrized as a learned homeomorphism implemented with an
Invertible Neural Network (INN). For each primitive, we seek to
learn a homeomorphism between the 3D space of a simple
genus-zero shape and the 3D space of the target object, such
that the deformed shape matches a part of the target object. Due
to its simple implicit surface definition and tesselation, we
employ a sphere as our genus-zero shape. Note that using an INN
allows us to efficiently compute the implicit and explicit representation of
the predicted shape and impose various constraints on the predicted parts.</p>
</div>
<div class="section-title">Results</div>
<div class="content">
In the following interactive visualization, the naming of the
parts has been done manually. However, <strong>the model had no part
supervision during training</strong>. The semantic parts have
emerged naturally from reconstructing the geometry.
<h3>Humans</h3>
<div id="humans">
<div class="controls">
<div class="left-controls">
Show
<input type="checkbox" id="humans_all" checked><label for="humans_all">all parts</label>
<input type="checkbox" id="humans_head"><label for="humans_head">heads</label>
<input type="checkbox" id="humans_body"><label for="humans_body">bodies</label>
<input type="checkbox" id="humans_left_hand"><label for="humans_left_hand">left-arms</label>
<input type="checkbox" id="humans_right_hand"><label for="humans_right_hand">right-arms</label>
<input type="checkbox" id="humans_left_leg"><label for="humans_left_leg">left-legs</label>
<input type="checkbox" id="humans_right_leg"><label for="humans_right_leg">right-legs</label>
</div>
<div class="right-controls">
<button>Randomize</button>
</div>
</div>
<div class="render_container">
<div data-size="400" class="render_window"></div><div data-size="400" class="render_window"></div><div data-size="400" class="render_window"></div>
</div>
</div>
<h3>Planes</h3>
<div id="planes">
<div class="controls">
<div class="left-controls">
Show
<input type="checkbox" id="planes_all" checked><label for="planes_all">all parts</label>
<input type="checkbox" id="planes_nose"><label for="planes_nose">noses</label>
<input type="checkbox" id="planes_body"><label for="planes_body">bodies</label>
<input type="checkbox" id="planes_left_wing"><label for="planes_left_wing">left-wings</label>
<input type="checkbox" id="planes_right_wing"><label for="planes_right_wing">right-wings</label>
<input type="checkbox" id="planes_tail"><label for="planes_tail">tails</label>
</div>
<div class="right-controls">
<button>Randomize</button>
</div>
</div>
<div class="render_container">
<div data-size="400" class="render_window"></div><div data-size="400" class="render_window"></div><div data-size="400" class="render_window"></div>
</div>
</div>
</div>
<div class="section-title">Comparison to Primitive-based Methods</div>
<div class="content">
<p>
We compare the representation power of Neural Parts to
other primitive-based methods by evaluating the
reconstruction quality with varying number of primitives on
three datasets. We observe that our model is <strong>more
geometrically accurate, more semantically consistent and
yields more meaningful parts</strong> (i.e. primitives are
identifiable parts such as thumbs, legs, wings, tires,
etc.) compared to simpler primitives.
</p>
<div class="glide">
<div class="glide__bullets" data-glide-el="controls[nav]">
<button class="glide__bullet" data-glide-dir="=0">Humans</button>
<button class="glide__bullet" data-glide-dir="=1">Hands</button>
<button class="glide__bullet" data-glide-dir="=2">Chairs</button>
<button class="glide__bullet" data-glide-dir="=3">Planes</button>
<button class="glide__bullet" data-glide-dir="=4">Cars</button>
<button class="glide__bullet" data-glide-dir="=5">Lamps</button>
</div>
<div class="glide__track" data-glide-el="track">
<ul class="glide__slides">
<li class="glide__slide"><img src="projects/neural_parts/comparison/humans.png"></li>
<li class="glide__slide"><img src="projects/neural_parts/comparison/hands.png"></li>
<li class="glide__slide"><img src="projects/neural_parts/comparison/chairs.png"></li>
<li class="glide__slide"><img src="projects/neural_parts/comparison/planes.png"></li>
<li class="glide__slide"><img src="projects/neural_parts/comparison/cars.png"></li>
<li class="glide__slide"><img src="projects/neural_parts/comparison/lamps.png"></li>
</ul>
</div>
</div>
</div>
<div class="section-title">Semantic Consistency</div>
<div class="content">
We observe that Neural Parts consistently use the same
primitive for representing the same object part regardless of
the breadth of the part's motion. Notably, this
<strong>temporal consistency is an emergent property</strong>
of our method and <strong>not one that is enforced with any
kind of loss</strong>.
<video class="centered" width="100%" controls muted loop autoplay>
<source
src="projects/neural_parts/semantic-consistency-shorter.mp4"
type="video/mp4" />
</video>
</div>
<div class="section-title">Acknowledgements</div>
<div class="content">
This research was supported by the Max Planck ETH Center for
Learning Systems.
</div>
</div>
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};
}
function show_group(elements, objects, N) {
var controls = [];
for (var i=0; i<objects.length; i++) {
controls.push(show_object(elements[i], objects[i], N));
}
return {
controls: controls,
show: function (indices) {
for (var i=0; i<controls.length; i++) {
controls[i].show(indices);
}
},
show_all: function () {
for (var i=0; i<controls.length; i++) {
controls[i].show_all();
}
}
};
}
// Humans
var humans = [
"https://superquadrics.com/neural_parts/humans/50002_chicken_wings",
"https://superquadrics.com/neural_parts/humans/50002_hips",
"https://superquadrics.com/neural_parts/humans/50002_jiggle_on_toes",
"https://superquadrics.com/neural_parts/humans/50002_jumping_jacks",
"https://superquadrics.com/neural_parts/humans/50002_jumping_jacks_00038",
"https://superquadrics.com/neural_parts/humans/50002_jumping_jacks_2",
"https://superquadrics.com/neural_parts/humans/50002_knees",
"https://superquadrics.com/neural_parts/humans/50004_punching",
"https://superquadrics.com/neural_parts/humans/50004_running_on_spot",
"https://superquadrics.com/neural_parts/humans/50004_running_on_spot_00220",
"https://superquadrics.com/neural_parts/humans/50004_running_on_spot_2",
"https://superquadrics.com/neural_parts/humans/50004_running_spot",
"https://superquadrics.com/neural_parts/humans/50007_jumping_jacks",
"https://superquadrics.com/neural_parts/humans/50009_chicken_wings",
"https://superquadrics.com/neural_parts/humans/50009_jumping_jacks",
"https://superquadrics.com/neural_parts/humans/50009_jumping_jacks_00140",
"https://superquadrics.com/neural_parts/humans/50009_one_leg_jump",
"https://superquadrics.com/neural_parts/humans/50009_one_leg_jump_00075",
"https://superquadrics.com/neural_parts/humans/50009_shake_hips",
"https://superquadrics.com/neural_parts/humans/50020_knees_00136",
"https://superquadrics.com/neural_parts/humans/50021_knees",
"https://superquadrics.com/neural_parts/humans/50021_knees_2",
"https://superquadrics.com/neural_parts/humans/50021_knees_3",
"https://superquadrics.com/neural_parts/humans/50021_knees_4",
"https://superquadrics.com/neural_parts/humans/50021_knees_5",
"https://superquadrics.com/neural_parts/humans/50021_knees_6",
"https://superquadrics.com/neural_parts/humans/50021_knees_7",
"https://superquadrics.com/neural_parts/humans/50021_one_leg_jump",
"https://superquadrics.com/neural_parts/humans/50021_running_on_spot",
"https://superquadrics.com/neural_parts/humans/50021_running_on_spot_2",
"https://superquadrics.com/neural_parts/humans/50022_punching_00069",
"https://superquadrics.com/neural_parts/humans/50022_shake_hips",
"https://superquadrics.com/neural_parts/humans/50026_knees",
"https://superquadrics.com/neural_parts/humans/50027_jumping_jacks",
"https://superquadrics.com/neural_parts/humans/50027_jumping_jacks_2",
"https://superquadrics.com/neural_parts/humans/50027_jumping_jacks_3",
"https://superquadrics.com/neural_parts/humans/50027_jumping_jacks_4",
"https://superquadrics.com/neural_parts/humans/50027_jumping_jacks_5",
];
var human_control = show_group(
document.getElementById("humans").getElementsByClassName("render_window"),
[humans[0], humans[1], humans[2]],
6
);
var human_checkboxes = document.querySelectorAll("#humans .controls input");
reset_checkboxes(human_checkboxes);
document.querySelector("#humans .controls").addEventListener(
"change",
function (ev) {
if (ev.target.id == "humans_all") {
Array.prototype.filter.call(
human_checkboxes,
(el) => el.id != "humans_all"
).forEach(function (el) {el.checked = false;});
} else if (ev.target.checked) {
human_checkboxes[0].checked = false;
}
var ids = new Set();
if (human_checkboxes[0].checked) {
ids = new Set([0, 1, 2, 3, 4, 5]);
}
var part_ids = [1, 2, 0, 4, 3, 5];
for (var i=1; i<human_checkboxes.length; i++) {
if (human_checkboxes[i].checked) {
ids.add(part_ids[i-1]);
}
}
human_control.show(Array.from(ids));
}
);
document.querySelector("#humans .controls button").addEventListener(
"click",
function (ev) {
reset_checkboxes(human_checkboxes);
var new_humans = random_choice(humans, 3);
var render_windows = document.getElementById("humans").getElementsByClassName("render_window");
Array.prototype.forEach.call(render_windows, function (r) {r.innerHTML = "";});
human_control = show_group(
render_windows,
new_humans,
6
);
}
);
// Planes
var planes = [
"https://superquadrics.com/neural_parts/planes/10af5de930178a161596c26b5af806fe",
"https://superquadrics.com/neural_parts/planes/1a32f10b20170883663e90eaf6b4ca52",
"https://superquadrics.com/neural_parts/planes/1a6ad7a24bb89733f412783097373bdc",
"https://superquadrics.com/neural_parts/planes/1b3c6b2fbcf834cf62b600da24e0965",
"https://superquadrics.com/neural_parts/planes/1c26ecb4cd01759dc1006ed55bc1a3fc",
"https://superquadrics.com/neural_parts/planes/284e6431669d46fd44797ce00623b3fd",
"https://superquadrics.com/neural_parts/planes/2c3ba3f35c5d2b0ce77e43d0a92bdc06",
"https://superquadrics.com/neural_parts/planes/315f523d0a924fb7ef70df8610b582b2",
"https://superquadrics.com/neural_parts/planes/343a607d1604335fb4f192eea1889928",
"https://superquadrics.com/neural_parts/planes/347d86d7001cef01232236eecec447b",
"https://superquadrics.com/neural_parts/planes/351c9235749e398162147e00e97e28b5",
"https://superquadrics.com/neural_parts/planes/3716ed4fa80dbf5f41392ab7a601818b",
"https://superquadrics.com/neural_parts/planes/384e72f69e6f24404cb288947cda4a2c",
"https://superquadrics.com/neural_parts/planes/440ac1b4ac3cbe114c3a35cee92bb95b",
"https://superquadrics.com/neural_parts/planes/440e5ba74ac8124e9751c7a6f15617f4",
"https://superquadrics.com/neural_parts/planes/48706d323b9041d5438a95791ca4064d",
"https://superquadrics.com/neural_parts/planes/563cef4df464ddb1e153dd90dac45a6d",
"https://superquadrics.com/neural_parts/planes/5c6590461085c93ea91e80f26309099e",
"https://superquadrics.com/neural_parts/planes/60b5f5da40e0dd33579f6385fdd4245b",
"https://superquadrics.com/neural_parts/planes/7b134f6573e7270fb0a79e28606cb167",
"https://superquadrics.com/neural_parts/planes/92a83ecaa10e8d3f78e919a72d9a39e7",
"https://superquadrics.com/neural_parts/planes/ed2aaca045fb1714cd4229f38ad0d015",
"https://superquadrics.com/neural_parts/planes/f12eefbbefabe566ca8607f540cc62ba",
];
var plane_control = show_group(
document.getElementById("planes").getElementsByClassName("render_window"),
[planes[7], planes[1], planes[2]],
5
);
var plane_checkboxes = document.querySelectorAll("#planes .controls input");
reset_checkboxes(plane_checkboxes);
document.querySelector("#planes .controls").addEventListener(
"change",
function (ev) {
if (ev.target.id == "planes_all") {
Array.prototype.filter.call(
plane_checkboxes,
(el) => el.id != "planes_all"
).forEach(function (el) {el.checked = false;});
} else if (ev.target.checked) {
plane_checkboxes[0].checked = false;
}
var ids = new Set();
if (plane_checkboxes[0].checked) {
ids = new Set([0, 1, 2, 3, 4]);
}
var part_ids = [4, 0, 3, 2, 1];
for (var i=1; i<plane_checkboxes.length; i++) {
if (plane_checkboxes[i].checked) {
ids.add(part_ids[i-1]);
}
}
plane_control.show(Array.from(ids));
}
);
document.querySelector("#planes .controls button").addEventListener(
"click",
function (ev) {
reset_checkboxes(plane_checkboxes);
var new_planes = random_choice(planes, 3);
var render_windows = document.getElementById("planes").getElementsByClassName("render_window");
Array.prototype.forEach.call(render_windows, function (r) {r.innerHTML = "";});
plane_control = show_group(
render_windows,
new_planes,
5
);
}
);
</script>
<script>
// Make the carousel for the comparisons
var glide = new Glide(".glide", {
type: "carousel",
startAt: 0,
perView: 1,
autoplay: 2000
}).mount();
</script>
</body>
</html>