<p>When they refer to canonical space, they are referring to vectors &amp; surfaces of R^3xN.</p>
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</blockquote>
<p>And so canonical just means standard basis vectors.</p>
<blockquote>
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</blockquote>
<p>Which are a set of linearly-independent (at right angles) vectors.
for instance in R^3, [1,0,0], [0,1,0], [0,0,1] are basis vectors because</p>
<p>When speaking of a coordinate space:</p>
<ol>
<li>they are all independent (can't be expressed as a combination of the others)</li>
<li>filled with either 0 or 1s</li>
</ol>

CC BY-SA 4.0
2022-06-04T07:45:34.357Z
Please, don't provide screenshots. Copy and paste the actual relevant text (and provide a reference to the original).
nbro
CC BY-SA 4.0
2022-06-04T05:19:29.167Z
2022-06-04T05:19:29.167Z
J.Kent
<p>I am reading the paper on 3D reconstruction, <a href="https://proceedings.neurips.cc/paper/2021/file/a11f9e533f28593768ebf87075ab34f2-Paper.pdf" rel="nofollow noreferrer">ViSER: Video-Specific Surface Embeddings for Articulated 3D Shape Reconstruction</a>, and I encountered the term &quot;canonical space&quot;.</p>
<p>What is a &quot;canonical space&quot;? Is it widely used? Is there other use of the term?</p>
<p>In my understanding, a canonical space is a standard, norm space. And we want to convert sample points into that space so that we can perform standard procedures. But I don’t know if that interpretation is correct or not. And I am also interest if it is a common term or very few people use it.</p>

CC BY-SA 4.0
2022-05-30T08:58:03.880Z
The term "canonical" pops up several times in computer vision. You could check e.g. the book "Multiple View Geometry in Computer Vision, Second Edition" for more details. I would need to read the paper to understand what they really mean by "canonical space" in that context (maybe later).
nbro
<deep-learning><computer-vision><terminology><papers>
What is a "canonical space"?
Trong-Thang Pham
# What is a "canonical space"?

(Asked by: username_0 on 2022-05-29)

I am reading the paper on 3D reconstruction, [ViSER: Video-Specific Surface Embeddings for Articulated 3D Shape Reconstruction](https://proceedings.neurips.cc/paper/2021/file/a11f9e533f28593768ebf87075ab34f2-Paper.pdf), and I encountered the term "canonical space".

What is a "canonical space"? Is it widely used? Is there other use of the term?

In my understanding, a canonical space is a standard, norm space. And we want to convert sample points into that space so that we can perform standard procedures. But I don’t know if that interpretation is correct or not. And I am also interest if it is a common term or very few people use it.

**Tags:** deep-learning, computer-vision, terminology, papers

> **Comments:**
> **username_1**: The term "canonical" pops up several times in computer vision. You could check e.g. the book "Multiple View Geometry in Computer Vision, Second Edition" for more details. I would need to read the paper to understand what they really mean by "canonical space" in that context (maybe later).  

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## 1 answers

### Answer by username_2 on 2022-06-04. Score: 1

When they refer to canonical space, they are referring to vectors & surfaces of R^3xN.

> [![enter image description here](https://i.sstatic.net/b4rtt.png)](https://i.sstatic.net/b4rtt.png)

And so canonical just means standard basis vectors.

> [![enter image description here](https://i.sstatic.net/jH8fB.png)](https://i.sstatic.net/jH8fB.png)

Which are a set of linearly-independent (at right angles) vectors.
for instance in R^3, [1,0,0], [0,1,0], [0,0,1] are basis vectors because

When speaking of a coordinate space:

1. they are all independent (can't be expressed as a combination of the others)
2. filled with either 0 or 1s

> **Comments:**
> **username_1**: Please, don't provide screenshots. Copy and paste the actual relevant text (and provide a reference to the original).  

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