Answers.Body: <p>When they refer to canonical space, they are referring to vectors &amp; surfaces of R^3xN.</p>
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  <p><a href="https://i.sstatic.net/b4rtt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/b4rtt.png" alt="enter image description here" /></a></p>
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  <p>And so canonical just means standard basis vectors.</p>
  <blockquote>
  <p><a href="https://i.sstatic.net/jH8fB.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/jH8fB.png" alt="enter image description here" /></a></p>
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  <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>
  
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Answers.Text: Please, don't provide screenshots. Copy and paste the actual relevant text (and provide a reference to the original).
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Body: <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>
  
Comments.ContentLicense: CC BY-SA 4.0
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Comments.Text: 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).
Comments.UserDisplayName: nbro
Tags: <deep-learning><computer-vision><terminology><papers>
Title: What is a "canonical space"?
UserDisplayName: Trong-Thang Pham
ThreadText: # 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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