<p>Generally a non-rigid transformation is motion that doesn't preserve the shape of objects. If you look at a typical transformation matrix, rigid transformations would include translation, rotation, and reflection. Things like shear, uniform or non-uniform scale, and perspective would be non-rigid. Shear and scale would fall into the category of affine transformations, and perspective is of course perspective transformation. So there's a hierarchy of types of transformations:</p>

<ol>
<li><a href="https://en.wikipedia.org/wiki/Rigid_transformation" rel="nofollow noreferrer">Rigid transforms</a> - translation, reflection, and rotation. These perserve the distances between every pair of points on objects.</li>
<li><a href="https://en.wikipedia.org/wiki/Affine_transformation" rel="nofollow noreferrer">Affine transforms</a> - rigid + shear and (possibly non-uniform) scale</li>
<li><a href="https://en.wikipedia.org/wiki/3D_projection" rel="nofollow noreferrer">Perspective transforms</a> - Affine plus perspective transforms (think of a rectangle rotated around the upward pointing axis - the part closer to the camera/viewer may be larger than the pre-transformed object, and the part farther away may be smaller)</li>
</ol>

<p>I haven't done a lot with optical flow, but I would guess that as you figure out the path of motion of various points on an object, you would be able to classify them into one of the above categories. If all the points in an object move in tandem, then you probably have rotation and/or translation only (rigid transforms), but if they don't then you may have an affine or perspective transform between the points.</p>

CC BY-SA 3.0
2017-10-17T16:34:12.210Z
2017-10-17T16:34:12.210Z
user1118321
<p>Can you explain me what a nonrigid motion is?
In German it would be a "unbewegliche Bewegung" but I think it has to be translated in a different way.
I could imagine that it means something like the scene window is moving but the elements in the scene are staying in the same position.</p>

<p>I read it in the context of a paper about quantitative optic flow comparison. </p>

CC BY-SA 3.0
2017-10-17T09:40:51.630Z
What's the context?
Dan Hulme
<motion>
What is a nonrigid motion?
baxbear
# What is a nonrigid motion?

(Asked by: username_0 on 2017-10-17)

Can you explain me what a nonrigid motion is?
In German it would be a "unbewegliche Bewegung" but I think it has to be translated in a different way.
I could imagine that it means something like the scene window is moving but the elements in the scene are staying in the same position.

I read it in the context of a paper about quantitative optic flow comparison.

**Tags:** motion

> **Comments:**
> **username_1**: What's the context?  

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## 1 answers

### Answer by username_2 on 2017-10-17. Score: 3 | Accepted answer

Generally a non-rigid transformation is motion that doesn't preserve the shape of objects. If you look at a typical transformation matrix, rigid transformations would include translation, rotation, and reflection. Things like shear, uniform or non-uniform scale, and perspective would be non-rigid. Shear and scale would fall into the category of affine transformations, and perspective is of course perspective transformation. So there's a hierarchy of types of transformations:

1. [Rigid transforms](https://en.wikipedia.org/wiki/Rigid_transformation) - translation, reflection, and rotation. These perserve the distances between every pair of points on objects.
2. [Affine transforms](https://en.wikipedia.org/wiki/Affine_transformation) - rigid + shear and (possibly non-uniform) scale
3. [Perspective transforms](https://en.wikipedia.org/wiki/3D_projection) - Affine plus perspective transforms (think of a rectangle rotated around the upward pointing axis - the part closer to the camera/viewer may be larger than the pre-transformed object, and the part farther away may be smaller)

I haven't done a lot with optical flow, but I would guess that as you figure out the path of motion of various points on an object, you would be able to classify them into one of the above categories. If all the points in an object move in tandem, then you probably have rotation and/or translation only (rigid transforms), but if they don't then you may have an affine or perspective transform between the points.


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