**comp.graphics.algorithms**

## Subject: **3D rotation estimate via least squares**

I need to estimate a camera orientation given only its relative

orientation with regard to some other cameras, and where the relative

orientations are not exact. For example, I would like to arrive at a

linear system of the form shown below, so that I can solve for C2 via

least squares:

C1 = C0 + R01

C2 = C1 + R12

C2 = C0 + R02

here Cx is a 3D rotation describing the orientation of camera x and Rxy is

the relative orientation (e.g. the first equations says that the

orientation of camera 1 is given by camera 0 rotated by R01). Note that

this is only a small example, in the real case, I need to solve for 10+

cameras.

Now if I could form equations like this, I would be able to solve them

easily. The trouble is, if I use, say, quaternions to describe the

rotations, then multiplication rather than addition should be used to

combine rotations, so the equations would instead look like:

C1 = C0 * R01

C2 = C1 * R12

C2 = C0 * R02

and this is no longer a set of linear equations that I can solve with

least-squares (e.g. SVD). (I think)

I'm hoping that someone can suggest how to 'linearize' this problem. For

example, is there is a way of expressing rotations so that combined

rotations are expressed as addition? I'm pretty sure that Euler angles

will not work here.

Thanks for any tips,

Jason.

Reply

View All Messages in

**comp.graphics.algorithms**

path:

Replies:

Re: 3D rotation estimate via least squares

Re: 3D rotation estimate via least squares

Re: 3D rotation estimate via least squares

Copyright © 2006 WatermarkFactory.com. All Rights Reserved.