Re: logm on 4x4 affine matrices.

[Andrew Janke]

On Mon, May 10, 2010 at 21:14, John Swensen <address@hidden> wrote:

>>> AVG = expm((logm(A000) + logm(A001)) / 2)
>>
>> However the "translation component" doesn't seem to behave as I would expect.
>>
> I don't know what the "right" answer is, but I know something that works.  It 
> seems that logm and expm should work from the mathematical perspective as 
> affine transformations are elements of the Lie group SE(3) and generated via 
> the exponential map from the Lie algebra se(3).  The problem may be that when 
> taking the matrix log of the identity rotation, the fact that it can be any 
> axis of rotation combined with a zero angle makes it not well defined.   I 
> have always seen people decompose the affine transformation into a rotation 
> and a translation for averaging purposes and use the Rodrigues formula and 
> its inverse, rather than matrix log, on the rotational part.

Thanks John

Your approach is working well for me.


-- 
Andrew Janke - address@hidden
Department of Geriatric Medicine, ANU
Canberra->Australia    +61 (402) 700 883