Computational Complexity of Affine Transformation

Hi All,

Does anyone know how to compute the computational complexity of an
affine transformation operation?

Regards,
Nathan

nathanwh71@gmail.com schrieb:

Do you mean projective transformations? Or the simpler similarity
transformations? Both are affin, the projective is more complex. The
similarity transformation uses an equal scale factor for all dimensions.

The similarity transformation uses less parameters. In 2D there are 4
parameters (the a_x's):

X = a_1 * x - a_2 * y + a_3
Y = a_2 * x + a_1 * y + a_4

(I hope I got the minus on the right place...)

X and Y are the transformed coordinate values, x and y are the observed
coordinates.

Now to the projected formulas:

X = a_1 * x + a_2 * y + a_3
Y = a_4 * x + a_5 * y + a_6

Now we have six parameters. In the 3D-case you have nine parameters for
the projective transformation and seven for similarity, called
"Helmert-Transformation".

Does this help you?

Best regards, Stefan



--
student of geoinformatic

ifgi - institute for geoinformatics
www.ifgi.de