A new method for multimodal 3-D image registration with external markers

The authors have developed a method for 3-D image registration from the positions of corresponding external point markers in two modalities and their measurement errors. The transformation is parametrised in terms of nine parameters: 3 Euler angles for rotations, 3 translations and 3 magnifications. They are estimated by minimizing a χ² function defined in terms of the squares of distances of corresponding markers in two modalities weighted by the corresponding measurement errors, using a sequence of non-linear minimization techniques. Also, a method for evaluation of multimodal 3-D image registration using Monte-Carlo generated images in two modalities as well as images of the external markers is developed. The authors have used this method to determine the minimum number of external markers needed for 3-D image registration with 9 parameters as well as various other aspects of 3-D image registration like the effects of the positioning errors of the markers