Intersection based registration of slice stacks to form 3D images of the human fetal brain

Clinical fetal MR imaging of the brain commonly makes use of fast 2D acquisitions of multiple sets of approximately orthogonal 2D slices. We and others have previously proposed an iterative slice-to-volume registration process to recover a geometrically consistent 3D image. However, these approaches depend on a 3D volume reconstruction step during the slice alignment. This is both computationally expensive and makes the convergence of the registration process poorly defined. In this paper our key contribution is a new approach which considers the collective alignment of all slices directly, via shared structure in their intersections, rather than to an estimated 3D volume. We derive an analytical expression for the gradient of the collective similarity of the slices along their intersections, with respect to the 3D location and orientation of each 2D slice. We include examples of the approach applied to simulated data and clinically acquired fetal images.