Accurate and robust brain image alignment using boundary-based registration

Abstract

The fine spatial scales of the structures in the human brain represent an enormous challenge to the successful integration of information from different images for both within- and between-subject analysis. While many algorithms to register image pairs from the same subject exist, visual inspection shows that their accuracy and robustness to be suspect, particularly when there are strong intensity gradients and/or only part of the brain is imaged. This paper introduces a new algorithm called Boundary-Based Registration, or BBR. The novelty of BBR is that it treats the two images very differently. The reference image must be of sufficient resolution and quality to extract surfaces that separate tissue types. The input image is then aligned to the reference by maximizing the intensity gradient across tissue boundaries. Several lower quality images can be aligned through their alignment with the reference. Visual inspection and fMRI results show that BBR is more accurate than correlation ratio or normalized mutual information and is considerably more robust to even strong intensity inhomogeneities. BBR also excels at aligning partial-brain images to whole-brain images, a domain in which existing registration algorithms frequently fail. Even in the limit of registering a single slice, we show the BBR results to be robust and accurate.

Figure 1

Diagram of how the BBR cost function is computed. (A) The gray scale background is a BOLD-weighted image approximately axially sliced through the central sulcus. The black line (“pial surface”) is the boundary between cortical gray matter and sulcal CSF. The white curve (“white surface”) is the boundary between cortical gray matter and white matter. The distance between the white and pial surfaces is the thickness, which is computed at each vertex V. The gray matter intensity at a vertex (g_V) is computed at a fractional distance Δ_gv along the surface normal (n_V) into cortex. The white matter intensity at a vertex (w_V) is computed at an absolute distance Δ_wv along the surface normal (n_V) into the white matter. The percent contrast at a vertex (Q_V, Equation 1) is then computed as the relative difference between the gray and white matter intensities. (B) Function that converts contrast into a cost, with large contrasts in the expected direction (positive for BOLD-weighted) having a low cost and those in the unexpected direction (negative) having a large but saturating cost.

Figure 2

FreeSurfer manual registration tool (tkregister2), coronal and sagittal views. (A) T1-weighted anatomical with white surface. (B) T2*-weighted Functional. The cortex can be seen as bright patches against the darker white matter. (C–D) Functional with surface placed by the given registration technique. (C) CR. (D) NMI. (E). BBR. The green arrows are in the same place relative to the surface in each panel and indicate places where the registration in CR or NMI are inaccurate.

Figure 3

Cost function (Equation 2) when each of the 6 DOF is parametrically varied. (A) Translations in the left-right (LR), superior-inferior (SI), and anterior-posterior (AP) directions. (B) Rotations about each of those axes. Each panel shows a different scale: (1) +/−100mm, (2) +/−10mm, (3), +/−0.2mm. This shows that the minimum is global and that the cost function is extremely smooth, even at the sub-millimeter level.

Figure 4

Robustness of BBR to random changes in initial position. Failure is defined as an inability to return to the original solution to within 0.100mm AAD. Panel A shows the probability of a failure as a function of maximum perturbation. The asterisks show the maximum perturbation for 18 subjects between their first fMRI run and their eighth within a scanning session. Panel B shows the value of the cost function for successes and failures (asterisks are individual data points) and demonstrates that the failures can be detected by a simple threshold.

Figure 5

The effect of reducing the number of slices on the ability of each registration algorithm to stay at the same position found from the full-brain registration. BBR maintains very good repeatability, even down to one slice. The large error bar for BBR on the single slice is because 1 of the 18 subjects failed. The confidence intervals represent 1 standard error.

Figure 6

The top panel shows a coronal slice of the functional for four values of α in order to demonstrate how the intensity of each slice was attenuated using a half-cosine intensity bias model. The white curve is the gray/white boundary. For α=0, there is no bias; α=1 gives the maximum bias. Bottom panel shows how each method performed as the bias parameter was changed. The confidence intervals represent 1 standard error.