There is great potential utility for information extracted from neuroimaging data to serve as biomarkers, to quantify neurodegeneration, and to evaluate the efficacy of disease-modifying therapies. Currently, the accurate and reliable registration of images presents a major challenge, due to a number of factors. These include differential distortions that affect longitudinal time points in different ways; true, localized anatomical change that can cause global offsets in the computed registration, and the lack of inverse consistency in which the registration of multiple images depends on the order of processing, which can lead to algorithm-induced artifacts in detected changes. Thus, the development of an accurate, robust and inverse consistent method is a critical first step to quantify change in neuroimaging or medical image data in general.
Since the object of interest is typically located differently in each acquired image, accurate geometric transformations are necessary to register the input images into a common space. Approaches based on robust statistics are extremely useful in this domain, as they provide a mechanism for discounting regions in the images that contain true differences, and allow one to recover the correct alignment based on the remainder of the data. Inverse consistency is critical to avoid introducing bias into longitudinal studies. A lack of inverse consistency in registration is likely to bias subsequent processing and analysis, as documented in Yushkevicha et al. (2009)
. The goal of this work is thus to develop a robust and inverse consistent registration method for use in the analysis of neuroimaging data. The core application of this technique is intra-modality and intra-subject registration with important implications for:
- Motion correction and averaging of several intra-session scans to increase the signal to noise ratio,
- highly accurate alignment of longitudinal image data and
- initial registration for higher-dimensional warps.
Although the remainder of this paper deals with neuroimaging data, the method can be used for other image registration task as well.
Highly accurate rigid registrations are of importance when averaging multiple scans
taken within a session to reduce the influence of noise or subject motion. Since it is nearly impossible for a person to remain motionless throughout a 20 minutes scan, image quality can be increased by taking shorter scans and performing retrospective motion correction (Kochunov et al., 2006
). Many common sequences are short enough to allow for several structural scans of the same modality within a session. Here even a slightly inaccurate registration will introduce additional artifacts into the final average and likely reduce the accuracy, sensitivity and robustness of downstream analysis.
Compared with cross-sectional studies, a longitudinal design
can significantly reduce the confounding effect of inter-individual morphological variability by using each subject as his or her own control. As a result, longitudinal imaging studies are becoming increasingly common in clinical and scientific neuroimaging. Degeneration in subcortical structures and cortical gray matter is, for example, manifested in aging (Jack et al., 1997
; Salat et al., 1999
; Sowell et al., 2003
), Alzheimer's disease (Dickerson et al., 2001
; Thompson et al., 2003
; Lerch et al., 2005
), Huntington's disease (Rosas et al., 2002
), multiple sclerosis (Sailer et al., 2003
) and Schizophrenia (Thompson et al., 2001
; Kuperberg et al., 2003
; Narr et al., 2005
) and has been useful towards understanding some of the major pathophysiological mechanisms involved in these conditions. As a result, in vivo cortical thickness and subcortical volume measures are employed as biomarkers of the evolution of an array of diseases, and are thus of great utility for evaluating the efficacy of disease-modifying therapies in drug trials. To enable the information exchange at specific locations in space, highly accurate and unbiased registrations across time are necessary. They need to be capable of efficiently dealing with change in the images, which can include true neurodegeneration, differential positioning of the tongue, jaws, eyes, neck, different cutting planes as well as session-dependent imaging distortions such as susceptibility effects.
As an example see showing longitudinal tumor data (same slice of five acquisitions at different times, MPRAGE, 256 × 256 × 176, 1mm voxels) registered to the first time point (left) with the proposed robust method. The five time points are: 5 days prior to treatment start, 1 day prior, 1 day after treatment start, and 28, 56 days after treatment start. Despite of the significant change in these images the registration is highly accurate (verified visually in non-tumor regions). The bottom row depicts the outlier weights (red/yellow overlay), which are blurry regions of values between 0 (outlier) and 1 (regular voxel) that label differences in the images. In addition to the longitudinal change in tumor regions and consequential deformation (e.g. at the ventricles), the robust method also picks up differences in the scalp, eye region and motion artifacts in the background. In our robust approach the influence of these differences (or outliers) is reduced when constructing the registrations, while they have a detrimental influence on the final registration result in non robust methods.
Figure 1 Robust registration of longitudinal tumor data (same slice of five acquisitions at different times). Left: target (first time point). Top row: aligned images. Bottom row: overlay of detected change/outlier regions (red/yellow). The outlier influence is (more ...)
Statistically, robust parameter estimation
has a history of supplying solutions to several computer vision problems (Stewart, 1999
) as it is capable of estimating accurate model parameters in the presence of noise, measurement error (outliers) or true differences (e.g. change over time). The approach presented here is based on robust statistics and inspired by Nestares and Heeger (2000)
, who describe a robust multi-resolutional registration approach to rigidly register a set of slices to a full resolution image. Our approach, however, is designed to be inverse consistent to avoid introducing a bias. It also allows the calculation of an additional global intensity scale parameter to adjust for different intensity scalings that can be present especially in longitudinal data. A more complex intensity preprocessing is therefore not needed in most cases. Furthermore, we automatically estimate the single parameter of the algorithm that controls its sensitivity to outliers. This is a necessary addition, since a fixed parameter cannot adequately deal with different image intensity scales, which are common in MRI. In addition to the multi resolutional approach described in Nestares and Heeger (2000)
we use moments for an initial coarse alignment to allow for larger displacements and situations where source and target may not overlap. Finally, we describe the registration of two full resolution images (instead of only a set of slices) and explain how both rigid and affine transformation models can be used in the symmetric algorithm. We demonstrate that our approach yields highly accurate registrations in brain regions and out-performs existing state-of-the-art registration algorithms.
The remainder of this paper is organized as follows. After discussing related work and introducing the theoretical background, such as robust statistics in Section 2, we present our symmetric registration model, different transformation models as well as intensity scaling in Section 3. Then we describe the registration algorithm in detail, taking care that the properties of the theory are carried over to the implementation (Section 4). We specifically focus on maintaining inverse consistency by resampling both images into a `half-way' space in intermediate steps as opposed to resampling the source at the estimated target location. This asymmetric sampling, which is commonly used, introduces a bias as the target image will not be resampled at all, and will thus be less smooth than the resampled source. In Section 5 we demonstrate the superiority of the proposed method over existing registration algorithms with respect to symmetry, robustness and accuracy on synthetic and real data as well as a motion correction application. The software implementing the presented robust registration is publicly distributed as part of the FreeSurfer (surfer.nmr.mgh.harvard.edu) software package as mri_robust_register.