Longitudinal atlas construction plays an important role in medical image analysis. Given a set of longitudinal images from different subjects, the task of longitudinal atlas construction is to build an atlas sequence which can represent the trend of anatomical changes of the population. The major challenge for longitudinal atlas construction is how to effectively incorporate both the subject-specific information and population information to build the unbiased atlases. In this paper, a novel groupwise longitudinal atlas construction framework is proposed to address this challenge, and the main contributions of the proposed framework lie in the following aspects: (1) The subject-specific longitudinal information is captured by building the growth model for each subject. (2) The longitudinal atlas sequence is constructed by performing groupwise registration among all the subject image sequences, and only one transformation is needed to transform each subject's image sequence to the atlas space. The constructed longitudinal atlases are unbiased and no explicit template is assumed. (3) The proposed method is general, where the number of longitudinal images of each subject and the time points at which they are taken can be different. The proposed method is extensively evaluated on two longitudinal databases, namely the BLSA and ADNI databases, to construct the longitudinal atlas sequence. It is also compared with a state-of-the-art longitudinal atlas construction algorithm based on kernel regression on the temporal domain. Experimental results demonstrate that the proposed method consistently achieves higher registration accuracies and more consistent spatial-temporal correspondences than the compared method on both databases. © 2011 Elsevier Inc. All rights reserved. Longitudinal atlas construction is an active research topic in longitudinal data analysis and it plays an important role in medical image analysis. Its applications include, but not limited to, disease tracking (Fox et al., 2000) , population analysis (Freeborough and Fox, 1997) and anatomical structure analysis (Cardenas et al., 2007) . The task of longitudinal atlas construction is to estimate an atlas sequence in the temporal domain which can reflect the trend of anatomical changes in the population based on a given set of longitudinal image sequences from different subjects. The major challenge for longitudinal atlas construction is how to effectively encode both the intra-subject longitudinal change and the inter-subject difference in the constructed atlas sequence. Longitudinal atlas construction methods can be broadly classified into two categories: (1) Longitudinal atlas construction by kernel regression or mixture modeling over the temporal domain (Davis et al., 2007 (Davis et al., , 2010 Sabuncu et al., 2009; Hart et al., 2010) ; (2) Longitudinal atlas sequence estimated by joint alignment of subject image sequences to a template sequence (Durrleman et al., 2009) . A representative of the kernel regression based atlas construction methods is the method proposed by Davis et al. (Davis et al., 2007 , where the longitudinal atlases at different time points are constructed by a kernel regression process over the temporal domain on the Riemannian manifold represented by diffeomorphisms. The contribution of each image during the regression process to construct the atlases is determined by the kernel weight. In Davis et al. (2007 Davis et al. ( , 2010 , the Nadaraya-Watson kernel regression process is extended by formulating the regression problem based on the Fréchet mean. This method is designed for random design data and therefore there is no subjectspecific longitudinal information considered. Also, it may lead to temporal inconsistency between the images taken at different time points of the same subject. The schematic representation of this method is shown by Fig. 1(a) . Also, Durrleman et al. (2009) E-mail address: dgshen@med.unc.edu (D. Shen). 1 Data used in preparation of this article were obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) database (adni.loni.ucla.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.ucla.edu/wpcontent/ uploads/how to apply/ADNI Authorship List.pdf.
A 4D atlas is a representation of the changes in anatomical structure of an object over time REF .
A novel framework for longitudinal atlas construction with groupwise registration of subject image sequences
NeuroImage
NeuroImage
Computer Science Medicine