Spatial normalization of DTI requies a transformation matrix to correct for the principle vector orientations (see Figure, )
(a) tensors in the native space (b) a plain rotation of the image without correcting for the principal fiber directions (c) corrected DTI
Similarly, dODF and fODF can be normalized to a standard space by multiplying a transformation matrix .
Publicly available atlas: ICBM-DTI-81 atlas (http://www.loni.usc.edu/ICBM/Downloads/Downloads_DTI-81.shtml), IIT(http://www.iit.edu/~mri/Home.html) , DTI-TK atlas (https://www.nitrc.org/projects/dtitk/)
Allow for spatial normalization of DTI
Enabled atlas construction
Enable tracks analysis in a standard space.
A tensor atlas allows for atlas-based analysis.
A DTI atlas inherits the limitations of DTI
Most studies did not use the full tensor in the analysis. The FA and ADC map does not need the orientation correction.
The spatially normalized dODF and fODF can be averaged to construct an atlas .
publicly availalbe atlas: CMU60 (http://www.psy.cmu.edu/~coaxlab/?page_id=423), HCP488 (http://dsi-studio.labsolver.org), IIT (http://www.iit.edu/~mri/Home.html) , NTU-DSI-122 (https://www.nitrc.org/projects/ntu-dsi-122/) 
One may track representative pathways using an dODF or fODF atlas:
Arcuate fasciculus tracked in a standard space compared with microdissection results
A HARDI or DSI atlas provides rich information in the standard space that allows for tissue characterization and atlas-based fiber tracking.
The low SNR near gray matter causes the reliability to decrease near cortical areas
1. A study aimed to construct a diffusion MRI atlas in the MNI space and apply fiber tracking on it. The tracks were analyzed by their volume and length. The results showed that the volume and length were substantially smaller than the normal population. What is the problem here?
1. Reconstruct more than 2 subjects' diffusion MRI data using QSDR with ODF exported (see Reconstruction(DTI, QBI, DSI, GQI, QSDR)). Construct the averaged ODF as a FIB file (see Construction of a high angular resolution atlas)
2. Run atlas-based fiber tracking to map major fiber pathways (e.g. CST, arcuate, ...etc)
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 Varentsova, Anna, Shengwei Zhang, and Konstantinos Arfanakis. "Development of a high angular resolution diffusion imaging human brain template." NeuroImage 91 (2014): 177-186.
 Hsu, Yung‐Chin, et al. "NTU‐DSI‐122: A diffusion spectrum imaging template with high anatomical matching to the ICBM‐152 space." Human brain mapping 36.9 (2015): 3528-3541.
 Wang, Yibao, et al. "Rethinking the role of the middle longitudinal fascicle in language and auditory pathways." Cerebral cortex (2012): bhs225.
 Fernández-Miranda, Juan C., et al. "Asymmetry, connectivity, and segmentation of the arcuate fascicle in the human brain." Brain Structure and Function 220.3 (2014): 1665-1680.
 Wang, Xuhui, et al. "Subcomponents and connectivity of the superior longitudinal fasciculus in the human brain." Brain Structure and Function (2015): 1-18.