Statistical normalization techniques for magnetic resonance imaging

Abstract

While computed tomography and other imaging techniques are measured in absolute units with physical meaning, magnetic resonance images are expressed in arbitrary units that are difficult to interpret and differ between study visits and subjects. Much work in the image processing literature on intensity normalization has focused on histogram matching and other histogram mapping techniques, with little emphasis on normalizing images to have biologically interpretable units. Furthermore, there are no formalized principles or goals for the crucial comparability of image intensities within and across subjects. To address this, we propose a set of criteria necessary for the normalization of images. We further propose simple and robust biologically motivated normalization techniques for multisequence brain imaging that have the same interpretation across acquisitions and satisfy the proposed criteria. We compare the performance of different normalization methods in thousands of images of patients with Alzheimer's disease, hundreds of patients with multiple sclerosis, and hundreds of healthy subjects obtained in several different studies at dozens of imaging centers.

Keywords: Image analysis; Magnetic resonance imaging; Normalization; Statistics.

Figures

Fig. A.1

Template image used for simulation experiments. Differing shades of gray indicate different tissue classes.

Fig. A.2

Bar plots showing the Hellinger distance-based variances before and after normalization in the simulation studies (shorter bars show more similarity in intensity distribution across images). Each plot corresponds to a different set of parameters (shown in Table 1) and each bar represents a single tissue class on a particular modality after a normalization (indicated by color, with green indicating raw images and orange indicating white stripe normalized images). Note that the method performs well throughout, but shows least benefit in setting 7 for which the variability in means across tissue classes is most similar to the variability within tissue classes.

Fig. A.3

Bar plots showing the Hellinger distance-based variances before and after normalization in the NINDS study for various values of α.

Fig. A.4

Bar plots showing the Hellinger distance-based variances before and after normalization in the NINDS study for various values of τ.

Fig. 1

Schematic showing the proposed normalization techniques. The steps shown in the cyan region are standard preprocessing steps, while the green region shows the white stripe normalization algorithm. The bottom right section in purple shows the hybrid white stripe normalization technique.

Fig. 2

Failure of histogram matching methods. First column: region of interest from patient with MCI shown before (A) and after (C) histogram matching. Red square indicates region of gray matter on raw image that disappears after histogram matching. Second column: histograms (shades of gray indicate different study visits) of the gray matter before (B) and after (D) histogram matching for subjects in ADNI. Note the large proportion of gray matter incorrectly matched to background (zero intensity). The green line shows the histogram for the image shown in the left column. (E) and (F) show the same image and histograms after the normalization proposed in this paper.

Fig. 3

Example of the white stripe normalization procedure. In the top left plot, the raw histogram of a T1-w image is shown. Using a peak-finding algorithm, μij1∗ and thus Ωi,j,τ are estimated. In the right column of the figure, Ωi,j,τ is shown before and after normalization. The density of the intensities in NAWM before (fij1) and after normalization g^ij2 is shown using dashed magenta lines. The bottom left plot shows the histogram after white stripe normalization.

Fig. 4

Histograms of intensities before and after normalization by tissue type in two large studies of AD. Rows indicate different normalization methods and columns correspond to MR sequence and anatomical structure.

Fig. 5

Histograms of intensities before and after normalization by tissue type in two large studies of MS. Rows indicate different normalization methods and columns correspond to MR sequence and anatomical structure.

Fig. 6

Bar plots showing the Hellinger distance-based variances before and after normalization in the four studies (shorter bars show more similarity in intensity distribution across images). Each plot corresponds to a single study and each bar represents a single tissue class on a particular modality after a normalization (indicated by color).