Image Harmonization using Robust Restricted CDF Matching

TL;DR

This paper presents a method of image harmonization using Cumulative Distribution Function (CDF) matching based on curve fitting for MRI images that offers a better and more intuitive control for the input data transformation compared to other methods, especially ML-based ones.

Abstract

Deployment of machine learning algorithms into real-world practice is still a difficult task. One of the challenges lies in the unpredictable variability of input data, which may differ significantly among individual users, institutions, scanners, etc. The input data variability can be decreased by using suitable data preprocessing with robust data harmonization. In this paper, we present a method of image harmonization using Cumulative Distribution Function (CDF) matching based on curve fitting. This approach does not ruin local variability and individual important features. The transformation of image intensities is non-linear but still ``smooth and elastic", as compared to other known histogram matching algorithms. Non-linear transformation allows for a very good match to the template. At the same time, elasticity constraints help to preserve local variability among individual inputs, which may encode important features for subsequent machine-learning processing. The pre-defined template CDF offers a better and more intuitive control for the input data transformation compared to other methods, especially ML-based ones. Even though we demonstrate our method for MRI images, the method is generic enough to apply to other types of imaging data.

Figures (4)

• Figure 1: Illustration of the main concepts for dual-scaling and CDF-matching using curve fitting -- we fit $\text{CDF}_I$ to match the $\text{CDF}_T$.
• Figure 2: Illustration of a) top-tail shrinking $LUT_T$ function, and b) an example of final intensity mapping from the original intensity range $\langle 5, 5418 \rangle$ to the normalized 12-bit range $\langle 1, 4095 \rangle$.
• Figure 3: An example of the harmonization process for 9 MRI T2 images. a) CDF functions of raw images, b) CDF functions after z-score normalization, c) template $\text{CDF}_T$ fitted to three control points (configured to utilize full 12-bit range) and comparison with the average CDF, d) CDF functions of harmonized images (please note the desired tiny local deviations from the $\text{CDF}_T$).
• Figure 4: An example of harmonized results of 5 patients (cols) and different harmonization algorithms: a) percentile stretch, b) z-score normalization, c) our CDF-matching with 2 control points $\pi_B, \pi_T$, d) our CDF-matching with all 3 control points yielding enhanced contrast. MRI channels FLAIR, T2 and T1ce are combined as RGB color.