# Robust Registration of Medical Images in the Presence of Spatially-Varying Noise
## 4 Discussion and Future Works  
Throughout this paper, we presented evidence on the advantage of using empirical mode decomposition in the registration of single modal MR images. However, we believe that EMD has potentially a wide variety of applications in multi-modal image registration, image fusion, and image denoising. Particularly, multi-modal image registration has great potential for more investigations because EMD-based features are relatively robust to the modality. IMFs are made of normalized minimum and maximum envelopes of intensity. Therefore, the effect of modality-related variabilities is much less in IMFS. The idea of using EMD for multi-modal registration has been previously discussed [31], however, a more careful investigation of the applications of EMD in multi-modal image registration, such as CT-MR image registration, is still necessary. Our findings in this study show the superior performance of EMD-based registration algorithms in registering 2D images. These image were either 2D planes from 3D MRIs or 2D retina images. In principle, both proposed algorithms could be used to register 3D images, however, the computational cost of determining EMD components could be considerably higher compared to 2D images. Our future work includes scaling up the implementation of EMD-based registration and explore the performance of proposed methods for 3D images. Additionally, our focus in this paper has been the correction of motion artifacts between acquisitions. Another type of motion artifact that is often present in medical images is distortions due to a patient's inability to stay still during the acquisition. Correcting this type of motion artifact is beyond the scope of our proposed registration algorithms and require other motion correction techniques. Figure 10: Registration of Retina images taken 2 years apart. **(A)** The set of IMFs and residuals for two levels of EMD are shown for both target and moving images. **(B)** Registered images using our two methods and intensity-based hierarchical algorithm. The second row shows the composite view through contour overlap after the registration. In regard to the nature of the spatially-varying noise, our simulation of the noise in the MR images is based on additive Gaussian noise. This model follows a strong body of previous studies [23; 24; 25; 26]. However, the intensity non-uniformity in MRI could be also modeled via multiplication by a non-uniform distribution. The multiplicative artifact could be modeled as an additive artifact in the log-transformed MRI. Therefore, decomposition-based robust registration methods such as our proposed algorithms should be able to address the multiplicative noise in the log-space. In our future work, we will systematically assess the performance of our proposed algorithms in the presence of multiplicative spatial noise. In this paper, we did not consider the problem of parametrization for the transformation. We have used free form deformation to formulate the transformation, however, EMD embedded in other transformation techniques needs further investigation. In particular, the application of nonlinear transforms such as neural networks [51] and random forest [52] in EMD-based registration needs extensive study. We believe that compressed non-linear networks [53] together with EMD could achieve fast and accurate registration in the presence of bias field noise. One advantage of these models is that the transform is more interpretable [54; 55; 56]. Other nonlinear modular techniques, such as the Hammerstein Wiener model, have shown impressive performance for applications such as nonlinear mapping in biomedical signal processing [57; 58] and computational Neuroscience [59]. Employing these models as a core transformation technique between two images and possible EMD-based boost remains for future work. Finally, we believe that EMD-based registration techniques generalize well to other registration applications.