Local up-sampling and morphological analysis of low-resolution magnetic resonance images

Limitations in the resolution of acquired images, which are due to sensor manufacturing and acquisition conditions, are reduced with the help of algorithms that enhance the spatial resolution by assigning pixel values that are interpolated or approximated from known pixels. We propose a variant of the moving least-squares approximation for image up-sampling, with a specific focus on biomedical MR images. For each evaluation point, we locally compute the best approximation by minimizing a weighted least-squares error between the input data and their approximation with an implicit function. The proposed approach provides a continuous approximation, an accuracy and extrapolation capabilities higher than previous work, and a lower computational cost. As main application, we consider the up-sampling of low field MR images, where the volumetric and meshless properties of the approximation allow us to easily process images with anisotropic voxel size by rescaling the image and inter-slices resolution. Finally, we include the resolution rescaling into a pipeline that performs a morphological characterization of 3D anatomical districts, which has been developed with a focus on rheumatoid arthritis evolution and provides a more accurate segmentation as an input to quantitative analysis.