Background and purpose: Magnetic resonance imaging (MRI) plays an important role in the field of MR-guided radiotherapy or personalised radiation oncology. The application of quantitative image analyses like radiomics as well as automated tissue characterisation is frequently disturbed by the effect of intensity non-uniformity. We present a novel fully automated physical correction model (PCM) for the reduction of intensity non-uniformity. Materials and methods: The proposed algorithm is based on a 3D physically motivated correction model, which maximises the image information expressed by the Shannon entropy. The PCM was evaluated using the coefficient of variation (cv) on 176 MRI datasets of the human brain and abdomen acquired on 1.5 Tesla and 3 Tesla MR scanners. The resulting cv was compared to the cv of the original images and to the results of the established N4 algorithm. Results: The PCM algorithm significantly improved the image quality of all considered 1.5 and 3.0 Tesla MR scans compared to the original images (p < .01). Furthermore, the PCM outperformed or competed with the N4 algorithm in terms of image quality. Additionally, the PCM approach preserved the tissue signal of different tissue types due to smooth correction gradients. Conclusion: The proposed PCM algorithm led to a significantly improved image quality compared to the originally acquired images, suggesting that it is applicable to the correction of MRI data. Thus it may help to reduce intensity non-uniformity which is an important step for advanced image analysis.